interactives/WA-Math-Standards-Explorer.html at main · bjmacnevin/interactives · GitHub

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<div class="header">
  <h1>Washington State K–12 Mathematics<br><em>Standards Progression Explorer</em></h1>
  <div class="header-meta">Initial Adoption — December 2025 v1.0<br>A draft generated by the Washington State Regional Coordinators</div>
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  <span class="ctrl-label">HS Pathway</span>
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    <button class="filter-btn" data-domain="Data Analysis" onclick="setDomain(this,'Data Analysis')">Data Analysis</button>
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  <span class="legend-label">Key</span>
  <div class="legend-item"><span class="legend-dot" style="background:#006E82"></span>Data Analysis</div>
  <div class="legend-item"><span class="legend-dot" style="background:#5B4A91"></span>Quantity</div>
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  <div class="legend-item"><span class="legend-dot" style="background:#2E7D5A"></span>Spatial Reasoning</div>
  <div class="legend-item"><span class="badge badge-new legend-badge">NEW</span>New standard in 2025</div>
  <div class="legend-item"><span class="badge badge-pri legend-badge">PRIORITY</span>Priority standard</div>
  <div class="legend-item" style="margin-left:6px;font-size:11px;color:#8a837a;font-style:italic;">Click any card for full text</div>
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Describe several measurable attributes of a single object.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.K.DA.MD.2","grade":"K","course":"K","domain":"Data Analysis","standard":"Directly compare two objects with a measurable attribute in common to see which object has \u201cmore of\u201d/\u201cless of\u201d the attribute and describe the difference.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.K.DA.MD.3","grade":"K","course":"K","domain":"Data Analysis","standard":"Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.K.Q.CC.1","grade":"K","course":"K","domain":"Quantity","standard":"Count to 100 by ones and by tens.","new":false,"priority":true,"level":"K-8","strand":"CC"},{"code":"M.K.Q.CC.2","grade":"K","course":"K","domain":"Quantity","standard":"Count forward beginning from a given number within the known sequence (instead of having to begin at 1).","new":false,"priority":false,"level":"K-8","strand":"CC"},{"code":"M.K.Q.CC.3","grade":"K","course":"K","domain":"Quantity","standard":"Write numbers from 0 to 20. Represent a number of objects with a written numeral 0\u201320 (with 0 representing a count of no objects).","new":false,"priority":true,"level":"K-8","strand":"CC"},{"code":"M.K.Q.CC.4","grade":"K","course":"K","domain":"Quantity","standard":"Understand the relationship between numbers and quantities; connect counting to the number of items in the set.\na. When counting objects, use number names in the correct order, matching each number to exactly one object and each object to exactly one number. \nb. Understand that the last number name said represents the number of objects counted, and that this total stays the same no matter how the objects are arranged or the order in which they are counted.\nc. Understand that each successive number name refers to a quantity that is one larger.","new":false,"priority":true,"level":"K-8","strand":"CC"},{"code":"M.K.Q.CC.5","grade":"K","course":"K","domain":"Quantity","standard":"Count to answer \u201chow many?\u201d questions about as many as 20 objects arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1\u201320, count out that many objects.","new":false,"priority":true,"level":"K-8","strand":"CC"},{"code":"M.K.Q.CC.6","grade":"K","course":"K","domain":"Quantity","standard":"Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group.","new":false,"priority":true,"level":"K-8","strand":"CC"},{"code":"M.K.Q.CC.7","grade":"K","course":"K","domain":"Quantity","standard":"Compare two numbers between 1 and 10 presented as written numerals.","new":false,"priority":false,"level":"K-8","strand":"CC"},{"code":"M.K.R.OA.1","grade":"K","course":"K","domain":"Relationships","standard":"Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.K.R.OA.2","grade":"K","course":"K","domain":"Relationships","standard":"Efficiently, flexibly, and accurately solve addition and subtraction word problems, and add and subtract within 10.","new":false,"priority":true,"level":"K-8","strand":"OA"},{"code":"M.K.R.OA.3","grade":"K","course":"K","domain":"Relationships","standard":"Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition with a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).","new":false,"priority":true,"level":"K-8","strand":"OA"},{"code":"M.K.R.OA.4","grade":"K","course":"K","domain":"Relationships","standard":"For any number from  1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.K.R.OA.5","grade":"K","course":"K","domain":"Relationships","standard":"Efficiently, flexibly, and accurately add and subtract within 5.","new":false,"priority":true,"level":"K-8","strand":"OA"},{"code":"M.K.R.NBT.1","grade":"K","course":"K","domain":"Relationships","standard":"Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition with a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.K.SR.G.1","grade":"K","course":"K","domain":"Spatial Reasoning","standard":"Describe objects in the student environment using names of shapes and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.K.SR.G.2","grade":"K","course":"K","domain":"Spatial Reasoning","standard":"Correctly name shapes regardless of their orientations or overall size.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.K.SR.G.3","grade":"K","course":"K","domain":"Spatial Reasoning","standard":"Identify shapes as two-dimensional (lying in a plane, \u201cflat\u201d) or three-dimensional (\u201csolid\u201d).","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.K.SR.G.4","grade":"K","course":"K","domain":"Spatial Reasoning","standard":"Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/\"corners\") and other attributes (e.g., having sides of equal length).","new":false,"priority":true,"level":"K-8","strand":"G"},{"code":"M.K.SR.G.5","grade":"K","course":"K","domain":"Spatial Reasoning","standard":"Model shapes in the world by building shapes from  components (e.g., sticks and clay balls) and/or drawing shapes.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.K.SR.G.6","grade":"K","course":"K","domain":"Spatial Reasoning","standard":"Use 2-dimensional shapes to compose a variety of larger shapes.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.1.DA.DS.1","grade":"1","course":"1","domain":"Data Analysis","standard":"Generate questions to investigate situations within the classroom.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.1.DA.DS.2","grade":"1","course":"1","domain":"Data Analysis","standard":"Collect and use data to consider and decide what data will answer the investigative question. Organize data with drawings, tally marks, or other visual representations.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.1.DA.DS.3","grade":"1","course":"1","domain":"Data Analysis","standard":"Analyze data sets with up to three categories by making comparisons and/or identifying patterns in the data.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.1.DA.DS.4","grade":"1","course":"1","domain":"Data Analysis","standard":"Interpret and communicate results through structured answers with teacher guidance.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.1.DA.MD.4","grade":"1","course":"1","domain":"Data Analysis","standard":"Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less in each category.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.1.Q.OA.1","grade":"1","course":"1","domain":"Quantity","standard":"Use addition and subtraction within 20 to efficiently, flexibly, and accurately solve real world word problems involving situations of adding to, taking from , putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and/or equations with a symbol for the unknown number to represent the problem.","new":false,"priority":true,"level":"K-8","strand":"OA"},{"code":"M.1.Q.OA.2","grade":"1","course":"1","domain":"Quantity","standard":"Efficiently, flexibly, and accurately solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and/or equations with a symbol for the unknown number to represent the problem.","new":false,"priority":true,"level":"K-8","strand":"OA"},{"code":"M.1.Q.OA.3","grade":"1","course":"1","domain":"Quantity","standard":"Apply and extend properties of operations by selecting and demonstrating strategies to add and subtract.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.1.Q.OA.4","grade":"1","course":"1","domain":"Quantity","standard":"Demonstrate understanding of subtraction as an unknown-addend problem.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.1.Q.OA.5","grade":"1","course":"1","domain":"Quantity","standard":"Apply and extend counting strategies to addition and subtraction (e.g., by counting on 2 to add 2).","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.1.Q.OA.6","grade":"1","course":"1","domain":"Quantity","standard":"Efficiently, flexibly, and accurately add within 20, f and subtract within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14, decomposing a number leading to a ten (e.g., 13 \u2013 4 = 13 \u2013 3 \u2013 1 = 10 \u2013 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 \u2013 8 = 4); and creating equivalent but easier or known sum s (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.1.Q.OA.7","grade":"1","course":"1","domain":"Quantity","standard":"Demonstrate understanding of the meaning of the equal sign and determine if equations involving addition and subtraction are true or false.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.1.Q.OA.8","grade":"1","course":"1","domain":"Quantity","standard":"Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.1.Q.MD.1","grade":"1","course":"1","domain":"Quantity","standard":"Order three objects according to their length; compare the lengths of two objects indirectly by using a third object.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.1.Q.MD.2","grade":"1","course":"1","domain":"Quantity","standard":"Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlap.","new":false,"priority":true,"level":"K-8","strand":"MD"},{"code":"M.1.Q.MD.3","grade":"1","course":"1","domain":"Quantity","standard":"Tell and write time to the hour and half-hour using analog and digital clocks.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.1.R.NBT.1","grade":"1","course":"1","domain":"Relationships","standard":"Count to 120, starting at any number less than 120. In this range, recognize and represent numerals and represent a number of objects with a written numeral.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.1.R.NBT.2","grade":"1","course":"1","domain":"Relationships","standard":"Understand that the digits of a two-digit number represent amounts of tens and ones. \na. 10 can be thought of as a bundle of ten ones - called a \"ten.\"\nb. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.\nc. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.1.R.NBT.3","grade":"1","course":"1","domain":"Relationships","standard":"Compare two two-digit numbers based on the values of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.1.R.NBT.4","grade":"1","course":"1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.1.R.NBT.5","grade":"1","course":"1","domain":"Relationships","standard":"Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.1.R.NBT.6","grade":"1","course":"1","domain":"Relationships","standard":"Subtract multiples of 10 in the range 10\u201390 from multiples of 10 in the range 10\u201390 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.1.SR.G.1","grade":"1","course":"1","domain":"Spatial Reasoning","standard":"Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus nondefining attributes (e.g., color, orientation, overall size) and represent shapes (build and/or draw) to possess defining attributes.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.1.SR.G.2","grade":"1","course":"1","domain":"Spatial Reasoning","standard":"Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape and create new shapes from the composite shape.","new":false,"priority":true,"level":"K-8","strand":"G"},{"code":"M.1.SR.G.3","grade":"1","course":"1","domain":"Spatial Reasoning","standard":"Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.2.DA.DS.1","grade":"2","course":"2","domain":"Data Analysis","standard":"Generate questions to investigate topics of interest to students within the classroom, school, or community.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.2.DA.DS.2","grade":"2","course":"2","domain":"Data Analysis","standard":"Collect and use data to consider and decide what data will answer the investigative question. Organize data with pictographs, line plots and bar graphs with single-unit scales. Recognize that data can vary for a variety of reasons.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.2.DA.DS.3","grade":"2","course":"2","domain":"Data Analysis","standard":"Analyze data sets with up to four categories by making comparisons, looking for patterns and/or making predictions.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.2.DA.DS.4","grade":"2","course":"2","domain":"Data Analysis","standard":"Interpret and communicate results through structured answers with teacher guidance. Make a statement(s) about the data collected to support the answer to the investigative question.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.2.DA.MD.9","grade":"2","course":"2","domain":"Data Analysis","standard":"Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.","new":false,"priority":true,"level":"K-8","strand":"MD"},{"code":"M.2.DA.MD.10","grade":"2","course":"2","domain":"Data Analysis","standard":"Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve one step put-together, take-apart, and compare probems using information presented in a bar graph.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.2.Q.NBT.2","grade":"2","course":"2","domain":"Quantity","standard":"Count within 1000; skip-count by 5s, 10s, and 100s.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.2.Q.NBT.3","grade":"2","course":"2","domain":"Quantity","standard":"Read and write numbers to 1000 using base-ten numerals, number names, and expanded form .","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.2.Q.NBT.4","grade":"2","course":"2","domain":"Quantity","standard":"Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.2.Q.NBT.5","grade":"2","course":"2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.2.Q.NBT.6","grade":"2","course":"2","domain":"Quantity","standard":"Add up to four two-digit numbers using strategies based on place value and properties of operations.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.2.Q.NBT.7","grade":"2","course":"2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Demonstrate understanding that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.2.Q.NBT.8","grade":"2","course":"2","domain":"Quantity","standard":"Use flexible and efficient strategies to mentally add 10 or 100 to a given number 100\u2013900, and mentally subtract 10 or 100 from a given number 100\u2013900.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.2.Q.NBT.9","grade":"2","course":"2","domain":"Quantity","standard":"Explain with words, numbers, and /or pictures why addition and subtraction strategies work, using place value and the properties of operations.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.2.Q.MD.1","grade":"2","course":"2","domain":"Quantity","standard":"Measure the length of an object by selecting and using appropriate tools.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.2.Q.MD.2","grade":"2","course":"2","domain":"Quantity","standard":"Measure the length of an object twice, using length units of different lengths for the two measurements; explain how the two measurements relate to the size of the unit chosen.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.2.Q.MD.3","grade":"2","course":"2","domain":"Quantity","standard":"Estimate lengths using units of inches, feet, centimeters, and meters.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.2.Q.MD.4","grade":"2","course":"2","domain":"Quantity","standard":"Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard-length unit.","new":false,"priority":true,"level":"K-8","strand":"MD"},{"code":"M.2.Q.MD.5","grade":"2","course":"2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately use addition and subtraction within 100 to solve real world word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.","new":false,"priority":true,"level":"K-8","strand":"MD"},{"code":"M.2.Q.MD.6","grade":"2","course":"2","domain":"Quantity","standard":"Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, . . . and represent whole-number sum s and differences within 100 on a number line diagram.","new":false,"priority":true,"level":"K-8","strand":"MD"},{"code":"M.2.Q.MD.8","grade":"2","course":"2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and \u00a2 symbols appropriately.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.2.R.NBT.1","grade":"2","course":"2","domain":"Relationships","standard":"Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.\na. 100 can be thought of as a bundle of ten tens - called a \"hundred.\"\nb. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.2.R.OA.1","grade":"2","course":"2","domain":"Relationships","standard":"Use addition and subtraction within 100 to efficiently, flexibly, and accurately solve one- and two-step real world word problems involving situations of adding to, taking from , putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.","new":false,"priority":true,"level":"K-8","strand":"OA"},{"code":"M.2.R.OA.2","grade":"2","course":"2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately add and subtract within 20 using flexible and efficient strategies.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.2.R.OA.3","grade":"2","course":"2","domain":"Relationships","standard":"Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even  number as a sum of two equal addends.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.2.SR.G.1","grade":"2","course":"2","domain":"Spatial Reasoning","standard":"Identify and draw shapes based on specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.2.SR.G.2","grade":"2","course":"2","domain":"Spatial Reasoning","standard":"Partition a rectangle into rows and columns of same-size squares and count to find the total number of them .","new":false,"priority":true,"level":"K-8","strand":"G"},{"code":"M.2.SR.G.3","grade":"2","course":"2","domain":"Spatial Reasoning","standard":"Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Demonstrate that equal shares of identical wholes need not have the same shape.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.2.SR.MD.7","grade":"2","course":"2","domain":"Spatial Reasoning","standard":"Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.2.SR.OA.4","grade":"2","course":"2","domain":"Spatial Reasoning","standard":"Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.3.DA.DS.1","grade":"3","course":"3","domain":"Data Analysis","standard":"Generate questions to investigate topics of interest to students that can be answered with a variety of data or data sets.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.3.DA.DS.2","grade":"3","course":"3","domain":"Data Analysis","standard":"Collect and consider data in a variety of ways including surveys, groupings, measurement, etc., and ask in what ways the data can be collected to capture as much inform ation as necessary to inform the investigative question.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.3.DA.DS.3","grade":"3","course":"3","domain":"Data Analysis","standard":"Represent data in a variety of ways including technology. Critically analyze data visualizations, including bar graphs, line plots, and scaled picture graphs with various scales. Analyze data sets with several categories by making comparisons, looking for patterns and/or making predictions and recognize the source and amount of data collected may impact the accuracy.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.3.DA.DS.4","grade":"3","course":"3","domain":"Data Analysis","standard":"Interpret and communicate results, describing difference between groups, with teacher guidance. Make a statement(s) about the data collected to support the answer to the investigative question.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.3.DA.MD.2","grade":"3","course":"3","domain":"Data Analysis","standard":"Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to efficiently, flexibly, and accurately solve one-step real world word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.3.DA.MD.3","grade":"3","course":"3","domain":"Data Analysis","standard":"Create a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step \"how many more\" and \"how many less\" problems using inform ation presented in scaled bar graphs.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.3.DA.MD.4","grade":"3","course":"3","domain":"Data Analysis","standard":"Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units according to the data\u2014 whole numbers, halves, or quarters.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.3.Q.OA.1","grade":"3","course":"3","domain":"Quantity","standard":"Interpret products of whole numbers, e.g., interpret 5 \u00d7 7 as the total number of objects in 5 groups of 7 objects each.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.3.Q.OA.2","grade":"3","course":"3","domain":"Quantity","standard":"Interpret whole-number quotients of whole numbers, e.g., interpret 56 \u00f7 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.3.Q.OA.3","grade":"3","course":"3","domain":"Quantity","standard":"Use multiplication and division within 100 to efficiently, flexibly, and accurately solve real world word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.","new":false,"priority":true,"level":"K-8","strand":"OA"},{"code":"M.3.Q.OA.4","grade":"3","course":"3","domain":"Quantity","standard":"Determine the unknown whole number in a multiplication or division equation relating three whole numbers.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.3.Q.OA.5","grade":"3","course":"3","domain":"Quantity","standard":"Use strategies to multiply and divide by applying and extending understanding of the properties of operations.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.3.Q.OA.6","grade":"3","course":"3","domain":"Quantity","standard":"Demonstrate understanding of division as an unknown-factor problem.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.3.Q.OA.7","grade":"3","course":"3","domain":"Quantity","standard":"Efficiently, flexibly, and accurately multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 \u00d7 5 = 40, one knows 40 \u00f7 5 = 8) or properties of operations.","new":false,"priority":true,"level":"K-8","strand":"OA"},{"code":"M.3.Q.OA.8","grade":"3","course":"3","domain":"Quantity","standard":"Efficiently, flexibly, and accurately solve two-step real world word problems using the four operations. Represent these problems using visual models and equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental and estimation strategies.","new":false,"priority":true,"level":"K-8","strand":"OA"},{"code":"M.3.Q.OA.9","grade":"3","course":"3","domain":"Quantity","standard":"Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.3.Q.NBT.1","grade":"3","course":"3","domain":"Quantity","standard":"Use place value understanding to round whole numbers to the nearest 10 or 100.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.3.Q.NBT.2","grade":"3","course":"3","domain":"Quantity","standard":"Efficiently, flexibly, and accurately add and subtract within 1000 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.3.Q.NBT.3","grade":"3","course":"3","domain":"Quantity","standard":"Multiply one-digit whole numbers by multiples of 10 in the range 10\u201390 (e.g., 9 \u00d7 80, 5 \u00d7 60) using strategies based on place value and properties of operations.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.3.R.NF.1","grade":"3","course":"3","domain":"Relationships","standard":"Understand a unit fraction as the quantity formed when a whole is partitioned into equal parts and explain that a unit fraction is one of those parts; understand fractions are quantities composed of unit fractions.","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.3.R.NF.2","grade":"3","course":"3","domain":"Relationships","standard":"Understand a fraction as a number; and represent fractions on a number line diagram.\na. Represent one part of a whole divided into equal pieces on a number line by using the segment from zero to one as the whole and dividing it into equal parts based on how many pieces the whole is split into. Understand that each part has the size of one divided by the total number of parts, and that the endpoint of the first part starting at zero marks the location of this fraction on the number line. \nb. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.3.R.NF.3","grade":"3","course":"3","domain":"Relationships","standard":"Explain equivalence of fractions and compare fractions by reasoning about their size.\na. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.\nb. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.\nc. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. \nd. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.3.R.MD.5","grade":"3","course":"3","domain":"Relationships","standard":"Recognize area as an attribute of plane figures and understand concepts of area measurement.\na. A square with side length 1 unit, called \"a unit square,\" is said to have \"one square unit\" of area, and can be used to measure area.\nb. A plane figure which can be covered without gaps or overlaps by a certain number of unit squares is said to have an area equal to that number of square units.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.3.R.MD.6","grade":"3","course":"3","domain":"Relationships","standard":"Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.3.R.MD.7","grade":"3","course":"3","domain":"Relationships","standard":"Relate area to the operations of multiplication and addition.\na. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.\nb. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.\nc. Use tiling to show in a concrete case that the area of a rectangle with one side split into two parts is equal to the sum of the areas of two smaller rectangles. Use area models to represent the distributive property in mathematical reasoning.\nd. Recognize area as additive. Find the area of figures made up of adjoining rectangles by decomposing them into non-overlapping rectangles and adding the areas, applying this technique to solve real world problems.","new":false,"priority":true,"level":"K-8","strand":"MD"},{"code":"M.3.SR.G.1","grade":"3","course":"3","domain":"Spatial Reasoning","standard":"Demonstrate understanding that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.3.SR.G.2","grade":"3","course":"3","domain":"Spatial Reasoning","standard":"Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.","new":false,"priority":true,"level":"K-8","strand":"G"},{"code":"M.3.SR.MD.1","grade":"3","course":"3","domain":"Spatial Reasoning","standard":"Tell and write time to the nearest minute and measure time intervals in minutes. Efficiently, flexibly, and accurately solve real world word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.3.SR.MD.8","grade":"3","course":"3","domain":"Spatial Reasoning","standard":"Efficiently, flexibly, and accurately solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknnown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.","new":false,"priority":true,"level":"K-8","strand":"MD"},{"code":"M.4.DA.DS.1","grade":"4","course":"4","domain":"Data Analysis","standard":"Generate questions of interest to the students that elicit data, generate ideas based on the questions, and refine the question as necessary.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.4.DA.DS.2","grade":"4","course":"4","domain":"Data Analysis","standard":"Determine strategies for collecting and considering data in a variety of ways including with the use of technology, evaluate whether additional data that should be collected to completely address the investigative question.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.4.DA.DS.3","grade":"4","course":"4","domain":"Data Analysis","standard":"Critically analyze data visualizations, including tables, bar graphs, line plots, or spreadsheets to support a claimrelated to the investigative question. Ask whether the data collected sufficiently addresses the investigative question.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.4.DA.DS.4","grade":"4","course":"4","domain":"Data Analysis","standard":"Interpret and communicate results, describing difference between groups, with teacher guidance. Make a statement(s) about the data collected to support the answer to the investigative question.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.4.DA.MD.4","grade":"4","course":"4","domain":"Data Analysis","standard":"Make a line plot to display a data set of measurements in fractions of a unit. Efficiently, flexibly, and accurately solve problems involving addition and subtraction of fractions by using inform ation presented in line plots.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.4.Q.OA.2","grade":"4","course":"4","domain":"Quantity","standard":"Multiply or divide to efficiently, flexibly, and accurately solve real world word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.","new":false,"priority":true,"level":"K-8","strand":"OA"},{"code":"M.4.Q.OA.3","grade":"4","course":"4","domain":"Quantity","standard":"Efficiently, flexibly, and accurately solve multistep real world word problems posed with whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using visual models and equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using estimation strategies.","new":false,"priority":true,"level":"K-8","strand":"OA"},{"code":"M.4.Q.OA.4","grade":"4","course":"4","domain":"Quantity","standard":"Find all factor pairs for a whole number in the range 1\u2013100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1\u2013100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1\u2013100 is prime or composite.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.4.Q.OA.5","grade":"4","course":"4","domain":"Quantity","standard":"Generate a number or shape pattern that follows a given rule. Identify and explain apparent features of the pattern that were not explicit in the rule itself. Explain why the numbers will continue to alternate in this way.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.4.Q.NBT.2","grade":"4","course":"4","domain":"Quantity","standard":"Read, write, and compare multi-digit whole numbers using base-ten numerals, number names, and expanded form using the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.4.Q.NBT.3","grade":"4","course":"4","domain":"Quantity","standard":"Use place value understanding of multi-digit whole numbers to generate estimates to any place less than or equal to 1,000,000 using a variety of estimation strategies.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.4.Q.NBT.4","grade":"4","course":"4","domain":"Quantity","standard":"Efficiently, flexibly, and accurately add and subtract multi-digit whole numbers using strategies or algorithms.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.4.Q.NBT.5","grade":"4","course":"4","domain":"Quantity","standard":"Efficiently, flexibly, and accurately multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.4.Q.NBT.6","grade":"4","course":"4","domain":"Quantity","standard":"Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using multiple strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.4.R.OA.1","grade":"4","course":"4","domain":"Relationships","standard":"Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 \u00d7 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent these comparison statements as multiplication equations.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.4.R.NBT.1","grade":"4","course":"4","domain":"Relationships","standard":"Understand that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.4.R.NF.1","grade":"4","course":"4","domain":"Relationships","standard":"Demonstrate understanding of why a fraction is equivalent to another fraction by using visual fraction models (e.g., tape diagrams and number lines), with attention to how the number and size of the parts differ even though the two fractions them selves are the same size. Understand and use general principles to recognize and generate equivalent fractions.","new":false,"priority":false,"level":"K-8","strand":"NF"},{"code":"M.4.R.NF.2","grade":"4","course":"4","domain":"Relationships","standard":"Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing them to a benchmark fraction. Understand that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.4.R.NF.3","grade":"4","course":"4","domain":"Relationships","standard":"Efficiently, flexibly, and accurately compose and decompose fractions with a numerator greater than 1 into unit fractions, including fractions greater than one or mixed numbers, to solve situations in context with addition and subtraction of fractions with like denominators.\na. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.\nb. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.\nc. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.\nd. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.4.R.NF.4","grade":"4","course":"4","domain":"Relationships","standard":"Flexibly apply and extend previous understandings of multiplication to multiply a fraction by a whole number using visual models in the context of word problems.\na. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4).\nb. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. \nc. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.","new":false,"priority":false,"level":"K-8","strand":"NF"},{"code":"M.4.R.NF.5","grade":"4","course":"4","domain":"Relationships","standard":"Explore and explain using models, words, and/or numbers that a fraction with a denominator of 10 is an equivalent fraction with denominator of 100 and use this technique to add two fractions with respective denominators of 10 and 100.","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.4.R.NF.6","grade":"4","course":"4","domain":"Relationships","standard":"Explore and explain decimal notation for fractions with denominators of 10 and 100 using models, words, and/or numbers.","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.4.R.NF.7","grade":"4","course":"4","domain":"Relationships","standard":"Compare two decimals to hundredths by reasoning about their size. Understand that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, < and justify the conclusions by using multiple strategies and/or visual models.","new":false,"priority":false,"level":"K-8","strand":"NF"},{"code":"M.4.R.MD.2","grade":"4","course":"4","domain":"Relationships","standard":"Use the four operations to efficiently, flexibly, and accurately solve real world word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using multiple visual models.","new":false,"priority":true,"level":"K-8","strand":"MD"},{"code":"M.4.R.MD.5","grade":"4","course":"4","domain":"Relationships","standard":"Demonstrate understanding of angles as geometric figures that are formed wherever two rays share a common endpoint and accurately measure an angle.\na. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a \"one-degree angle,\" and can be used to measure angles.\nb. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.4.R.MD.7","grade":"4","course":"4","domain":"Relationships","standard":"Demonstrate understanding that when an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Efficiently, flexibly, and accurately solve addition and subtraction problems to find unknown angles on a diagram in real world and mathem atical problems.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.4.SR.G.1","grade":"4","course":"4","domain":"Spatial Reasoning","standard":"Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these features in two-dimensional figures.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.4.SR.G.2","grade":"4","course":"4","domain":"Spatial Reasoning","standard":"Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category and identify right triangles.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.4.SR.G.3","grade":"4","course":"4","domain":"Spatial Reasoning","standard":"Recognize a line of symmetry for a two-dimensional figure as a line separating the figure such that the figure can be folded along the line into identical parts. Identify line-symmetric figures and draw lines of symmetry.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.4.SR.MD.1","grade":"4","course":"4","domain":"Spatial Reasoning","standard":"Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec., and express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.4.SR.MD.3","grade":"4","course":"4","domain":"Spatial Reasoning","standard":"Apply the area and perimeter formulas for rectangles in real world and mathematical problems.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.4.SR.MD.6","grade":"4","course":"4","domain":"Spatial Reasoning","standard":"Measure angles in whole-number degrees using a protractor. Represent angles of specified measure.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.5.DA.DS.1","grade":"5","course":"5","domain":"Data Analysis","standard":"Generate questions of interest to the students that elicit data, generate ideas based on the questions, and refine the question as necessary. Pose statistical questions that can compare two variables withing a group, setting, or situation.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.5.DA.DS.2","grade":"5","course":"5","domain":"Data Analysis","standard":"Determine strategies for collecting and considering data in a variety of ways including with the use of technology. Understand that data may contain errors (missing values, etc.) and decisions have to be made on how to account for or resolve these issues.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.5.DA.DS.3","grade":"5","course":"5","domain":"Data Analysis","standard":"Critically analyze data visualizations, including tables, bar graphs, line plots, or spreadsheets to support a claimrelated to the investigative question. Compare and contrast different data visualizations to determine which transparently communicate results and interpretations.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.5.DA.DS.4","grade":"5","course":"5","domain":"Data Analysis","standard":"Interpret and communicate results, describing difference between groups, with teacher guidance. Make a statement(s) about the data collected to support the answer to the investigative question. Describe the difference between two groups with different conditions.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.5.DA.MD.2","grade":"5","course":"5","domain":"Data Analysis","standard":"Make a line plot to display a data set of measurements in fractions of a unit. Use operations on fractions to solve problems involving inform ation presented in line plots.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.5.DA.OA.3","grade":"5","course":"5","domain":"Data Analysis","standard":"Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.5.Q.NF.1","grade":"5","course":"5","domain":"Quantity","standard":"Add and subtract fractions with unlike denominators (including mixed numbers) using flexible and efficient strategies, including replacing given fractions with equivalent fractions with like denominators. Justify using visual models (e.g., tape diagrams or number lines).","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.5.Q.NF.2","grade":"5","course":"5","domain":"Quantity","standard":"Efficiently, flexibly, and accurately solve real world word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.5.Q.NF.3","grade":"5","course":"5","domain":"Quantity","standard":"Interpret a fraction as division, where a quantity (the numerator) is divided into equal parts (the denominator). Flexibly and efficiently solve real world word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Assess the reasonableness of answers using estimation strategies.","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.5.Q.NF.4","grade":"5","course":"5","domain":"Quantity","standard":"Apply and extend previous understandings of multiplication to efficiently, flexibly, and accurately multiply a fraction or whole number by a fraction.\na. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q \u00f7 b. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. \nb. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.5.Q.NF.5","grade":"5","course":"5","domain":"Quantity","standard":"Interpret multiplication as scaling (resizing) by estimating whether a product will be larger or smaller than a given factor based on the size of the other factor, without performing the indicated multiplication.\na. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.\nb. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a)/(n x b) to the effect of multiplying a/b by 1.","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.5.Q.NF.6","grade":"5","course":"5","domain":"Quantity","standard":"Efficiently and flexibly solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using fraction models or equations to represent the problem. Assess the reasonableness of answers using mental and estimation strategies.","new":false,"priority":false,"level":"K-8","strand":"NF"},{"code":"M.5.Q.NF.7","grade":"5","course":"5","domain":"Quantity","standard":"Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions using fraction models and equations to represent the problem.\na. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) \u00f7 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3)\u00f7 4 = 1/12 because (1/12) x 4 = 1/3.\nb.  Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 \u00f7 (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 \u00f7 (1/5) = 20 because 20 x (1/5) = 4.\nc. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?","new":false,"priority":true,"level":"K-8","strand":"NF"},{"code":"M.5.Q.NBT.3","grade":"5","course":"5","domain":"Quantity","standard":"Read, write, and compare decimals to thousandths.\na. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.\nb. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.5.Q.NBT.5","grade":"5","course":"5","domain":"Quantity","standard":"Efficiently, flexibly, and accurately multiply mult-digit whole numbers using strategies or algorithms.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.5.R.OA.1","grade":"5","course":"5","domain":"Relationships","standard":"Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.5.R.OA.2","grade":"5","course":"5","domain":"Relationships","standard":"Write expressions that record calculations with numbers and interpret numerical expressions without evaluating them . For example, express the calculation \u201cadd 8 and 7, then multiply by 2\u201d as 2 x (8+7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.","new":false,"priority":false,"level":"K-8","strand":"OA"},{"code":"M.5.R.NBT.1","grade":"5","course":"5","domain":"Relationships","standard":"Understand that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and of what it represents in the place to its left.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.5.R.NBT.2","grade":"5","course":"5","domain":"Relationships","standard":"Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.5.R.NBT.4","grade":"5","course":"5","domain":"Relationships","standard":"Use place value understanding of decimals to generate estimates to any place using a variety of estimation strategies.","new":false,"priority":false,"level":"K-8","strand":"NBT"},{"code":"M.5.R.NBT.6","grade":"5","course":"5","domain":"Relationships","standard":"Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors using strategies based on place value, properties of operations, and connected to the relationship between multiplication and division including rectangular arrays, partial quotients, and/or area models.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.5.R.NBT.7","grade":"5","course":"5","domain":"Relationships","standard":"Efficiently, flexibly, and accurately add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.","new":false,"priority":true,"level":"K-8","strand":"NBT"},{"code":"M.5.SR.G.1","grade":"5","course":"5","domain":"Spatial Reasoning","standard":"Use a pair of perpendicular number lines, called axes, to define a coordinate system , with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.5.SR.G.2","grade":"5","course":"5","domain":"Spatial Reasoning","standard":"Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.","new":false,"priority":true,"level":"K-8","strand":"G"},{"code":"M.5.SR.G.3","grade":"5","course":"5","domain":"Spatial Reasoning","standard":"Demonstrate understanding that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.5.SR.G.4","grade":"5","course":"5","domain":"Spatial Reasoning","standard":"Classify two-dimensional figures into categories based on properties.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.5.SR.MD.1","grade":"5","course":"5","domain":"Spatial Reasoning","standard":"Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real world problems. Assess the reasonableness of answers using mental and estimation strategies.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.5.SR.MD.3","grade":"5","course":"5","domain":"Spatial Reasoning","standard":"Identify volume as an attribute of solid figures and understand concepts of volume measurement.\na. A cube with side length 1 unit, called a \"unit cube,\" is said to have \"one cubic unit\" of volume, and can be used to measure volume.\nb. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.5.SR.MD.4","grade":"5","course":"5","domain":"Spatial Reasoning","standard":"Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.","new":false,"priority":false,"level":"K-8","strand":"MD"},{"code":"M.5.SR.MD.5","grade":"5","course":"5","domain":"Spatial Reasoning","standard":"Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.\na. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.\nb. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.\nc. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.","new":false,"priority":true,"level":"K-8","strand":"MD"},{"code":"M.6.DA.DS.1","grade":"6","course":"6","domain":"Data Analysis","standard":"Formulate and recognize statistical investigative questions that are of interest to students to collect data from online sources and websites, smartphones, sensors, publicly available government agencies, and other modern devices.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.6.DA.DS.2","grade":"6","course":"6","domain":"Data Analysis","standard":"Collect and record data with technology to identify and describe the characteristics of data sets. Understand that data can be collected (primary data) or existing data can be obtained from other sources (secondary data).","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.6.DA.DS.3","grade":"6","course":"6","domain":"Data Analysis","standard":"Analyze data visualizations and describe measures of center and variability of quantitative data using appropriate displays (dot plots, boxplots). Describe key features of distributions for the variables including center, variability, and shape.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.6.DA.DS.4","grade":"6","course":"6","domain":"Data Analysis","standard":"Use statistical evidence from analyses to answer the statistical investigative question and communicate results with comprehensive answers with some teacher guidance.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.6.DA.SP.1","grade":"6","course":"6","domain":"Data Analysis","standard":"Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.6.DA.SP.2","grade":"6","course":"6","domain":"Data Analysis","standard":"Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.6.DA.SP.3","grade":"6","course":"6","domain":"Data Analysis","standard":"Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.6.DA.SP.4","grade":"6","course":"6","domain":"Data Analysis","standard":"Display numerical data in plots on a number line, including dot plots, histograms, and box plots.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.6.DA.SP.5","grade":"6","course":"6","domain":"Data Analysis","standard":"Summarize numerical data sets in relation to their context.\na. Reporting data points as the set of a number of observations.\nb. Describe what's being measured including how it was measured and its units of measurement.\nc. Calculate measures of center (mean and/or median) and variability (interquartile range and/or mean absolute deviation) of the data. Understand the shape of the data and identify any striking deviations (outliers) and connect these features to the context where the data came from.\nd. Communicate choice for selecting a given measure of center and variability and the connection to the shape of the data distribution related to the context in which the data were gathered.","new":false,"priority":true,"level":"K-8","strand":"SP"},{"code":"M.6.Q.NS.2","grade":"6","course":"6","domain":"Quantity","standard":"Efficiently, flexibly, and accurately divide multi-digit numbers using strategies or algorithms.","new":false,"priority":false,"level":"K-8","strand":"NS"},{"code":"M.6.Q.NS.3","grade":"6","course":"6","domain":"Quantity","standard":"Efficiently, flexibly, and accurately add, subtract, multiply, and divide multi-digit decimals using strategies or algorithms for each operation.","new":false,"priority":false,"level":"K-8","strand":"NS"},{"code":"M.6.Q.NS.5","grade":"6","course":"6","domain":"Quantity","standard":"Explain how positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.","new":false,"priority":false,"level":"K-8","strand":"NS"},{"code":"M.6.Q.NS.6","grade":"6","course":"6","domain":"Quantity","standard":"Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to place any number (integer or rational, positive or negative) on the line (horizontal or vertical), and in the plane.\na. Understand opposite signs of numbers as indicating locations on opposite sides of 0 on the number line, and recognize that, in situations like -(-3), the opposite of the opposite of a number is the number itself (in this example, 3).\nb. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.\nc. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.","new":false,"priority":true,"level":"K-8","strand":"NS"},{"code":"M.6.Q.NS.7","grade":"6","course":"6","domain":"Quantity","standard":"Understand ordering and absolute value of positive and negative rational numbers. \na. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.\nb. Write, interpret, and explain order for rational numbers on a number line in real-world contexts, including the use of inequalities. \nc. Interpret absolute value as the distance a number is from zero on a number line, and understand the magnitude of absolute value in real world contexts like comparing temperatures, or understanding the size of a debt.\nd. Distinguish comparisons of absolute value from statements about order.","new":false,"priority":false,"level":"K-8","strand":"NS"},{"code":"M.6.R.RP.1","grade":"6","course":"6","domain":"Relationships","standard":"Explain the concept of a ratio and efficiently, flexibly, and accurately use ratio language to describe a ratio relationship between two quantities.","new":false,"priority":true,"level":"K-8","strand":"RP"},{"code":"M.6.R.RP.2","grade":"6","course":"6","domain":"Relationships","standard":"Understand the concept of a unit rate a/b associated with a ratio a:b with b \u2260\u00a0 0, and use rate language in the context of a ratio relationship.","new":false,"priority":false,"level":"K-8","strand":"RP"},{"code":"M.6.R.RP.3","grade":"6","course":"6","domain":"Relationships","standard":"Efficiently, flexibly, and accurately demonstrate understanding of ratio and rate reasoning by solving real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations to find different ways to express the same ratio.\na. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.\nb. Solve unit rate problems (like price per item and constant speed)\nc. Find percent of a quantity as a rate per 100 (a special ratio out of 100), including finding the whole, a part, and the percent as appropriate for a given context. \nd. Use ratios to convert between different measurement units, like inches to feet, considering when it is appropriate to multiply or divide quantities.","new":false,"priority":true,"level":"K-8","strand":"RP"},{"code":"M.6.R.NS.1","grade":"6","course":"6","domain":"Relationships","standard":"Interpret and efficiently, flexibly, and accurately determine quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.","new":false,"priority":true,"level":"K-8","strand":"NS"},{"code":"M.6.R.NS.4","grade":"6","course":"6","domain":"Relationships","standard":"Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1\u2013100 with a common factor as a multiple of a sum of two whole numbers with no common factor.","new":false,"priority":false,"level":"K-8","strand":"NS"},{"code":"M.6.R.EE.1","grade":"6","course":"6","domain":"Relationships","standard":"Efficiently, flexibly, and accurately write and evaluate numerical expressions involving whole-number exponents.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.6.R.EE.2","grade":"6","course":"6","domain":"Relationships","standard":"Read, and evaluate expressions efficiently, flexibly, and accurately. \na.  Write expressions in which letters stand for numbers to write general instructions like \"subtract y from 5\" as a mathematical expression (5 - y).\nb. Break down expressions into smaller parts using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.\nc. Replace values for the variables (evaluating the expression) and use the Order of Operations where appropriate to solve problems including using real-world formulas, and formulas with whole-number exponents.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.6.R.EE.3","grade":"6","course":"6","domain":"Relationships","standard":"Apply the properties of operations (including the distributive property) efficiently, flexibly, and accurately to generate equivalent expressions.","new":false,"priority":true,"level":"K-8","strand":"EE"},{"code":"M.6.R.EE.4","grade":"6","course":"6","domain":"Relationships","standard":"Identify whether two expressions are equivalent (including expressions with one or more variables) as both expressions will always yield the same outcome for any value of a given variable.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.6.R.EE.5","grade":"6","course":"6","domain":"Relationships","standard":"Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.6.R.EE.6","grade":"6","course":"6","domain":"Relationships","standard":"Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or depending on the purpose at hand, any number in a specified set.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.6.R.EE.7","grade":"6","course":"6","domain":"Relationships","standard":"Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p,q and x are all nonnegative rational numbers.","new":false,"priority":true,"level":"K-8","strand":"EE"},{"code":"M.6.R.EE.8","grade":"6","course":"6","domain":"Relationships","standard":"Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.6.R.EE.9","grade":"6","course":"6","domain":"Relationships","standard":"Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables and relate these to the equation.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.6.SR.G.1","grade":"6","course":"6","domain":"Spatial Reasoning","standard":"Find the area of right triangles, other triangles, special quadrilaterals, and polygons by efficiently, flexibly, and accurately composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.6.SR.G.2","grade":"6","course":"6","domain":"Spatial Reasoning","standard":"Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.","new":false,"priority":true,"level":"K-8","strand":"G"},{"code":"M.6.SR.G.3","grade":"6","course":"6","domain":"Spatial Reasoning","standard":"Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.6.SR.G.4","grade":"6","course":"6","domain":"Spatial Reasoning","standard":"Represent three-dimensional figures using nets made up of rectangles and triangles and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.6.SR.NS.8","grade":"6","course":"6","domain":"Spatial Reasoning","standard":"Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.","new":false,"priority":true,"level":"K-8","strand":"NS"},{"code":"M.7.DA.DS.1","grade":"7","course":"7","domain":"Data Analysis","standard":"Pose statistical investigative questions about a broader population using samples taken from the population.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.7.DA.DS.2","grade":"7","course":"7","domain":"Data Analysis","standard":"Understand information from a sample is valid only if the sample is representative of that population. Understand data can be used to make comparisons between different groups at one point in time and the same group over time.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.7.DA.DS.3","grade":"7","course":"7","domain":"Data Analysis","standard":"Identify, determine, and interpret measures of center (mean and median) and measures of variability (range, interquartile range) to answer a statistically investigative question, summarizing the distribution of data using the measures of center and variability. Use reasoning about distributions to compare two groups based on the variables.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.7.DA.DS.4","grade":"7","course":"7","domain":"Data Analysis","standard":"Acknowledge that looking beyond the data is feasible and recognize the uncertainty caused by sample-to-sample variability when making comparisons and/or conclusions from data to answer the investigative question.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.7.DA.SP.1","grade":"7","course":"7","domain":"Data Analysis","standard":"Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.7.DA.SP.2","grade":"7","course":"7","domain":"Data Analysis","standard":"Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.","new":false,"priority":true,"level":"K-8","strand":"SP"},{"code":"M.7.DA.SP.3","grade":"7","course":"7","domain":"Data Analysis","standard":"Informally assess the degree of overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.7.DA.SP.4","grade":"7","course":"7","domain":"Data Analysis","standard":"Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.7.DA.SP.5","grade":"7","course":"7","domain":"Data Analysis","standard":"Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.","new":false,"priority":true,"level":"K-8","strand":"SP"},{"code":"M.7.DA.SP.6","grade":"7","course":"7","domain":"Data Analysis","standard":"Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency and predict the approximate relative frequency given the probability.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.7.DA.SP.7","grade":"7","course":"7","domain":"Data Analysis","standard":"Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.7.DA.SP.8","grade":"7","course":"7","domain":"Data Analysis","standard":"Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.\na. Understand the probability of a compound event is a fraction of the outcomes of the sample space.\nb. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., \"rolling double sixes\"), identify the outcomes in the sample space which compose the event.\nc. Design and use a simulation to generate frequencies for compound events.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.7.Q.NS.1","grade":"7","course":"7","domain":"Quantity","standard":"Efficiently, flexibly, and accurately apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. \na. Describe situations in which opposite quantities combine to make 0.\nb. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.\nc. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.\nd. Apply properties of operations as strategies to add and subtract rational numbers.","new":false,"priority":false,"level":"K-8","strand":"NS"},{"code":"M.7.Q.NS.2","grade":"7","course":"7","domain":"Quantity","standard":"Efficiently, flexibly, and accurately apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. \na. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.\nb. Understand integers can be divided as long as the divisor isn't zero, resulting in rational numbers.\nc.  Apply properties of operations as strategies to multiply and divide rational numbers.\nd. Convert rational numbers into decimals using flexible, efficient, and accurate strategies, recognizing that the decimal form either ends in 0s or repeats eventually.","new":false,"priority":true,"level":"K-8","strand":"NS"},{"code":"M.7.Q.G.1","grade":"7","course":"7","domain":"Quantity","standard":"Efficiently, flexibly, and accurately solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing, and reproducing a scale drawing at a different scale.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.7.R.RP.1","grade":"7","course":"7","domain":"Relationships","standard":"Efficiently, flexibly, and accurately compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.","new":false,"priority":false,"level":"K-8","strand":"RP"},{"code":"M.7.R.RP.2","grade":"7","course":"7","domain":"Relationships","standard":"Recognize and represent proportional relationships between quantities.\na. Decide whether  the relationship between two quantities is proportional using equivalent ratios in a table, graphing on the coordinate plane to see of the graph is a straight line through origin.\nb.  Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.\nc. Write equations for proportional relationships.\nd. Analyze graphs to understand what the data points indicate about the real-world situation, focusing on points like (0, 0) and (1, r) where r is the unit rate.","new":false,"priority":true,"level":"K-8","strand":"RP"},{"code":"M.7.R.RP.3","grade":"7","course":"7","domain":"Relationships","standard":"Efficiently, flexibly, and accurately use proportional relationships to solve multistep ratio and percent problems.","new":false,"priority":false,"level":"K-8","strand":"RP"},{"code":"M.7.R.EE.1","grade":"7","course":"7","domain":"Relationships","standard":"Efficiently, flexibly, and accurately use properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.7.R.EE.2","grade":"7","course":"7","domain":"Relationships","standard":"Understand that rewriting an expression in different forms in a problem context can bring awareness to parts of the problem and how the quantities in it are related.","new":false,"priority":true,"level":"K-8","strand":"EE"},{"code":"M.7.R.EE.3","grade":"7","course":"7","domain":"Relationships","standard":"Efficiently, flexibly, and accurately solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.7.R.EE.4","grade":"7","course":"7","domain":"Relationships","standard":"Use variables to represent quantities in a real-world or mathematical problem and write equations and inequalities to efficiently, flexibly, and accurately to solve problems by reasoning about the quantities. \na.  Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Compare solving the same problem algebraically vs. with arithmetic, explaining the steps involved in each approach.\nb. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solutions of these inequalities and interpret them in context of the problem.","new":false,"priority":true,"level":"K-8","strand":"EE"},{"code":"M.7.SR.G.2","grade":"7","course":"7","domain":"Spatial Reasoning","standard":"Draw geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.7.SR.G.3","grade":"7","course":"7","domain":"Spatial Reasoning","standard":"Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.7.SR.G.4","grade":"7","course":"7","domain":"Spatial Reasoning","standard":"Know the formulas for the area and circumference of a circle and use them to solve problems; informally show the relationship between the circumference and area of a circle.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.7.SR.G.5","grade":"7","course":"7","domain":"Spatial Reasoning","standard":"Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve  equations for an unknown angle in a figure.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.7.SR.G.6","grade":"7","course":"7","domain":"Spatial Reasoning","standard":"Efficiently, flexibly, and accurately solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.","new":false,"priority":true,"level":"K-8","strand":"G"},{"code":"M.8.DA.DS.1","grade":"8","course":"8","domain":"Data Analysis","standard":"Formulate statistical investigative questions to articulate research topics and uncover patterns of association seen in bivariate categorical data, that multiple investigative questions may exist for a research topic and must take into account context.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.8.DA.DS.2","grade":"8","course":"8","domain":"Data Analysis","standard":"Understand how to interrogate the data to determine how the data were collected, from whom they were collected, what types of variables are in the data, how the variables were measured, and possible outcomes for the variables.","new":true,"priority":false,"level":"K-8","strand":"DS"},{"code":"M.8.DA.DS.3","grade":"8","course":"8","domain":"Data Analysis","standard":"Create data visualizations about a data set. Organize and present the data in appropriate ways, including in tables and scatter plots, and incorporate other relevant information that helps to tell a story and support a claim about the data.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.8.DA.DS.4","grade":"8","course":"8","domain":"Data Analysis","standard":"Generalize beyond the sample providing statistical evidence for the conclusion, being sure to address limitations of the sample, evidenced in the data. Consider the reasonableness of the results.","new":true,"priority":true,"level":"K-8","strand":"DS"},{"code":"M.8.DA.SP.1","grade":"8","course":"8","domain":"Data Analysis","standard":"Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.8.DA.SP.2","grade":"8","course":"8","domain":"Data Analysis","standard":"Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.8.DA.SP.3","grade":"8","course":"8","domain":"Data Analysis","standard":"Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.","new":false,"priority":true,"level":"K-8","strand":"SP"},{"code":"M.8.DA.SP.4","grade":"8","course":"8","domain":"Data Analysis","standard":"Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.","new":false,"priority":false,"level":"K-8","strand":"SP"},{"code":"M.8.Q.NS.1","grade":"8","course":"8","domain":"Quantity","standard":"Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers efficiently, flexibly, and accurately show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.","new":false,"priority":true,"level":"K-8","strand":"NS"},{"code":"M.8.Q.NS.2","grade":"8","course":"8","domain":"Quantity","standard":"Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., \u03c0\u00b2).","new":false,"priority":false,"level":"K-8","strand":"NS"},{"code":"M.8.Q.EE.1","grade":"8","course":"8","domain":"Quantity","standard":"Know and apply the properties of integer exponents to generate equivalent numerical expressions.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.8.Q.EE.2","grade":"8","course":"8","domain":"Quantity","standard":"Use square roots and cube roots where p is a positive rational number. Use square root symbols to represent solutions to equations of the form x\u00b2 = p. Evaluate square roots of perfect squares. Use cube root symbols to represent solutions to equations of the form x\u00b3 = p and evaluate cube roots of perfect cubes. Know that \u221a2 is irrational.","new":false,"priority":true,"level":"K-8","strand":"EE"},{"code":"M.8.Q.EE.3","grade":"8","course":"8","domain":"Quantity","standard":"Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.8.Q.EE.4","grade":"8","course":"8","domain":"Quantity","standard":"Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.8.R.EE.5","grade":"8","course":"8","domain":"Relationships","standard":"Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.8.R.EE.6","grade":"8","course":"8","domain":"Relationships","standard":"Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.","new":false,"priority":false,"level":"K-8","strand":"EE"},{"code":"M.8.R.EE.7","grade":"8","course":"8","domain":"Relationships","standard":"Efficiently, flexibly, and accurately solve linear equations in one variable.\na. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).\nb. Solve linear equations with rational number coefficients where solution paths may require using the distributive property and combining like terms.","new":false,"priority":true,"level":"K-8","strand":"EE"},{"code":"M.8.R.EE.8","grade":"8","course":"8","domain":"Relationships","standard":"Analyze and efficiently, flexibly, and accurately solve pairs of simultaneous linear equations.\na. Understand the solution to a system of linear equations is the point of intersection, because the intersection is a solution to both equations.\nb. Solve systems of linear equations using a variety of strategies (algebraically, graphically, numerically in tables, verbally, etc.) \nc. Solve real-world and mathematical problems leading to two linear equations in two variables.","new":false,"priority":true,"level":"K-8","strand":"EE"},{"code":"M.8.R.F.1","grade":"8","course":"8","domain":"Relationships","standard":"Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.","new":false,"priority":false,"level":"K-8","strand":"F"},{"code":"M.8.R.F.2","grade":"8","course":"8","domain":"Relationships","standard":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).","new":false,"priority":false,"level":"K-8","strand":"F"},{"code":"M.8.R.F.3","grade":"8","course":"8","domain":"Relationships","standard":"Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.","new":false,"priority":false,"level":"K-8","strand":"F"},{"code":"M.8.R.F.4","grade":"8","course":"8","domain":"Relationships","standard":"Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including  from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.","new":false,"priority":true,"level":"K-8","strand":"F"},{"code":"M.8.R.F.5","grade":"8","course":"8","domain":"Relationships","standard":"Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described informally.","new":false,"priority":false,"level":"K-8","strand":"F"},{"code":"M.8.SR.G.1","grade":"8","course":"8","domain":"Spatial Reasoning","standard":"Verify experimentally the properties of rotations, reflections, and translations.\na. Line and segment lengths are preserved in rotations, reflections, and translations.\nb. Angles are taken to angles of the same measure.\nc. Parallel lines are taken to parallel lines.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.8.SR.G.2","grade":"8","course":"8","domain":"Spatial Reasoning","standard":"Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.8.SR.G.3","grade":"8","course":"8","domain":"Spatial Reasoning","standard":"Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.8.SR.G.4","grade":"8","course":"8","domain":"Spatial Reasoning","standard":"Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.","new":false,"priority":true,"level":"K-8","strand":"G"},{"code":"M.8.SR.G.5","grade":"8","course":"8","domain":"Spatial Reasoning","standard":"Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.8.SR.G.6","grade":"8","course":"8","domain":"Spatial Reasoning","standard":"Efficiently, flexibly, and accurately explain a proof of the Pythagorean Theorem and its converse.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.8.SR.G.7","grade":"8","course":"8","domain":"Spatial Reasoning","standard":"Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.","new":false,"priority":true,"level":"K-8","strand":"G"},{"code":"M.8.SR.G.8","grade":"8","course":"8","domain":"Spatial Reasoning","standard":"Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.8.SR.G.9","grade":"8","course":"8","domain":"Spatial Reasoning","standard":"Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.","new":false,"priority":false,"level":"K-8","strand":"G"},{"code":"M.HS.DA.DS.1","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Formulate multivariable statistical investigative questions and determine how data can be collected and provide an answer, consider causality and prediction when posing the question.","new":true,"priority":true,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.2","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Understand the issues of bias and confounding variables when collecting data and their impact on interpretation. Understand practices for collecting and handling data, including sensitive information and concerns for privacy and how that may affect data collection.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.3","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Create and analyze data sets using technology to clean, sort, or filter data. Summarize, and describe relationships between quantitative variables using data displays including but not limited to scatter plots, regressions, histograms, and boxplots.","new":true,"priority":true,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.4","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Acknowledge the presence of missing data values and understand how missing values may add bias to analysis and interpretation. Examine and discuss competing explanations for data trends observed such as confounding variables. Respond to competing arguments or interpretations of the data of different community groups, paying careful attention to what conclusions the data supports, taking into account correlation versus causation.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.FIF.1","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Understand that a function has a domain (input, dependent elements) and range (output, independent elements), and assigns to each domain element exactly one range element. If f is a function and x is a value of its domain, then the output of f corresponds to the input x. The graph of f is the graph of the equation y=f(x).","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.DA.FIF.2","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.DA.SID.1","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Represent data with plots on the real number line (dot plots, histograms, and box plots).","new":false,"priority":true,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.2","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.3","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).","new":false,"priority":true,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.5","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.6","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Represent data on two quantitative variables on a scatter plot and describe how the variables are related. Solve problems in context by fitting functions to the data and explaining trends and relationships within the data.\na.\tWhen fitting a function to the data, use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.\nc.\tFit a linear function for a scatter plot that suggests a linear association.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.7","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.","new":false,"priority":true,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.8","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Compute (using technology) and interpret the correlation coefficient of a linear fit.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.9","grade":"HS","course":"INT 1","domain":"Data Analysis","standard":"Distinguish between correlation and causation.","new":false,"priority":true,"level":"HS","strand":"SID"},{"code":"M.HS.Q.NQ.1","grade":"HS","course":"INT 1","domain":"Quantity","standard":"Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.","new":false,"priority":true,"level":"HS","strand":"NQ"},{"code":"M.HS.Q.NQ.2","grade":"HS","course":"INT 1","domain":"Quantity","standard":"Define appropriate quantities for the purpose of descriptive modeling.","new":false,"priority":true,"level":"HS","strand":"NQ"},{"code":"M.HS.Q.NQ.3","grade":"HS","course":"INT 1","domain":"Quantity","standard":"Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.","new":false,"priority":true,"level":"HS","strand":"NQ"},{"code":"M.HS.Q.ASSE.1","grade":"HS","course":"INT 1","domain":"Quantity","standard":"Interpret expressions that represent a quantity in terms of its context within linear, exponential, and quadratic functions.\na.\tInterpret parts of an expression, such as terms, factors, and coefficients.\nb.\tInterpret complicated expressions by viewing one or more of their parts as a single entity.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.FIF.7","grade":"HS","course":"INT 1","domain":"Quantity","standard":"Graph linear, exponential, and quadratic functions from their symbolic forms by hand or with technology, and identify key features including intercepts, intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries, and end behavior.\na.\tincluding intercepts, maxima, and minima.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FIF.9","grade":"HS","course":"INT 1","domain":"Quantity","standard":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Functions could be linear, exponential, or quadratic.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.ACED.3","grade":"HS","course":"INT 1","domain":"Quantity","standard":"Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context within linear, quadratic, and exponential equations.","new":false,"priority":false,"level":"HS","strand":"ACED"},{"code":"M.HS.Q.ACED.4","grade":"HS","course":"INT 1","domain":"Quantity","standard":"Efficiently, flexibly, and accurately rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations within linear, quadratic, and exponential equations.","new":false,"priority":true,"level":"HS","strand":"ACED"},{"code":"M.HS.Q.FBF.1","grade":"HS","course":"INT 1","domain":"Quantity","standard":"Efficiently, flexibly, and accurately write a function that describes a relationship between two quantities, including linear and exponential relationships, and arithmetic and geometric sequences in context.\na.\tDetermine an explicit expression, a recursive process, or steps for calculation from a context.\nb.\tCombine standard function types using arithmetic operations.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.FIF.3","grade":"HS","course":"INT 1","domain":"Quantity","standard":"Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FBF.3","grade":"HS","course":"INT 1","domain":"Quantity","standard":"Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k  (both positive and negative); find the value of k  given the graphs. Using a variety of strategies, experiment with cases and illustrate an explanation of the effects on the graph using technology, within linear, exponential, and quadratic functions.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.R.FIF.4","grade":"HS","course":"INT 1","domain":"Relationships","standard":"For a function that models a relationship between two quantities in context of the relationship, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; and symmetries. Functions could be linear, exponential, or quadratic.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FIF.5","grade":"HS","course":"INT 1","domain":"Relationships","standard":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes in context. Functions could be linear, exponential, or quadratic relationships.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FIF.6","grade":"HS","course":"INT 1","domain":"Relationships","standard":"Calculate and interpret the average rate of change of a function (represented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.R.ACED.1","grade":"HS","course":"INT 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately create equations and inequalities in one variable that model a situation, and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.","new":false,"priority":true,"level":"HS","strand":"ACED"},{"code":"M.HS.R.ACED.2","grade":"HS","course":"INT 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.","new":false,"priority":true,"level":"HS","strand":"ACED"},{"code":"M.HS.R.FLE.1","grade":"HS","course":"INT 1","domain":"Relationships","standard":"Distinguish between situations that can be modeled with linear functions and with exponential functions, including:\na. Linear functions grow with equal differences over equal intervals and with exponential functions grow with equal factors over equal intervals.\nb. Recognizing constant rates per unit interval relative to another.\nc. Recognize contexts of growth or decay by a constant percent rate per unit interval relative to another.","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.R.FLE.2","grade":"HS","course":"INT 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately construct linear and exponential functions given a graph, a description of a relationship, or two input-output pairs (including reading these from a table).","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.R.FLE.3","grade":"HS","course":"INT 1","domain":"Relationships","standard":"Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically.","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.R.FLE.5","grade":"HS","course":"INT 1","domain":"Relationships","standard":"Interpret the parameters in a linear or exponential function in terms of a context.","new":false,"priority":true,"level":"HS","strand":"FLE"},{"code":"M.HS.R.AREI.1","grade":"HS","course":"INT 1","domain":"Relationships","standard":"Given that an original equation has a solution, efficiently, flexibly, and accurately select and use strategies to solve the equation, explaining each step, and construct a viable argument to justify a solution method.","new":false,"priority":true,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.3","grade":"HS","course":"INT 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.5","grade":"HS","course":"INT 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately demonstrate that systems of two equations in two variables maintain the same solution set when one equation is replaced by the sum of that equation and a multiple of the other equation.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.6","grade":"HS","course":"INT 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.SR.AREI.10","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.SR.AREI.11","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Using a variety of strategies explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, exponential, and quadratic.","new":false,"priority":true,"level":"HS","strand":"AREI"},{"code":"M.HS.SR.AREI.12","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.SR.GGPE.4","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Use coordinates to prove simple geometric theorems algebraically.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.5","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.6","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Find the point on a directed line segment between two given points that partitions the segment in a given ratio.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.7","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GCO.1","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.","new":false,"priority":true,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.2","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Efficiently, flexibly, and accurately represent transformations in the plane, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.3","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.4","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.","new":false,"priority":true,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.5","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Efficiently, flexibly, and accurately specify a sequence of transformations that will carry a given figure onto another.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.6","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.","new":false,"priority":true,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.7","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.8","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.12","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Make formal geometric constructions with a variety of tools and methods.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.13","grade":"HS","course":"INT 1","domain":"Spatial Reasoning","standard":"Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.DA.DS.1","grade":"HS","course":"INT 2","domain":"Data Analysis","standard":"Formulate multivariable statistical investigative questions and determine how data can be collected and provide an answer, consider causality and prediction when posing the question.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.2","grade":"HS","course":"INT 2","domain":"Data Analysis","standard":"Understand the issues of bias and confounding variables when collecting data and their impact on interpretation. Understand practices for collecting and handling data, including sensitive information and concerns for privacy and how that may affect data collection.","new":true,"priority":true,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.3","grade":"HS","course":"INT 2","domain":"Data Analysis","standard":"Create and analyze data sets using technology to clean, sort, or filter data. Summarize, and describe relationships between quantitative variables using data displays including but not limited to scatter plots, regressions, histograms, and boxplots.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.4","grade":"HS","course":"INT 2","domain":"Data Analysis","standard":"Acknowledge the presence of missing data values and understand how missing values may add bias to analysis and interpretation. Examine and discuss competing explanations for data trends observed such as confounding variables. Respond to competing arguments or interpretations of the data of different community groups, paying careful attention to what conclusions the data supports, taking into account correlation versus causation.","new":true,"priority":true,"level":"HS","strand":"DS"},{"code":"M.HS.DA.SCP.1","grade":"HS","course":"INT 2","domain":"Data Analysis","standard":"Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (\"or,\" \"and,\" \"not\").","new":false,"priority":true,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.2","grade":"HS","course":"INT 2","domain":"Data Analysis","standard":"Understand that two events, A and B, are independent if the probability of  and  occurring together is the product of their probabilities and use this characterization to determine if they are independent.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.3","grade":"HS","course":"INT 2","domain":"Data Analysis","standard":"Understand the conditional probability of A given B as (P(A and B),)/(P(B)) and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.4","grade":"HS","course":"INT 2","domain":"Data Analysis","standard":"Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.5","grade":"HS","course":"INT 2","domain":"Data Analysis","standard":"Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.","new":false,"priority":true,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.6","grade":"HS","course":"INT 2","domain":"Data Analysis","standard":"Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A and interpret the answer in terms of the model.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.7","grade":"HS","course":"INT 2","domain":"Data Analysis","standard":"Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.Q.GSRT.3","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.Q.GSRT.6","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.Q.GSRT.7","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Explain and use the relationship between the sine and cosine of complementary angles.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.Q.GSRT.8","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.Q.ASSE.1","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Interpret expressions that represent a quantity in terms of its context within linear, exponential, and quadratic functions.\na.\tInterpret parts of an expression, such as terms, factors, and coefficients.\nb.\tInterpret complicated expressions by viewing one or more of their parts as a single entity.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.ASSE.2","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Use the structure or pattern of an expression to identify ways to rewrite it such as the difference of squares, compound interest, and others.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.FIF.7","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Graph linear, exponential, and quadratic functions from their symbolic forms by hand or with technology, and identify key features including intercepts, intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries, and end behavior.\na.\tIncluding intercepts, maxima, and minima","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FIF.8","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately, and integer constants for exponential growth and decay, rewrite a function in different equivalent forms.\na.\tFactor quadratic functions to verify and explain various properties on graphs, such as zeros and symmetry in terms of a context.\nb.\tUse properties of exponents to interpret expressions for exponential functions.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FIF.9","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Functions could be linear, exponential, or quadratic.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.ACED.4","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations within linear, quadratic, and exponential equations.","new":false,"priority":true,"level":"HS","strand":"ACED"},{"code":"M.HS.Q.FBF.1","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately write a function that describes a relationship between two quantities, including linear and exponential relationships, and arithmetic and geometric sequences in context.\na.\tDetermine an explicit expression, a recursive process, or steps for calculation from a context.\nb.\tCombine standard function types using arithmetic operations.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.FBF.3","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Identify the effect on the graph of replacing f(x) by f(x) + k,k f(x),f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Using a variety of strategies, experiment with cases and illustrate an explanation of the effects on the graph using technology, within linear, exponential, and quadratic functions.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.NRN.1","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values using a variety of strategies, allowing for a notation for radicals in terms of rational exponents.","new":false,"priority":false,"level":"HS","strand":"NRN"},{"code":"M.HS.Q.NRN.2","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Rewrite expressions involving radicals and rational exponents using the properties of exponents.","new":false,"priority":false,"level":"HS","strand":"NRN"},{"code":"M.HS.Q.NRN.3","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.","new":false,"priority":false,"level":"HS","strand":"NRN"},{"code":"M.HS.Q.AAPR.1","grade":"HS","course":"INT 2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately demonstrate that polynomials form a system with a structure similar to that of integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials, limited to quadratic equations.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.R.FIF.4","grade":"HS","course":"INT 2","domain":"Relationships","standard":"For a function that models a relationship between two quantities in context of the relationship, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; and symmetries. Functions could be linear, exponential, or quadratic.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FIF.5","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes in context. Functions could be linear, exponential, or quadratic relationships.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FIF.6","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Calculate and interpret the average rate of change of a function (represented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.R.ASSE.3","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately rewrite expressions to equivalent forms that are suitable for the purpose of revealing and explaining a specific property about those functions (linear, quadratic, exponential)\na.\tFactor a quadratic expression to reveal the zeros of the function it defines.\nc.\tUse the properties of exponents to transform expressions for exponential functions.","new":false,"priority":true,"level":"HS","strand":"ASSE"},{"code":"M.HS.R.ACED.1","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately create equations and inequalities in one variable that model a situation, and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.","new":false,"priority":true,"level":"HS","strand":"ACED"},{"code":"M.HS.R.ACED.2","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.","new":false,"priority":false,"level":"HS","strand":"ACED"},{"code":"M.HS.R.FLE.3","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically.","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.R.AREI.4","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Solve quadratic equations in one variable using a process of identifying solutions as appropriate to the initial form of the equation.\nb. Solve by inspection (e.g., for x2=49), taking square roots, and factoring, as appropriate to the initial equation.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.7","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.GCO.9","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove theorems about lines and angles: vertical angles, transversals, alternate interior and exterior angles, perpendicular bisectors, etc","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.R.GCO.10","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove theorems about triangles: interior angles, base angles, segments joining midpoint of two sides, and medians of a triangle.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.R.GCO.11","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove theorems about parallelograms: congruence of opposite sides and opposite angles, properties of diagonals.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.R.GSRT.4","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove theorems about triangles including proportionality, triangle similarity, and the Pythagorean Theorem.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.R.GSRT.5","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.","new":false,"priority":true,"level":"HS","strand":"GSRT"},{"code":"M.HS.R.GC.1","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove that all circles are similar.","new":false,"priority":false,"level":"HS","strand":"GC"},{"code":"M.HS.R.GC.2","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Identify and describe relationships among inscribed angles, radii, and chords, including how angles formed inside the circle, the circle's radius, and line segments within the circle are related. Understand special cases including angles formed by diameters and how the circle's edge interacts with its radius.","new":false,"priority":true,"level":"HS","strand":"GC"},{"code":"M.HS.R.GC.5","grade":"HS","course":"INT 2","domain":"Relationships","standard":"Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.","new":false,"priority":false,"level":"HS","strand":"GC"},{"code":"M.HS.SR.GC.3","grade":"HS","course":"INT 2","domain":"Spatial Reasoning","standard":"Construct the inscribed and circumscribed circles of a triangle and efficiently, flexibly, and accurately prove properties of angles for a quadrilateral inscribed in a circle.","new":false,"priority":false,"level":"HS","strand":"GC"},{"code":"M.HS.SR.GSRT.1","grade":"HS","course":"INT 2","domain":"Spatial Reasoning","standard":"Verify experimentally how lines are affected by the center of dilation and how the scale factor changes line segments.\na. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.\nb. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.","new":false,"priority":true,"level":"HS","strand":"GSRT"},{"code":"M.HS.SR.GSRT.2","grade":"HS","course":"INT 2","domain":"Spatial Reasoning","standard":"Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.","new":false,"priority":true,"level":"HS","strand":"GSRT"},{"code":"M.HS.SR.GGPE.1","grade":"HS","course":"INT 2","domain":"Spatial Reasoning","standard":"Derive the equation of a circle of given center and radius using the Pythagorean Theorem.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.4","grade":"HS","course":"INT 2","domain":"Spatial Reasoning","standard":"Use coordinates to prove simple geometric theorems algebraically.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGMD.1","grade":"HS","course":"INT 2","domain":"Spatial Reasoning","standard":"Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.","new":false,"priority":false,"level":"HS","strand":"GGMD"},{"code":"M.HS.SR.GGMD.3","grade":"HS","course":"INT 2","domain":"Spatial Reasoning","standard":"Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.","new":false,"priority":true,"level":"HS","strand":"GGMD"},{"code":"M.HS.SR.GGMD.4","grade":"HS","course":"INT 2","domain":"Spatial Reasoning","standard":"Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.","new":false,"priority":false,"level":"HS","strand":"GGMD"},{"code":"M.HS.SR.GMG.1","grade":"HS","course":"INT 2","domain":"Spatial Reasoning","standard":"Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).","new":false,"priority":true,"level":"HS","strand":"GMG"},{"code":"M.HS.SR.GMG.2","grade":"HS","course":"INT 2","domain":"Spatial Reasoning","standard":"Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).","new":false,"priority":true,"level":"HS","strand":"GMG"},{"code":"M.HS.SR.GMG.3","grade":"HS","course":"INT 2","domain":"Spatial Reasoning","standard":"Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).","new":false,"priority":true,"level":"HS","strand":"GMG"},{"code":"M.HS.DA.DS.1","grade":"HS","course":"INT 3","domain":"Data Analysis","standard":"Formulate multivariable statistical investigative questions and determine how data can be collected and provide an answer, consider causality and prediction when posing the question.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.2","grade":"HS","course":"INT 3","domain":"Data Analysis","standard":"Understand the issues of bias and confounding variables when collecting data and their impact on interpretation. Understand practices for collecting and handling data, including sensitive information and concerns for privacy and how that may affect data collection.","new":true,"priority":true,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.3","grade":"HS","course":"INT 3","domain":"Data Analysis","standard":"Create and analyze data sets using technology to clean, sort, or filter data. Summarize, and describe relationships between quantitative variables using data displays including but not limited to scatter plots, regressions, histograms, and boxplots.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.4","grade":"HS","course":"INT 3","domain":"Data Analysis","standard":"Acknowledge the presence of missing data values and understand how missing values may add bias to analysis and interpretation. Examine and discuss competing explanations for data trends observed such as confounding variables. Respond to competing arguments or interpretations of the data of different community groups, paying careful attention to what conclusions the data supports, taking into account correlation versus causation.","new":true,"priority":true,"level":"HS","strand":"DS"},{"code":"M.HS.DA.SIC.1","grade":"HS","course":"INT 3","domain":"Data Analysis","standard":"Understand statistics as a process for making inferences about population parameters based on a random sample from that population.","new":false,"priority":false,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.2","grade":"HS","course":"INT 3","domain":"Data Analysis","standard":"Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.","new":false,"priority":false,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.3","grade":"HS","course":"INT 3","domain":"Data Analysis","standard":"Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.","new":false,"priority":true,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.4","grade":"HS","course":"INT 3","domain":"Data Analysis","standard":"Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.","new":false,"priority":true,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.5","grade":"HS","course":"INT 3","domain":"Data Analysis","standard":"Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.","new":false,"priority":false,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.6","grade":"HS","course":"INT 3","domain":"Data Analysis","standard":"Evaluate reports based on data.","new":false,"priority":true,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SID.4","grade":"HS","course":"INT 3","domain":"Data Analysis","standard":"Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.6","grade":"HS","course":"INT 3","domain":"Data Analysis","standard":"Represent data on two quantitative variables on a scatter plot and describe how the variables are related. Solve problems in context by fitting functions to the data and explaining trends and relationships within the data.\na.\tWhen fitting a function to the data, use given functions or choose a function suggested by the context. Models may include any family of functions.\nb.\tInformally assess the fit of a function by plotting and analyzing residuals. \nc.\tFit a linear function for a scatter plot that suggests a linear association.","new":false,"priority":true,"level":"HS","strand":"SID"},{"code":"M.HS.Q.ASSE.1","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Interpret expressions that represent a quantity in terms of its context in any family of functions.\na.\tInterpret parts of an expression, such as terms, factors, and coefficients.\nb.\tInterpret complicated expressions by viewing one or more of their parts as a single entity.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.ASSE.2","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Use the structure of an expression to identify ways to rewrite it.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.FBF.1","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Efficiently, flexibly, and accurately write a function that describes a relationship between two quantities, including linear and exponential relationships, and arithmetic and geometric sequences in context.\na.\tDetermine an explicit expression, a recursive process, or steps for calculation from a context.\nb.\tCombine standard function types using arithmetic operations.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.FBF.2","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model linear and exponential situations, and translate between the two forms.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.ASSE.4","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Derive the formula for the sum of a finite geometric series (when the common ratio is not 1) and use the formula to solve problems.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.FIF.7","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Graph families of functions from their symbolic forms by hand or with technology, and identify key features including intercepts, intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries, and end behavior.\na.\tincluding intercepts, maxima, and minima.\nb.\tGraph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.\nc.\tGraph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.\ne.\tGraph logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FIF.8","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Efficiently, flexibly, and accurately, write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.\na.\tFactor quadratic functions and completing the square to show zeros, extreme values and symmetry in terms of a context.\nb.\tUse properties of exponents to interpret expressions for exponential functions, including non-integer constants for time when applicable in contexts of exponential growth or decay.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FIF.9","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Functions can include polynomial, radical, rational, logarithms, absolute value, piecewise, trigonometric, and increasingly complex linear, exponential, and quadratic relationships.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FBF.3","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Using a variety of strategies, experiment with cases and illustrate an explanation of the effects on the graph using technology.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.ACED.3","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. May include any families of functions.","new":false,"priority":true,"level":"HS","strand":"ACED"},{"code":"M.HS.Q.ACED.4","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Efficiently, flexibly, and accurately rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. May include any families of functions.","new":false,"priority":true,"level":"HS","strand":"ACED"},{"code":"M.HS.Q.NCN.1","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Know there is a complex number i such that i\u00b2 = -1, and every complex number has the form a + bi with a and b real.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NCN.2","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Use the relation i\u00b2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NCN.7","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Solve quadratic equations with real coefficients that have complex solutions.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.AAPR.1","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Efficiently, flexibly, and accurately demonstrate that polynomials form a system with a structure similar to that of integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.2","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.3","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.4","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Prove polynomial identities and use them to describe numerical relationships.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.6","grade":"HS","course":"INT 3","domain":"Quantity","standard":"Efficiently, flexibly, and accurately rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.R.ACED.1","grade":"HS","course":"INT 3","domain":"Relationships","standard":"Efficiently, flexibly, and accurately create equations and inequalities in one variable that model a situation, and use them to solve problems.","new":false,"priority":false,"level":"HS","strand":"ACED"},{"code":"M.HS.R.ACED.2","grade":"HS","course":"INT 3","domain":"Relationships","standard":"Efficiently, flexibly, and accurately create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.","new":false,"priority":false,"level":"HS","strand":"ACED"},{"code":"M.HS.R.ASSE.3","grade":"HS","course":"INT 3","domain":"Relationships","standard":"Efficiently, flexibly, and accurately rewrite expressions to equivalent forms that are suitable for the purpose of revealing and explaining a specific property about those functions \na.\tFactor a quadratic expression to reveal the zeros of the function it defines.\nb.\tComplete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.\nc.\tUse the properties of exponents to transform expressions for exponential functions.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.R.AREI.4","grade":"HS","course":"INT 3","domain":"Relationships","standard":"Solve quadratic equations in one variable using a process of identifying solutions as appropriate to the initial form of the equation.\na. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x-p)2=q that has the same solutions. Derive the quadratic formula from this form.\nb. Solve quadratic equations by inspection (e.g., for x2=49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate. Recognize when the quadratic formula gives complex solutions and write them as a+bi for real numbers a and b.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.2","grade":"HS","course":"INT 3","domain":"Relationships","standard":"Solve rational and radical equations in one variable and give examples showing how extraneous solutions may arise.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.FIF.4","grade":"HS","course":"INT 3","domain":"Relationships","standard":"For any function that models a relationship between two quantities in context of the relationship, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; and symmetries. May include any families of functions, and relative maximums and minimums, end behavior, and periodicity.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FIF.5","grade":"HS","course":"INT 3","domain":"Relationships","standard":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes in context. Functions can include polynomial, radical, rational, logarithms, absolute value, piecewise, trigonometric, and increasingly complex linear, exponential, and quadratic relationships.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FIF.6","grade":"HS","course":"INT 3","domain":"Relationships","standard":"Calculate and interpret the average rate of change of a non-linear function (represented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FBF.4","grade":"HS","course":"INT 3","domain":"Relationships","standard":"Find inverse functions through focus on relationships between inputs and outputs.\na. Solve and equation of the form f(x) = c that has an inverse and write an equation for the inverse.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.R.FLE.4","grade":"HS","course":"INT 3","domain":"Relationships","standard":"For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.SR.AREI.11","grade":"HS","course":"INT 3","domain":"Spatial Reasoning","standard":"Using a variety of strategies explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.","new":false,"priority":true,"level":"HS","strand":"AREI"},{"code":"M.HS.SR.FTF.1","grade":"HS","course":"INT 3","domain":"Spatial Reasoning","standard":"Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.2","grade":"HS","course":"INT 3","domain":"Spatial Reasoning","standard":"Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.5","grade":"HS","course":"INT 3","domain":"Spatial Reasoning","standard":"Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.","new":false,"priority":true,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.8","grade":"HS","course":"INT 3","domain":"Spatial Reasoning","standard":"Prove the Pythagorean identity sin2(\u03b8) + cos2(\u03b8) = 1 and use it to find sin(\u03b8), cos(\u03b8), or tan(\u03b8), given sin(\u03b8), cos(\u03b8), or tan(\u03b8) and the quadrant of the angle.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.GGPE.1","grade":"HS","course":"INT 3","domain":"Spatial Reasoning","standard":"Derive the equation of a circle of given center and radius using the Pythagorean Theorem.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.2","grade":"HS","course":"INT 3","domain":"Spatial Reasoning","standard":"Derive the equation of a parabola given a focus and directrix.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGMD.4","grade":"HS","course":"INT 3","domain":"Spatial Reasoning","standard":"Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.","new":false,"priority":false,"level":"HS","strand":"GGMD"},{"code":"M.HS.DA.DS.1","grade":"HS","course":"GEO","domain":"Data Analysis","standard":"Formulate multivariable statistical investigative questions and determine how data can be collected and provide an answer, consider causality and prediction when posing the question.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.2","grade":"HS","course":"GEO","domain":"Data Analysis","standard":"Understand the issues of bias and confounding variables when collecting data and their impact on interpretation. Understand practices for collecting and handling data, including sensitive information and concerns for privacy and how that may affect data collection.","new":true,"priority":true,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.3","grade":"HS","course":"GEO","domain":"Data Analysis","standard":"Create and analyze data sets using technology to clean, sort, or filter data. Summarize, and describe relationships between quantitative variables using data displays including but not limited to scatter plots, regressions, histograms, and boxplots.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.4","grade":"HS","course":"GEO","domain":"Data Analysis","standard":"Acknowledge the presence of missing data values and understand how missing values may add bias to analysis and interpretation. Examine and discuss competing explanations for data trends observed such as confounding variables. Respond to competing arguments or interpretations of the data of different community groups, paying careful attention to what conclusions the data supports, taking into account correlation versus causation.","new":true,"priority":true,"level":"HS","strand":"DS"},{"code":"M.HS.DA.SCP.1","grade":"HS","course":"GEO","domain":"Data Analysis","standard":"Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (\"or,\" \"and,\" \"not\").","new":false,"priority":true,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.2","grade":"HS","course":"GEO","domain":"Data Analysis","standard":"Understand that two events, A and B, are independent if the probability of  and  occurring together is the product of their probabilities and use this characterization to determine if they are independent.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.3","grade":"HS","course":"GEO","domain":"Data Analysis","standard":"Understand the conditional probability of A given B as (P(A and B),)/(P(B)) and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.4","grade":"HS","course":"GEO","domain":"Data Analysis","standard":"Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.5","grade":"HS","course":"GEO","domain":"Data Analysis","standard":"Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.","new":false,"priority":true,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.6","grade":"HS","course":"GEO","domain":"Data Analysis","standard":"Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A and interpret the answer in terms of the model.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.7","grade":"HS","course":"GEO","domain":"Data Analysis","standard":"Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.Q.GSRT.3","grade":"HS","course":"GEO","domain":"Quantity","standard":"Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.Q.GSRT.6","grade":"HS","course":"GEO","domain":"Quantity","standard":"Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.Q.GSRT.7","grade":"HS","course":"GEO","domain":"Quantity","standard":"Explain and use the relationship between the sine and cosine of complementary angles.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.Q.GSRT.8","grade":"HS","course":"GEO","domain":"Quantity","standard":"Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.R.GCO.9","grade":"HS","course":"GEO","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove theorems about lines and angles: vertical angles, transversals, alternate interior and exterior angles, perpendicular bisectors, etc","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.R.GCO.10","grade":"HS","course":"GEO","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove theorems about triangles: interior angles, base angles, segments joining midpoint of two sides, and medians of a triangle.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.R.GCO.11","grade":"HS","course":"GEO","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove theorems about parallelograms: congruence of opposite sides and opposite angles, properties of diagonals.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.R.GSRT.4","grade":"HS","course":"GEO","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove theorems about triangles including proportionality, triangle similarity, and the Pythagorean Theorem.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.R.GSRT.5","grade":"HS","course":"GEO","domain":"Relationships","standard":"Efficiently, flexibly, and accurately use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.","new":false,"priority":true,"level":"HS","strand":"GSRT"},{"code":"M.HS.R.GC.1","grade":"HS","course":"GEO","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove that all circles are similar.","new":false,"priority":false,"level":"HS","strand":"GC"},{"code":"M.HS.R.GC.2","grade":"HS","course":"GEO","domain":"Relationships","standard":"Identify and describe relationships among inscribed angles, radii, and chords, including how angles formed inside the circle, the circle's radius, and line segments within the circle are related. Understand special cases including angles formed by diameters and how the circle's edge interacts with its radius.","new":false,"priority":true,"level":"HS","strand":"GC"},{"code":"M.HS.R.GC.5","grade":"HS","course":"GEO","domain":"Relationships","standard":"Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.","new":false,"priority":false,"level":"HS","strand":"GC"},{"code":"M.HS.SR.GGPE.4","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Use coordinates to prove simple geometric theorems algebraically.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.5","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.6","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Find the point on a directed line segment between two given points that partitions the segment in a given ratio.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.7","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GCO.1","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.","new":false,"priority":true,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.2","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Efficiently, flexibly, and accurately represent transformations in the plane, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.3","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.4","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.","new":false,"priority":true,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.5","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Efficiently, flexibly, and accurately specify a sequence of transformations that will carry a given figure onto another.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.6","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.","new":false,"priority":true,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.7","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.8","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.12","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Make formal geometric constructions with a variety of tools and methods.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.13","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GC.3","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Construct the inscribed and circumscribed circles of a triangle and efficiently, flexibly, and accurately prove properties of angles for a quadrilateral inscribed in a circle.","new":false,"priority":false,"level":"HS","strand":"GC"},{"code":"M.HS.SR.GSRT.1","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Verify experimentally how lines are affected by the center of dilation and how the scale factor changes line segments.\na. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.\nb. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.","new":false,"priority":true,"level":"HS","strand":"GSRT"},{"code":"M.HS.SR.GSRT.2","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.","new":false,"priority":true,"level":"HS","strand":"GSRT"},{"code":"M.HS.SR.GGPE.1","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Derive the equation of a circle of given center and radius using the Pythagorean Theorem.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGMD.1","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.","new":false,"priority":false,"level":"HS","strand":"GGMD"},{"code":"M.HS.SR.GGMD.3","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.","new":false,"priority":true,"level":"HS","strand":"GGMD"},{"code":"M.HS.SR.GGMD.4","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.","new":false,"priority":false,"level":"HS","strand":"GGMD"},{"code":"M.HS.SR.GMG.1","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).","new":false,"priority":true,"level":"HS","strand":"GMG"},{"code":"M.HS.SR.GMG.2","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).","new":false,"priority":true,"level":"HS","strand":"GMG"},{"code":"M.HS.SR.GMG.3","grade":"HS","course":"GEO","domain":"Spatial Reasoning","standard":"Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).","new":false,"priority":true,"level":"HS","strand":"GMG"},{"code":"M.HS.DA.DS.1","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Formulate multivariable statistical investigative questions and determine how data can be collected and provide an answer, consider causality and prediction when posing the question.","new":true,"priority":true,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.2","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Understand the issues of bias and confounding variables when collecting data and their impact on interpretation. Understand practices for collecting and handling data, including sensitive information and concerns for privacy and how that may affect data collection.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.3","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Create and analyze data sets using technology to clean, sort, or filter data. Summarize, and describe relationships between quantitative variables using data displays including but not limited to scatter plots, regressions, histograms, and boxplots.","new":true,"priority":true,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.4","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Acknowledge the presence of missing data values and understand how missing values may add bias to analysis and interpretation. Examine and discuss competing explanations for data trends observed such as confounding variables. Respond to competing arguments or interpretations of the data of different community groups, paying careful attention to what conclusions the data supports, taking into account correlation versus causation.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.FIF.1","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Understand that a function has a domain (input, dependent elements) and range (output, independent elements), and assigns to each domain element exactly one range element. If f is a function and x is a value of its domain, then the output of f corresponds to the input x. The graph of f is the graph of the equation y=f(x).","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.DA.FIF.2","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.DA.SID.1","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Represent data with plots on the real number line (dot plots, histograms, and box plots).","new":false,"priority":true,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.2","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.3","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).","new":false,"priority":true,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.5","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.6","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Represent data on two quantitative variables on a scatter plot and describe how the variables are related. Solve problems in context by fitting functions to the data and explaining trends and relationships within the data.\na.\tWhen fitting a function to the data, use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.\nc.\tFit a linear function for a scatter plot that suggests a linear association.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.7","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.","new":false,"priority":true,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.8","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Compute (using technology) and interpret the correlation coefficient of a linear fit.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.9","grade":"HS","course":"ALG 1","domain":"Data Analysis","standard":"Distinguish between correlation and causation.","new":false,"priority":true,"level":"HS","strand":"SID"},{"code":"M.HS.Q.NQ.1","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.","new":false,"priority":true,"level":"HS","strand":"NQ"},{"code":"M.HS.Q.NQ.2","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Define appropriate quantities for the purpose of descriptive modeling.","new":false,"priority":true,"level":"HS","strand":"NQ"},{"code":"M.HS.Q.NQ.3","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.","new":false,"priority":true,"level":"HS","strand":"NQ"},{"code":"M.HS.Q.ASSE.1","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Interpret expressions that represent a quantity in terms of its context within linear, exponential, and quadratic functions.\na.\tInterpret parts of an expression, such as terms, factors, and coefficients.\nb.\tInterpret complicated expressions by viewing one or more of their parts as a single entity.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.ASSE.2","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Use the structure or pattern of an expression to identify ways to rewrite it including the difference of squares, compound interest and others.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.FIF.7","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Graph linear, exponential, and quadratic functions from their symbolic forms by hand or with technology, and identify key features including intercepts, intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries, and end behavior.\na.\tIncluding intercepts, maxima, and minima.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FIF.8","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Efficiently, flexibly, and accurately, write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.\na.\tFactor quadratic functions to verify and explain various properties on graphs, such as zeros and symmetry in terms of a context.\nb.\tUse properties of exponents to interpret expressions for exponential functions.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FIF.9","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Functions could be linear, exponential, or quadratic.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.ACED.3","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context within linear, quadratic, and exponential equations.","new":false,"priority":false,"level":"HS","strand":"ACED"},{"code":"M.HS.Q.ACED.4","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Efficiently, flexibly, and accurately rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations within linear, quadratic, and exponential equations.","new":false,"priority":false,"level":"HS","strand":"ACED"},{"code":"M.HS.Q.FBF.1","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Efficiently, flexibly, and accurately write a function that describes a relationship between two quantities, including linear and exponential relationships, and arithmetic and geometric sequences in context.\na.\tDetermine an explicit expression, a recursive process, or steps for calculation from a context.\nb.\tCombine standard function types using arithmetic operations.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.FIF.3","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FBF.3","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Using a variety of strategies, experiment with cases and illustrate an explanation of the effects on the graph using technology, within linear, exponential, and quadratic functions.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.NRN.1","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Efficiently, flexibly, and accurately explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values using a variety of strategies, allowing for a notation for radicals in terms of rational exponents.","new":false,"priority":false,"level":"HS","strand":"NRN"},{"code":"M.HS.Q.NRN.2","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Rewrite expressions involving radicals and rational exponents using the properties of exponents.","new":false,"priority":false,"level":"HS","strand":"NRN"},{"code":"M.HS.Q.NRN.3","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.","new":false,"priority":false,"level":"HS","strand":"NRN"},{"code":"M.HS.Q.AAPR.1","grade":"HS","course":"ALG 1","domain":"Quantity","standard":"Efficiently, flexibly, and accurately demonstrate that polynomials form a system with a structure similar to that of integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials., limited to quadratic equations.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.R.FIF.4","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"For a function that models a relationship between two quantities in context of the relationship, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; and symmetries. Functions could be linear, exponential, or quadratic.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FIF.5","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes in context. Functions could be linear, exponential, or quadratic relationships.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FIF.6","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Calculate and interpret the average rate of change of a function (represented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.R.ASSE.3","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately rewrite expressions to equivalent forms that are suitable for the purpose of revealing and explaining a specific property about those functions (linear, quadratic, exponential)\na.\tFactor a quadratic expression to reveal the zeros of the function it defines.\nc.\tUse the properties of exponents to transform expressions for exponential functions.","new":false,"priority":true,"level":"HS","strand":"ASSE"},{"code":"M.HS.R.ACED.1","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately create equations and inequalities in one variable that model a situation, and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.","new":false,"priority":true,"level":"HS","strand":"ACED"},{"code":"M.HS.R.ACED.2","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.","new":false,"priority":true,"level":"HS","strand":"ACED"},{"code":"M.HS.R.FLE.1","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Distinguish between situations that can be modeled with linear functions and with exponential functions, including:\na. Linear functions grow with equal differences over equal intervals and with exponential functions grow with equal factors over equal intervals.\nb. Recognizing constant rates per unit interval relative to another.\nc. Recognize contexts of growth or decay by a constant percent rate per unit interval relative to another.","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.R.FLE.2","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately construct linear and exponential functions given a graph, a description of a relationship, or two input-output pairs (including reading these from a table).","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.R.FLE.3","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly and quadratically.","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.R.FLE.5","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Interpret the parameters in a linear or exponential function in terms of a context.","new":false,"priority":true,"level":"HS","strand":"FLE"},{"code":"M.HS.R.AREI.1","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Given that an original equation has a solution, efficiently, flexibly, and accurately select and use strategies to solve the equation, explaining each step, and construct a viable argument to justify a solution method.","new":false,"priority":true,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.3","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.4","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Solve quadratic equations in one variable using a process of identifying solutions as appropriate to the initial form of the equation.\nb. Solve by inspection (e.g., for x\u00b2 = 49), taking square roots, and factoring, as appropriate to the initial equation.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.5","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately demonstrate that systems of two equations in two variables maintain the same solution set when one equation is replaced by the sum of that equation and a multiple of the other equation.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.6","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.7","grade":"HS","course":"ALG 1","domain":"Relationships","standard":"Efficiently, flexibly, and accurately solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.SR.AREI.10","grade":"HS","course":"ALG 1","domain":"Spatial Reasoning","standard":"Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.SR.AREI.11","grade":"HS","course":"ALG 1","domain":"Spatial Reasoning","standard":"Using a variety of strategies explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, exponential, and quadratic.","new":false,"priority":true,"level":"HS","strand":"AREI"},{"code":"M.HS.SR.AREI.12","grade":"HS","course":"ALG 1","domain":"Spatial Reasoning","standard":"Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.DA.DS.1","grade":"HS","course":"ALG 2","domain":"Data Analysis","standard":"Formulate multivariable statistical investigative questions and determine how data can be collected and provide an answer, consider causality and prediction when posing the question.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.2","grade":"HS","course":"ALG 2","domain":"Data Analysis","standard":"Understand the issues of bias and confounding variables when collecting data and their impact on interpretation. Understand practices for collecting and handling data, including sensitive information and concerns for privacy and how that may affect data collection.","new":true,"priority":true,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.3","grade":"HS","course":"ALG 2","domain":"Data Analysis","standard":"Create and analyze data sets using technology to clean, sort, or filter data. Summarize, and describe relationships between quantitative variables using data displays including but not limited to scatter plots, regressions, histograms, and boxplots.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.4","grade":"HS","course":"ALG 2","domain":"Data Analysis","standard":"Acknowledge the presence of missing data values and understand how missing values may add bias to analysis and interpretation. Examine and discuss competing explanations for data trends observed such as confounding variables. Respond to competing arguments or interpretations of the data of different community groups, paying careful attention to what conclusions the data supports, taking into account correlation versus causation.","new":true,"priority":true,"level":"HS","strand":"DS"},{"code":"M.HS.DA.SIC.1","grade":"HS","course":"ALG 2","domain":"Data Analysis","standard":"Understand statistics as a process for making inferences about population parameters based on a random sample from that population.","new":false,"priority":false,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.2","grade":"HS","course":"ALG 2","domain":"Data Analysis","standard":"Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.","new":false,"priority":false,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.3","grade":"HS","course":"ALG 2","domain":"Data Analysis","standard":"Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.","new":false,"priority":true,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.4","grade":"HS","course":"ALG 2","domain":"Data Analysis","standard":"Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.","new":false,"priority":true,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.5","grade":"HS","course":"ALG 2","domain":"Data Analysis","standard":"Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.","new":false,"priority":false,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.6","grade":"HS","course":"ALG 2","domain":"Data Analysis","standard":"Evaluate reports based on data.","new":false,"priority":true,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SID.4","grade":"HS","course":"ALG 2","domain":"Data Analysis","standard":"Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.6","grade":"HS","course":"ALG 2","domain":"Data Analysis","standard":"Represent data on two quantitative variables on a scatter plot and describe how the variables are related. Solve problems in context by fitting functions to the data and explaining trends and relationships within the data.\na.\tWhen fitting a function to the data, use given functions or choose a function suggested by the context. Models may include any family of functions.\nb.\tInformally assess the fit of a function by plotting and analyzing residuals. \nc.\tFit a linear function for a scatter plot that suggests a linear association.","new":false,"priority":true,"level":"HS","strand":"SID"},{"code":"M.HS.Q.ASSE.1","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Interpret expressions that represent a quantity in terms of its context in any family of functions.\na.\tInterpret parts of an expression, such as terms, factors, and coefficients.\nb.\tInterpret complicated expressions by viewing one or more of their parts as a single entity.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.ASSE.2","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Use the structure of an expression to identify ways to rewrite it.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.FBF.1","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately write a function that describes a relationship between two quantities, including linear and exponential relationships, and arithmetic and geometric sequences in context.\na.\tDetermine an explicit expression, a recursive process, or steps for calculation from a context.\nb.\tCombine standard function types using arithmetic operations.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.FBF.2","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model linear and exponential situations, and translate between the two forms.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.ASSE.4","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Derive the formula for the sum of a finite geometric series (when the common ratio is not 1) and use the formula to solve problems.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.FIF.7","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Graph linear, exponential, and quadratic functions from their symbolic forms by hand or with technology, and identify key features including intercepts, intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries, and end behavior.\na. Including intercepts, maxima, and minima.\nb. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.\nc. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.\ne. Graph logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FIF.8","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately, write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.\na.\tFactor quadratic functions and completing the square to show zeros, extreme values and symmetry in terms of a context.\nb.\tUse properties of exponents to interpret expressions for exponential functions, including non-integer constants for time when applicable in contexts of exponential growth or decay.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FIF.9","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Functions can include polynomial, radical, rational, logarithms, absolute value, piecewise, trigonometric, and increasingly complex linear, exponential, and quadratic relationships.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FBF.3","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Using a variety of strategies, experiment with cases and illustrate an explanation of the effects on the graph using technology.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.ACED.3","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. May include any families of functions.","new":false,"priority":true,"level":"HS","strand":"ACED"},{"code":"M.HS.Q.ACED.4","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately rearrange formulas with multiple quantities of interests to highlight and contextualize a specific quantity, using the same reasoning as in solving equations. May include any families of functions.","new":false,"priority":true,"level":"HS","strand":"ACED"},{"code":"M.HS.Q.NCN.1","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Know there is a complex number i such that i\u00b2 = -1, and every complex number has the form a + bi with a and b real.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NCN.2","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Use the relation i\u00b2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NCN.7","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Solve quadratic equations with real coefficients that have complex solutions.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.AAPR.1","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately demonstrate that polynomials form a system with a structure similar to that of integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.2","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.3","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.4","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Prove polynomial identities and use them to describe numerical relationships.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.6","grade":"HS","course":"ALG 2","domain":"Quantity","standard":"Efficiently, flexibly, and accurately rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.R.ACED.1","grade":"HS","course":"ALG 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately create equations and inequalities in one variable that model a situation, and use them to solve problems.","new":false,"priority":false,"level":"HS","strand":"ACED"},{"code":"M.HS.R.ACED.2","grade":"HS","course":"ALG 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.","new":false,"priority":false,"level":"HS","strand":"ACED"},{"code":"M.HS.R.ASSE.3","grade":"HS","course":"ALG 2","domain":"Relationships","standard":"Efficiently, flexibly, and accurately rewrite expressions to equivalent forms that are suitable for the purpose of revealing and explaining a specific property about those functions\na.\tFactor a quadratic expression to reveal the zeros of the function it defines.\nb.\tComplete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.\nc.\tUse the properties of exponents to transform expressions for exponential functions.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.R.AREI.4","grade":"HS","course":"ALG 2","domain":"Relationships","standard":"Solve quadratic equations in one variable using a process of identifying solutions as appropriate to the initial form of the equation.\na. Use the method of completing the square to transform any quadratic equation in x into an equation of the  form (x - p)\u00b2 = q that has the same solutions. Derive the quadratic formula from this form.\nb. Solve quadratic equations by inspection (e.g., for x\u00b2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate. Recognize when the quadratic formula gives complex solutions and write them as a \u00b1 bi for real numbers a and b.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.2","grade":"HS","course":"ALG 2","domain":"Relationships","standard":"Solve rational and radical equations in one variable and give examples showing how extraneous solutions may arise.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.FIF.4","grade":"HS","course":"ALG 2","domain":"Relationships","standard":"For any function that models a relationship between two quantities in context of the relationship, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Functions can include polynomial, radical, rational, logarithms, absolute value, piecewise, trigonometric, and increasingly complex linear, exponential, and quadratic relationships.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FIF.5","grade":"HS","course":"ALG 2","domain":"Relationships","standard":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes in context. Functions can include polynomial, radical, rational, logarithms, absolute value, piecewise, trigonometric, and increasingly complex linear, exponential, and quadratic relationships.","new":false,"priority":true,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FIF.6","grade":"HS","course":"ALG 2","domain":"Relationships","standard":"Calculate and interpret the average rate of change of a non-linear function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FBF.4","grade":"HS","course":"ALG 2","domain":"Relationships","standard":"Find inverse functions through focus on relationships between inputs and outputs.\na. Solve an equation of the form f(x) = c that has an inverse and write an equation for the inverse.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.R.FLE.4","grade":"HS","course":"ALG 2","domain":"Relationships","standard":"For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.SR.AREI.11","grade":"HS","course":"ALG 2","domain":"Spatial Reasoning","standard":"Using a variety of strategies explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.","new":false,"priority":true,"level":"HS","strand":"AREI"},{"code":"M.HS.SR.FTF.1","grade":"HS","course":"ALG 2","domain":"Spatial Reasoning","standard":"Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.2","grade":"HS","course":"ALG 2","domain":"Spatial Reasoning","standard":"Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.5","grade":"HS","course":"ALG 2","domain":"Spatial Reasoning","standard":"Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.","new":false,"priority":true,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.8","grade":"HS","course":"ALG 2","domain":"Spatial Reasoning","standard":"Prove the Pythagorean identity sin2(\u03b8) + cos2(\u03b8) = 1 and use it to find sin(\u03b8), cos(\u03b8), or tan(\u03b8), given sin(\u03b8), cos(\u03b8), or tan(\u03b8) and the quadrant of the angle.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.GGPE.1","grade":"HS","course":"ALG 2","domain":"Spatial Reasoning","standard":"Derive the equation of a circle of given center and radius using the Pythagorean Theorem.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.2","grade":"HS","course":"ALG 2","domain":"Spatial Reasoning","standard":"Derive the equation of a parabola given a focus and directrix.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.DA.DS.1","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Formulate multivariable statistical investigative questions and determine how data can be collected and provide an answer, consider causality and prediction when posing the question.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.2","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Understand the issues of bias and confounding variables when collecting data and their impact on interpretation. Understand practices for collecting and handling data, including sensitive information and concerns for privacy and how that may affect data collection.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.3","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Create and analyze data sets using technology to clean, sort, or filter data. Summarize, and describe relationships between quantitative variables using data displays including but not limited to scatter plots, regressions, histograms, and boxplots.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.DS.4","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Acknowledge the presence of missing data values and understand how missing values may add bias to analysis and interpretation. Examine and discuss competing explanations for data trends observed such as confounding variables. Respond to competing arguments or interpretations of the data of different community groups, paying careful attention to what conclusions the data supports, taking into account correlation versus causation.","new":true,"priority":false,"level":"HS","strand":"DS"},{"code":"M.HS.DA.FIF.1","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Understand that a function has a domain (input, dependent elements) and range (output, independent elements), and assigns to each domain element exactly one range element. If f is a function and x is a value of its domain, then the output of f corresponds to the input x. The graph of f is the graph of the equation y=f(x).","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.DA.FIF.2","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.DA.SID.1","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Represent data with plots on the real number line (dot plots, histograms, and box plots).","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.2","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.3","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.4","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.5","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.6","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Represent data on two quantitative variables on a scatter plot and describe how the variables are related. Solve problems in context by fitting functions to the data and explaining trends and relationships within the data.\na.\tWhen fitting a function to the data, use given functions or choose a function suggested by the context. Models may include any family of functions.\nb.\tInformally assess the fit of a function by plotting and analyzing residuals. \nc.\tFit a linear function for a scatter plot that suggests a linear association.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.7","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.8","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Compute (using technology) and interpret the correlation coefficient of a linear fit.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SID.9","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Distinguish between correlation and causation.","new":false,"priority":false,"level":"HS","strand":"SID"},{"code":"M.HS.DA.SIC.1","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Understand statistics as a process for making inferences about population parameters based on a random sample from that population.","new":false,"priority":false,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.2","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.","new":false,"priority":false,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.3","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.","new":false,"priority":false,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.4","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.","new":false,"priority":false,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.5","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.","new":false,"priority":false,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SIC.6","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Evaluate reports based on data.","new":false,"priority":false,"level":"HS","strand":"SIC"},{"code":"M.HS.DA.SCP.1","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (\"or,\" \"and,\" \"not\").","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.2","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Understand that two events, A and B, are independent if the probability of  and  occurring together is the product of their probabilities and use this characterization to determine if they are independent.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.3","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Understand the conditional probability of A given B as (P(A and B),)/(P(B)) and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.4","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.5","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.6","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A and interpret the answer in terms of the model.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.7","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.8","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SCP.9","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Use permutations and combinations to compute probabilities of compound events and solve problems.","new":false,"priority":false,"level":"HS","strand":"SCP"},{"code":"M.HS.DA.SMD.1","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.","new":false,"priority":false,"level":"HS","strand":"SMD"},{"code":"M.HS.DA.SMD.2","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.","new":false,"priority":false,"level":"HS","strand":"SMD"},{"code":"M.HS.DA.SMD.3","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.","new":false,"priority":false,"level":"HS","strand":"SMD"},{"code":"M.HS.DA.SMD.4","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.","new":false,"priority":false,"level":"HS","strand":"SMD"},{"code":"M.HS.DA.SMD.5","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.\na. Find the expected payoff for a game of chance. \nb. Evaluate and compare strategies on the basis of expected values.","new":false,"priority":false,"level":"HS","strand":"SMD"},{"code":"M.HS.DA.SMD.6","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).","new":false,"priority":false,"level":"HS","strand":"SMD"},{"code":"M.HS.DA.SMD.7","grade":"HS","course":"HS-3rd Cr+","domain":"Data Analysis","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).","new":false,"priority":false,"level":"HS","strand":"SMD"},{"code":"M.HS.Q.NQ.1","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.","new":false,"priority":false,"level":"HS","strand":"NQ"},{"code":"M.HS.Q.NQ.2","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Define appropriate quantities for the purpose of descriptive modeling.","new":false,"priority":false,"level":"HS","strand":"NQ"},{"code":"M.HS.Q.NQ.3","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.","new":false,"priority":false,"level":"HS","strand":"NQ"},{"code":"M.HS.Q.ASSE.1","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Interpret expressions that represent a quantity in terms of its context in any family of functions.\na.\tInterpret parts of an expression, such as terms, factors, and coefficients.\nb.\tInterpret complicated expressions by viewing one or more of their parts as a single entity.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.ASSE.2","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Use the structure of an expression to identify ways to rewrite it.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.FIF.7","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Graph families of functions from their symbolic forms by hand or with technology, and identify key features including intercepts, intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries, and end behavior.\na.\tIncluding intercepts, maxima, and minima.\nb.\tGraph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.\nc.\tGraph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.\nd.\tGraph logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.\nPlus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\ne.\t(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FIF.8","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Efficiently, flexibly, and accurately, write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.\na.\tFactor quadratic functions and completing the square to show zeros, extreme values and symmetry in terms of a context.\nb.\tUse properties of exponents to interpret expressions for exponential functions, including non-integer constants for time when applicable in contexts of exponential growth or decay.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.FIF.9","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Functions can include polynomial, radical, rational, logarithms, absolute value, piecewise, trigonometric, and increasingly complex linear, exponential, and quadratic relationships.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.ACED.3","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. May include any families of functions.","new":false,"priority":false,"level":"HS","strand":"ACED"},{"code":"M.HS.Q.ACED.4","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Efficiently, flexibly, and accurately rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. May include any families of functions.","new":false,"priority":false,"level":"HS","strand":"ACED"},{"code":"M.HS.Q.FBF.1","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Efficiently, flexibly, and accurately write a function that describes a relationship between two quantities, including linear and exponential relationships, and arithmetic and geometric sequences in context.\na. Determine an explicit expression, a recursive process, or steps for calculation from a context.\nb.  Combine standard function types using arithmetic operations.\nPlus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\nc. (+) Compose functions.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.FBF.2","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model linear and exponential situations, and translate between the two forms.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.FIF.3","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.Q.ASSE.4","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Derive the formula for the sum of a finite geometric series (when the common ratio is not 1) and use the formula to solve problems.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.Q.FBF.3","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Using a variety of strategies, experiment with cases and illustrate an explanation of the effects on the graph using technology.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.Q.NRN.1","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Efficiently, flexibly, and accurately explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values using a variety of strategies, allowing for a notation for radicals in terms of rational exponents.","new":false,"priority":false,"level":"HS","strand":"NRN"},{"code":"M.HS.Q.NRN.2","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Rewrite expressions involving radicals and rational exponents using the properties of exponents.","new":false,"priority":false,"level":"HS","strand":"NRN"},{"code":"M.HS.Q.NRN.3","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.","new":false,"priority":false,"level":"HS","strand":"NRN"},{"code":"M.HS.Q.NCN.1","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Know there is a complex number i such that i\u00b2 = -1, and every complex number has the form a + bi with a and b real.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NCN.2","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Use the relation i\u00b2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NCN.3","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NCN.4","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NCN.5","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NCN.6","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NCN.7","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Solve quadratic equations with real coefficients that have complex solutions.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NCN.8","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Extend polynomial identities to the complex numbers. For example, rewrite x\u00b2 + 4 as (x + 2i)(x - 2i).","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NCN.9","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.","new":false,"priority":false,"level":"HS","strand":"NCN"},{"code":"M.HS.Q.NVM.1","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).","new":false,"priority":false,"level":"HS","strand":"NVM"},{"code":"M.HS.Q.NVM.2","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.","new":false,"priority":false,"level":"HS","strand":"NVM"},{"code":"M.HS.Q.NVM.3","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Solve problems involving velocity and other quantities that can be represented by vectors.","new":false,"priority":false,"level":"HS","strand":"NVM"},{"code":"M.HS.Q.NVM.4","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Add and subtract vectors.\na. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.\nb. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.\nc. Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.","new":false,"priority":false,"level":"HS","strand":"NVM"},{"code":"M.HS.Q.NVM.5","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Multiply a vector by a scalar.\na. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).\nb. (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.","new":false,"priority":false,"level":"HS","strand":"NVM"},{"code":"M.HS.Q.NVM.6","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.","new":false,"priority":false,"level":"HS","strand":"NVM"},{"code":"M.HS.Q.NVM.7","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.","new":false,"priority":false,"level":"HS","strand":"NVM"},{"code":"M.HS.Q.NVM.8","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Add, subtract, and multiply matrices of appropriate dimensions.","new":false,"priority":false,"level":"HS","strand":"NVM"},{"code":"M.HS.Q.NVM.9","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.","new":false,"priority":false,"level":"HS","strand":"NVM"},{"code":"M.HS.Q.NVM.10","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.","new":false,"priority":false,"level":"HS","strand":"NVM"},{"code":"M.HS.Q.NVM.11","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.","new":false,"priority":false,"level":"HS","strand":"NVM"},{"code":"M.HS.Q.NVM.12","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Work with 2 x 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.","new":false,"priority":false,"level":"HS","strand":"NVM"},{"code":"M.HS.Q.AREI.8","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Represent a system of linear equations as a single matrix equation in a vector variable.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.Q.AREI.9","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 x  3 or greater).","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.Q.AAPR.1","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Efficiently, flexibly, and accurately demonstrate that polynomials form a system with a structure similar to that of integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.2","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.3","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.4","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Prove polynomial identities and use them to describe numerical relationships.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.5","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.6","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Efficiently, flexibly, and accurately rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.AAPR.7","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.","new":false,"priority":false,"level":"HS","strand":"AAPR"},{"code":"M.HS.Q.GSRT.3","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.Q.GSRT.6","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.Q.GSRT.7","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Explain and use the relationship between the sine and cosine of complementary angles.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.Q.GSRT.8","grade":"HS","course":"HS-3rd Cr+","domain":"Quantity","standard":"Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.R.FIF.4","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"For any function that models a relationship between two quantities in context of the relationship, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; and symmetries. May include any families of functions, and relative maximums and minimums, end behavior, and periodicity.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FIF.5","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes in context. Functions can include polynomial, radical, rational, logarithms, absolute value, piecewise, trigonometric, and increasingly complex linear, exponential, and quadratic relationships.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.R.FIF.6","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Calculate and interpret the average rate of change of a non-linear function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.","new":false,"priority":false,"level":"HS","strand":"FIF"},{"code":"M.HS.R.ACED.1","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately create equations and inequalities in one variable that model a situation, and use them to solve problems.","new":false,"priority":false,"level":"HS","strand":"ACED"},{"code":"M.HS.R.ACED.2","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.","new":false,"priority":false,"level":"HS","strand":"ACED"},{"code":"M.HS.R.ASSE.3","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately rewrite expressions to equivalent forms that are suitable for the purpose of revealing and explaining a specific property about those functions.\na.\tFactor a quadratic expression to reveal the zeros of the function it defines.\nb.\tComplete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.\nc.\tUse the properties of exponents to transform expressions for exponential functions.","new":false,"priority":false,"level":"HS","strand":"ASSE"},{"code":"M.HS.R.AREI.4","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Solve quadratic equations in one variable using a process of identifying solutions as appropriate to the initial form of the equation.\na. Use the method of completing the square to transform any quadratic equation in x into an equation of the  form (x - p)\u00b2 = q that has the same solutions. Derive the quadratic formula from this form.\nb. Solve quadratic equations by inspection (e.g., for x\u00b2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate. Recognize when the quadratic formula gives complex solutions and write them as a \u00b1 bi for real numbers a and b.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.FLE.1","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Distinguish between situations that can be modeled with linear functions and with exponential functions, including:\na. Linear functions grow with equal differences over equal intervals and with exponential functions grow with equal factors over equal intervals.\nb. Recognizing constant rates per unit interval relative to another.\nc. Recognize contexts of growth or decay by a constant percent rate per unit interval relative to another.","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.R.FLE.2","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately construct linear and exponential functions given a graph, a description of a relationship, or two input-output pairs (including reading these from a table).","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.R.FLE.3","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly and quadratically, or as a polynomial function.","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.R.FLE.5","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Interpret the parameters in a linear or exponential function in terms of a context.","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.R.AREI.1","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Given that an original equation has a solution, efficiently, flexibly, and accurately select and use strategies to solve the equation, explaining each step, and construct a viable argument to justify a solution method.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.3","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.5","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately demonstrate that systems of two equations in two variables maintain the same solution set when one equation is replaced by the sum of that equation and a multiple of the other equation.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.6","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.7","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.AREI.2","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Solve rational and radical equations in one variable and give examples showing how extraneous solutions may arise.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.R.FBF.4","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Find inverse functions through focus on relationships between inputs and outputs.\na. Solve an equation of the form f(x) = c that has an inverse and write an equation for the inverse.\nPlus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\nb. (+) Verify by composition that one function is the inverse of another.\nc. (+) Read values of an inverse function from a graph or a table, given that the function has an inverse.\nd. (+) Produce an invertible function from a non-invertible function by restricting the domain.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.R.FBF.5","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.","new":false,"priority":false,"level":"HS","strand":"FBF"},{"code":"M.HS.R.FLE.4","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.","new":false,"priority":false,"level":"HS","strand":"FLE"},{"code":"M.HS.R.GCO.9","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove theorems about lines and angles: vertical angles, transversals, alternate interior and exterior angles, perpendicular bisectors, etc","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.R.GCO.10","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove theorems about triangles: interior angles, base angles, segments joining midpoint of two sides, and medians of a triangle.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.R.GCO.11","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove theorems about parallelograms: congruence of opposite sides and opposite angles, properties of diagonals.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.R.GSRT.4","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove theorems about triangles including proportionality, triangle similarity, and the Pythagorean Theorem.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.R.GSRT.5","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.R.GSRT.9","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.R.GSRT.10","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Prove the Laws of Sines and Cosines and use them to solve problems.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.R.GSRT.11","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.R.GC.1","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Efficiently, flexibly, and accurately prove that all circles are similar.","new":false,"priority":false,"level":"HS","strand":"GC"},{"code":"M.HS.R.GC.2","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Identify and describe relationships among inscribed angles, radii, and chords, including how angles formed inside the circle, the circle's radius, and line segments within the circle are related. Understand special cases including angles formed by diameters and how the circle's edge interacts with its radius.","new":false,"priority":false,"level":"HS","strand":"GC"},{"code":"M.HS.R.GC.5","grade":"HS","course":"HS-3rd Cr+","domain":"Relationships","standard":"Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.","new":false,"priority":false,"level":"HS","strand":"GC"},{"code":"M.HS.SR.FTF.1","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.2","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.3","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for \u03c0/3, \u03c0/4 and \u03c0/6,  and use the unit circle to express the values of sine, cosine, and tangent for \u03c0-x, \u03c0+x, and 2\u03c0-x in terms of their values for x, where x is any real number.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.4","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.5","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.6","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.7","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.8","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Prove the Pythagorean identity sin2(\u03b8) + cos2(\u03b8) = 1 and use it to find sin(\u03b8), cos(\u03b8), or tan(\u03b8), given sin(\u03b8), cos(\u03b8), or tan(\u03b8) and the quadrant of the angle.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.FTF.9","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.","new":false,"priority":false,"level":"HS","strand":"FTF"},{"code":"M.HS.SR.GGPE.1","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Derive the equation of a circle of given center and radius using the Pythagorean Theorem.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.2","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Derive the equation of a parabola given a focus and directrix.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.3","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.4","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Use coordinates to prove simple geometric theorems algebraically.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.5","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.6","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Find the point on a directed line segment between two given points that partitions the segment in a given ratio.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GGPE.7","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.","new":false,"priority":false,"level":"HS","strand":"GGPE"},{"code":"M.HS.SR.GCO.1","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.2","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Efficiently, flexibly, and accurately represent transformations in the plane, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.3","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.4","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.5","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Efficiently, flexibly, and accurately specify a sequence of transformations that will carry a given figure onto another.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.6","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.7","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.8","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.12","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Make formal geometric constructions with a variety of tools and methods.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GCO.13","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.","new":false,"priority":false,"level":"HS","strand":"GCO"},{"code":"M.HS.SR.GC.3","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Construct the inscribed and circumscribed circles of a triangle and efficiently, flexibly, and accurately prove properties of angles for a quadrilateral inscribed in a circle.","new":false,"priority":false,"level":"HS","strand":"GC"},{"code":"M.HS.SR.GC.4","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Construct a tangent line from a point outside a given circle to the circle.","new":false,"priority":false,"level":"HS","strand":"GC"},{"code":"M.HS.SR.GSRT.1","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Verify experimentally how lines are affected by the center of dilation and how the scale factor changes line segments.\na. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.\nb. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.SR.GSRT.2","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.","new":false,"priority":false,"level":"HS","strand":"GSRT"},{"code":"M.HS.SR.GGMD.1","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.","new":false,"priority":false,"level":"HS","strand":"GGMD"},{"code":"M.HS.SR.GGMD.2","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Plus standards are addressed in credits 3 and 4 mathematics in courses aligned with a student's High School and Beyond Plan\n(+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.","new":false,"priority":false,"level":"HS","strand":"GGMD"},{"code":"M.HS.SR.GGMD.3","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.","new":false,"priority":false,"level":"HS","strand":"GGMD"},{"code":"M.HS.SR.GGMD.4","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.","new":false,"priority":false,"level":"HS","strand":"GGMD"},{"code":"M.HS.SR.AREI.10","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.SR.AREI.11","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Using a variety of strategies explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.SR.AREI.12","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.","new":false,"priority":false,"level":"HS","strand":"AREI"},{"code":"M.HS.SR.GMG.1","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).","new":false,"priority":false,"level":"HS","strand":"GMG"},{"code":"M.HS.SR.GMG.2","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).","new":false,"priority":false,"level":"HS","strand":"GMG"},{"code":"M.HS.SR.GMG.3","grade":"HS","course":"HS-3rd Cr+","domain":"Spatial Reasoning","standard":"Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).","new":false,"priority":false,"level":"HS","strand":"GMG"}];
var STRAND_LABELS = {
  DS:'Data Science Cycle', MD:'Measurement & Data', SP:'Statistics & Probability',
  CC:'Counting & Cardinality', NBT:'Number & Operations in Base Ten',
  NF:'Number & Operations—Fractions', NS:'The Number System',
  NQ:'Quantities', NRN:'Real Number System', NCN:'Complex Number System', NVM:'Vector & Matrix',
  OA:'Operations & Algebraic Thinking', EE:'Expressions & Equations',
  RP:'Ratios & Proportional Relationships', F:'Functions',
  ASSE:'Algebra—Seeing Structure', AAPR:'Algebra—Polynomial Arithmetic',
  ACED:'Algebra—Creating Equations', AREI:'Algebra—Reasoning with Equations',
  FBF:'Functions—Building', FIF:'Functions—Interpreting',
  FLE:'Functions—Linear & Exponential', FTF:'Functions—Trigonometric',
  G:'Geometry', GCO:'Geometry—Congruence', GGPE:'Geometry—Expressing Properties',
  GGMD:'Geometry—Measurement & Dimensions', GMG:'Geometry—Modeling',
  GC:'Geometry—Circles', GSRT:'Geometry—Similarity & Right Triangles',
  SID:'Statistics—Interpreting Data', SIC:'Statistics—Making Inferences',
  SCP:'Conditional Probability', SMD:'Statistical Models & Decisions'
};
var DOMAIN_COLORS = {'Data Analysis':'#006E82','Quantity':'#5B4A91','Relationships':'#1B5E8A','Spatial Reasoning':'#2E7D5A'};
var TRAD = ['ALG 1','GEO','ALG 2'];
var INTG = ['INT 1','INT 2','INT 3'];
var K8_GRADES = ['K','1','2','3','4','5','6','7','8'];
var GRADE_LABELS = {K:'Kindergarten','1':'Grade 1','2':'Grade 2','3':'Grade 3','4':'Grade 4','5':'Grade 5','6':'Grade 6','7':'Grade 7','8':'Grade 8'};
var HS_LABELS = {'ALG 1':'Algebra 1','ALG 2':'Algebra 2','GEO':'Geometry','INT 1':'Integrated 1','INT 2':'Integrated 2','INT 3':'Integrated 3','HS-3rd Cr+':'3rd Credit & Beyond'};

var state = {pathway:'traditional', domain:'all', showNew:false, showPriority:false, search:''};
var activeCard = null;

function setFontSize(sz) {
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}

function setDomain(btn, d) {
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}

function toggleNew() {
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}

function togglePriority() {
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}

function onSearch() {
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}

function clearAll() {
  state.domain = 'all'; state.showNew = false; state.showPriority = false; state.search = '';
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}

function matchesFilters(s) {
  if (state.domain !== 'all' && s.domain !== state.domain) return false;
  if (state.showNew && !s['new']) return false;
  if (state.showPriority && !s.priority) return false;
  if (state.search) {
    var q = state.search;
    if (s.standard.toLowerCase().indexOf(q) === -1 &&
        s.code.toLowerCase().indexOf(q) === -1 &&
        s.domain.toLowerCase().indexOf(q) === -1 &&
        s.strand.toLowerCase().indexOf(q) === -1) return false;
  }
  return true;
}

function makeCard(s, course) {
  var card = document.createElement('div');
  card.className = 'card';
  card.setAttribute('data-domain', s.domain);

  var top = document.createElement('div');
  top.className = 'card-top';

  var code = document.createElement('div');
  code.className = 'card-code';
  code.textContent = s.code;

  var badges = document.createElement('div');
  badges.className = 'card-badges';
  if (s['new']) {
    var bn = document.createElement('span');
    bn.className = 'badge badge-new';
    bn.textContent = 'NEW';
    badges.appendChild(bn);
  }
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    var bp = document.createElement('span');
    bp.className = 'badge badge-pri';
    bp.textContent = 'PRIORITY';
    badges.appendChild(bp);
  }

  top.appendChild(code);
  top.appendChild(badges);

  var txt = document.createElement('div');
  txt.className = 'card-text';
  var snip = document.createElement('div');
  snip.className = 'card-text-snippet';
  snip.textContent = s.standard;
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  card.appendChild(top);
  card.appendChild(txt);

  card.onclick = (function(std, c) {
    return function() { openModal(std, c); };
  })(s, course);

  return card;
}

function openModal(s, course) {
  var color = DOMAIN_COLORS[s.domain] || '#006E82';
  document.getElementById('modal-bar').style.background = color;
  document.getElementById('modal-code').textContent = s.code;
  var strandName = STRAND_LABELS[s.strand] || s.strand;
  document.getElementById('modal-strand').textContent = s.domain + '  •  ' + strandName;
  document.getElementById('modal-text').textContent = s.standard;

  var mb = document.getElementById('modal-badges');
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  if (s['new']) {
    var bn = document.createElement('span');
    bn.className = 'badge badge-new';
    bn.style.fontSize = '9px'; bn.style.padding = '2px 7px';
    bn.textContent = 'New in 2025';
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    var bp = document.createElement('span');
    bp.className = 'badge badge-pri';
    bp.style.fontSize = '9px'; bp.style.padding = '2px 7px';
    bp.textContent = 'Priority Standard';
    mb.appendChild(bp);
  }

  var cl = (HS_LABELS[course] || GRADE_LABELS[course] || course);
  document.getElementById('modal-meta').textContent = cl + '  •  ' + s.domain;

  document.getElementById('modal-overlay').className = 'modal-overlay open';
}

function closeModal() {
  document.getElementById('modal-overlay').className = 'modal-overlay';
}

function render() {
  var main = document.getElementById('main');
  main.innerHTML = '';

  var hsCourses = state.pathway === 'traditional' ? TRAD : INTG;
  var totalVisible = 0;

  // K-8 section
  var k8section = document.createElement('div');
  var k8hdr = document.createElement('div');
  k8hdr.className = 'section-header';
  k8hdr.textContent = 'Elementary & Middle School  —  Kindergarten through Grade 8';
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  var k8swim = document.createElement('div');
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  var k8count = 0;
  for (var gi = 0; gi < K8_GRADES.length; gi++) {
    var grade = K8_GRADES[gi];
    var gradeStds = STANDARDS.filter(function(s) { return s.level === 'K-8' && s.grade === grade; });
    var visible = gradeStds.filter(matchesFilters);
    k8count += visible.length;
    totalVisible += visible.length;

    var labelCell = document.createElement('div');
    labelCell.className = 'grade-label-cell';
    var gradeNum = document.createElement('div');
    gradeNum.className = 'grade-num';
    gradeNum.textContent = grade === 'K' ? 'K' : grade;
    var gradeTag = document.createElement('div');
    gradeTag.className = 'grade-tag';
    gradeTag.textContent = grade === 'K' ? 'Kindergarten' : 'Grade ' + grade;
    labelCell.appendChild(gradeNum);
    labelCell.appendChild(gradeTag);

    var cardsCell = document.createElement('div');
    cardsCell.className = 'cards-cell';

    if (visible.length === 0) {
      var nr = document.createElement('div');
      nr.className = 'no-results';
      nr.textContent = 'No standards match current filters.';
      cardsCell.appendChild(nr);
    } else {
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        cardsCell.appendChild(makeCard(visible[si], grade));
      }
    }

    k8swim.appendChild(labelCell);
    k8swim.appendChild(cardsCell);
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  k8section.appendChild(k8swim);
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  // HS section
  var hsLabel = state.pathway === 'traditional' ? 'High School — Traditional Pathway  (Algebra 1, Geometry, Algebra 2)' : 'High School — Integrated Pathway  (Integrated 1, 2, 3)';
  var hssection = document.createElement('div');
  var hshdr = document.createElement('div');
  hshdr.className = 'section-header';
  hshdr.textContent = hsLabel;
  hssection.appendChild(hshdr);

  var hsswim = document.createElement('div');
  hsswim.className = 'swimlane';

  var hsLabelCell = document.createElement('div');
  hsLabelCell.className = 'grade-label-cell';
  var hsNum = document.createElement('div');
  hsNum.className = 'grade-num';
  hsNum.textContent = 'HS';
  var hsTag = document.createElement('div');
  hsTag.className = 'grade-tag';
  hsTag.textContent = 'High School';
  hsLabelCell.appendChild(hsNum);
  hsLabelCell.appendChild(hsTag);
  hsLabelCell.style.gridRow = 'span ' + hsCourses.length;

  hsswim.appendChild(hsLabelCell);

  var hsCount = 0;
  for (var ci = 0; ci < hsCourses.length; ci++) {
    var course = hsCourses[ci];
    var courseStds = STANDARDS.filter(function(c) { return function(s) { return s.level === 'HS' && s.course === c; }; }(course));
    var visibleHS = courseStds.filter(matchesFilters);
    hsCount += visibleHS.length;
    totalVisible += visibleHS.length;

    var courseContainer = document.createElement('div');
    courseContainer.style.gridColumn = '2';
    courseContainer.style.borderTop = ci > 0 ? '1px dashed #d8d2ca' : 'none';
    courseContainer.style.paddingTop = ci > 0 ? '8px' : '0';
    courseContainer.style.marginBottom = '4px';

    var courseLbl = document.createElement('div');
    courseLbl.style.fontFamily = "'DM Mono', monospace";
    courseLbl.style.fontSize = '9.5px';
    courseLbl.style.fontWeight = '500';
    courseLbl.style.color = '#8a837a';
    courseLbl.style.textTransform = 'uppercase';
    courseLbl.style.letterSpacing = '0.08em';
    courseLbl.style.paddingLeft = '20px';
    courseLbl.style.paddingBottom = '6px';
    courseLbl.textContent = HS_LABELS[course] || course;

    var courseCards = document.createElement('div');
    courseCards.className = 'cards-cell';
    courseCards.style.paddingTop = '0';

    if (visibleHS.length === 0) {
      var nr2 = document.createElement('div');
      nr2.className = 'no-results';
      nr2.textContent = 'No standards match current filters.';
      courseCards.appendChild(nr2);
    } else {
      for (var si2 = 0; si2 < visibleHS.length; si2++) {
        courseCards.appendChild(makeCard(visibleHS[si2], course));
      }
    }

    courseContainer.appendChild(courseLbl);
    courseContainer.appendChild(courseCards);
    hsswim.appendChild(courseContainer);
  }

  hssection.appendChild(hsswim);
  if (hsCount > 0 || state.domain === 'all') main.appendChild(hssection);

  document.getElementById('results-bar').innerHTML = 'Showing <strong>' + totalVisible + '</strong> standards' +
    (state.domain !== 'all' || state.showNew || state.showPriority || state.search ?
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}

document.getElementById('modal-overlay').addEventListener('click', function(e) {
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});
document.addEventListener('keydown', function(e) { if (e.key === 'Escape') closeModal(); });

render();

</script>
</body>
</html>