# BPS District Mathematics Standards Book

 Site: Learnbps Course: BPSS (MAT) Mathematics Standards Book: BPS District Mathematics Standards Book
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# Mathematics Standards

The BPSS (MAT) Mathematics Standards course in Learnbps is Bismarck Public School District's current progress on prioritizing and deconstructing standards to provide a consistent, clear understanding of what students are expected to learn. The standards are designed to provide guidance so teachers and parents know what they need to do to help students. Plus help students reflect on the knowledge and skills that they need for success.

# MAT-02.NBT.01

The Bismarck Public School District Standards-Based Progress Report displays grades at the Strand level. Therefore Bismarck Public School District has modified the North Dakota DPI Identifiers to fit into our student information system PowerSchool for Standards-Based grading. Above is a BPS-Standards MAT identifier with smaller muted text showing the addition  to the identifier that are the components that BPS adds to the State code.

## MAT-02.NBT.01

click on the identifier components for more explanations

MAT-02.NBT.01 Demonstrate understanding that the three digits of a three-digit number represent amounts of hundreds, tens, and ones, including:
Note how the identifiers auto-link to the standards global glossaries.

## 2.NBT.1

click on the identifier components for more explanations

State individual grade-specific standards can be identified by their grade, domain, and standard, so that 2.NBT.1 for example, stands for MAT Number and Operations Base Ten and standard 1.

### Kindergarten

Kindergarten Math
"I can ... statements"

Young children arrive in kindergarten with widely varying knowledge in math. By the end of the year, your child must have some important foundations in place. One of the most important skills your child should develop is the ability to add and subtract small numbers and use addition and subtraction to solve word problems. This will rely on gaining some fundamentals early in the year, such as counting objects to tell how many there are. Addition and subtraction will continue to be a very strong focus in math through 2nd grade.

### MAT-00.CC Domain:

• MAT-00.CC.01 Count to 100 by ones and by tens. Count backward from 20 by ones
• MAT-00.CC.02 Count forward beginning from a given number within 100. Count backward from a given number within 10
• MAT-00.CC.03 - Write numbers sequentially from 0 to 20. Write a given number from 0 to 20
• MAT-00.CC.04 Understand the relationship between numbers and quantities up to 20; connect counting to cardinality.
• MAT-00.CC.04.a Use one to one correspondence when counting objects.
• MAT-00.CC.04.b Understand that the last number name said tells the number of objects counted, regardless of their arrangement or order in which they were counted.
• MAT-00.CC.04.c Understand that each successive number name refers to a quantity that is one more.
• MAT-00.CC.05 Count to answer how many? questions.
• MAT-00.CC.05.a Tell how many objects up to 20 are in an arranged pattern or up to 10 objects in a scattered configuration.
• MAT-00.CC.05.b Represent a number of objects up to 20 with a written numeral.
• MAT-00.CC.05.c Given a number from 1-20, count out that many objects.
• MAT-00.CC.06 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, using groups of up to 10 objects.
• MAT-00.CC.07 Compare two numbers between 1 and 10 presented as written numerals.

### MAT-00.OA Domain:

• MAT-00.OA.01 Represent addition and subtraction in a variety of ways
• MAT-00.OA.02 Use an appropriate strategy to solve word problems that involve adding and subtracting within 10.
• MAT-00.OA.03 Decompose numbers less than or equal to 10 into multiple combinations of two parts. Record each decomposition with a drawing or equation.
• MAT-00.OA.04 Find the number that makes 10 when added to a given number from 1 to 9. Record with a drawing or equation.
• MAT-00.OA.05 Fluently add and subtract within 5.

### MAT-00.NBT Domain:

• MAT-00.NBT.01 Compose and decompose numbers from 11 to 19 using a group of ten ones and additional ones. Record each composition or decomposition with a drawing or equation.

### MAT-00.MD Domain:

• MAT-00.MD.01 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object
• MAT-00.MD.02 Compare two objects with a common measurable attribute and describe the difference
• MAT-00.MD.03 Classify objects into given categories limiting the number in each category to 10 or less. Count the numbers of objects in each category and sort the categories by count

### MAT-00.G Domain:

• MAT-00.G.01 Describe objects in the environment using names of shapes and solids.
• MAT-00.G.02 Correctly name shapes and solids regardless of their orientations or overall size
• MAT-00.G.03 Identify shapes and solids as two-dimensional or three-dimensional
• MAT-00.G.04 Compare and classify two-dimensional shapes of different sizes and orientations, using informal language to describe their similarities, differences, and attributes
• MAT-00.G.06 Compose a new shape by combining two or more simple shapes.

### A Sample of What Your Child Will Be Working on in Kindergarten

• Counting objects to tell how many there are
• Comparing two groups of objects to tell which group, if either, has more; comparing two written numbers to tell which is greater
• Acting out addition and subtraction word problems and drawing diagrams to represent them
• Adding with a sum of 10 or less; subtracting from a number 10 or less; and solving addition and subtraction word problems
• Adding and subtracting very small numbers quickly and accurately (e.g., 3 + 1)
• Correctly naming shapes regardless of orientation or size (e.g., a square oriented as a “diamond” is still a square)

"I can ... statements"

In 1st grade, your child will build on last year’s work and gain important new skills. One of the most important outcomes for the year is to improve speed and accuracy adding with a sum of 20 or less and subtracting from a number 20 or less (e.g., 17 – 8). Another important goal in 1st grade is adding with a sum of 100 or less; this will rely on understanding what the digits mean in a number such as 63 (namely, 63 is six tens and three ones). Working with multi-digit addition this year will set the stage for 2nd grade, when your child will be working with three-digit numbers and adding and subtracting with larger numbers.

### MAT-01.OA Domain:

• MAT-01.OA.01 Use strategies to add and subtract within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions
• MAT-01.OA.02 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20.
• MAT-01.OA.03 Apply properties of operations as strategies to add and subtract
• MAT-01.OA.04 Demonstrate understanding of subtraction as an unknown-addend problem
• MAT-01.OA.05 Relate counting to addition and subtraction
• MAT-01.OA.06 Use strategies to add and subtract within 20. Fluently add and subtract within 10.
• MAT-01.OA.07 Demonstrate understanding of the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false
• MAT-01.OA.08 Determine the unknown whole number in an addition or subtraction equation that uses three whole numbers.

### MAT-01.NBT Domain:

• MAT-01.NBT.01 Count forward and backward within 120, starting at any given number.
Read and write numerals within 120.
Represent a number of objects up to 120 with a written numeral.
• MAT-01.NBT.02 Demonstrate understanding that the two digits of a two-digit number represent amounts of tens and ones, including
• MAT-01.NBT.02.a 10 can be thought of as a bundle of ten ones - called a ten.
• MAT-01.NBT.02.b The numbers from 11 to 19 are composed of a ten and additional ones.
• MAT-01.NBT.02.c Multiples of 10 up to 90 represent a number of tens and 0 ones.
• MAT-01.NBT.03 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >,=, and <.
• MAT-01.NBT.04 Demonstrate understanding of place value when adding two-digit numbers within 100. Use concrete models or drawing strategies based on place value, properties of operations, and/or the relationship between addition and subtraction to add and subtract within 100. Relate the strategy to a written method and explain the reasoning used.
• MAT-01.NBT.05 Mentally add or subtract 10 to or from a given two-digit number. Explain the reasoning used
• MAT-01.NBT.06 Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction to subtract multiples of 10 in the range of 10-90 from multiples of 10 in the same range resulting in a positive or zero difference. Use a written method to explain the strategy.

### MAT-01.MD Domain:

• MAT-01.MD.01 Order three objects by length. Compare the lengths of two objects indirectly by using a third object.
• MAT-01.MD.02 Demonstrate understanding that the length measurement of an object is the number of same-size length units that span the object with no gaps or overlaps. Measure and express the length of an object using whole non-standards units.
• MAT-01.MD.03 Tell and Write time to the hour and half-hour using analog and digital clocks
• MAT-01.MD.04 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 are in one category than in another
• MAT-01.MD.05 Identify and tell the value of a dollar bill, quarter, dime, nickel, and penny
• MAT-01.MD.06 Count and tell the value of combinations of dimes and pennies up to one dollar

### MAT-01.G Domain:

• MAT-01.G.01 Distinguish between defining attributes versus non-defining attributes. Use defining attributes to build and draw two-dimensional shapes (squares, circles, triangles, rectangles, trapezoids, rhombuses, pentagons, hexagons, octagons).
• MAT-01.G.02 Compose a new shape or solid from two-dimensional shapes and/or three-dimensional solids (squares, circles, triangles, rectangles, trapezoids, rhombuses, pentagons, hexagons, octagons, cubes, spheres, cylinders, cones, triangular prisms, and rectangular prisms).
• MAT-01.G.03 Partition circles and rectangles into two equal shares. Describe the shares using the word halves, and Use the phrase half of. Describe the whole as two of the shares

### A Sample of What Your Child Will Be Working on in Grade 01

• Solving addition and subtraction word problems in situations of adding to, taking from, putting together, taking apart, and comparing (e.g., a taking from situation would be: “Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?”)
• Adding with a sum of 20 or less, and subtracting from a number 20 or less, for example by using strategies based around the number 10 (e.g., to solve 13 – 4, one can start with 13, subtract 3 to reach 10, and then subtract 1 more to reach 9)
• Quickly and accurately adding with a sum of 10 or less, and quickly and accurately subtracting from a number 10 or less (e.g., 2 + 5, 7 – 5)
• Understanding what the digits mean in two-digit numbers (place value)
• Using understanding of place value to add and subtract (e.g., 38 + 5, 29 + 20, 64 + 27, 80 – 50)
• Measuring lengths of objects by using a shorter object as a unit of length
• Making composite shapes by joining shapes together, and dividing circles and rectangles into halves or fourths

"I can ... statements"

In 2nd grade, your child will build on last year’s work and gain important new skills. One of the most important outcomes for the year is to add and subtract two-digit numbers quickly and accurately (e.g., 77 – 28). Another important goal in 2nd grade is to understand what the digits mean in a three-digit number such as 463 (namely, 463 is four hundreds, six tens, and three ones). Your child also will build expertise with solving addition and subtraction word problems. Mastering addition and subtraction at the 2nd grade level is important so that your child will not have to review and repeat this material in 3rd grade, when the study of multiplication, division, and fractions will start.

### MAT-02.OA Domain:

• MAT-02.OA.01 Use strategies to add and subtract within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions
• MAT-02.OA.02 Use mental strategies to fluently add and subtract within 20.
• MAT-02.OA.02.a Fluently add basic facts within 20 using mental strategies* MAT-02.OA.02.b Fluently subtract basic facts within 20 using mental strategies*
• MAT-02.OA.03 Determine whether a given number of objects up to 20 is odd or even. Write an equation to represent an even number using two equal addends or groups of 2.
• MAT-02.OA.04 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.

### MAT-02.NBT Domain:

• MAT-02.NBT.01 - Demonstrate understanding that the three digits of a three-digit number represent amounts of hundreds, tens, and ones, including:
• MAT-02.NBT.01.a 100 can be thought of as a bundle of ten tens called a hundred.
• MAT-02.NBT.01.b Multiples of 100 represent a number of hundreds, 0 tens, and 0 ones.
• MAT-02.NBT.02 Count forward and backward from any given number within 1000. Skip-count by 5s, 10s, and 100s.
• MAT-02.NBT.03 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
• MAT-02.NBT.04 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, recording the results of comparisons with the symbols >,=, <
• MAT-02.NBT.05 - Use strategies based on place value, properties of operations, and/or the relationship between addition and subtraction to fluently add and subtract within 100.
• MAT-02.NBT.06 Use strategies based on place value and properties of operations to add up to four two-digit numbers
• MAT-02.NBT.07 Demonstrate understanding of place value within 1000 when adding and subtracting three-digit numbers. Use concrete models or drawings and strategies based on place value, properties of operation, and/or the relationship between addition and subtraction to add and subtract within 1000. Use a written method to explain the strategy.
• MAT-02.NBT.08 - Mentally add or subtract 10 or 100 to or from a given number between 100 and 900

### MAT-02.MD Domain:

• MAT-02.MD.01 Select and use appropriate tools to measure the length of an object
• MAT-02.MD.02 Measure the length of an object using two different standard units of measurement. Describe how the two measurements relate to the size of the units chosen.
• MAT-02.MD.03 Estimate lengths using units of inches, feet, centimeters, and meters
• MAT-02.MD.04 Measure to determine how much longer one object is than another, expressing the difference with a standard unit of measurement
• MAT-02.MD.06 Represent whole numbers on a number line diagram with equally spaced points. Represent whole-number sums and differences within 100 on a number line diagram.
• MAT-02.MD.07 Tell and Write time to the nearest five minutes with a.m. and p.m. using analog and digital clocks
• MAT-02.MD.08 solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using dollar and cent symbols appropriately
• MAT-02.MD.09 Generate data by measuring lengths of objects to the nearest whole standard unit. Show the measurements by making a line plot, using a horizontal scale marked off in whole-number units
• MAT-02.MD.10 Draw picture graphs and bar graphs with single-unit scales to represent data sets with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

### MAT-02.G Domain:

• MAT-02.G.01 Identify trapezoids, rhombuses, pentagons, hexagons, octagons, parallelograms, quadrilaterals, cubes, spheres, cylinders, cones, triangular prisms, rectangular prisms. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.
• MAT-02.G.02 Partition a rectangle into rows and columns of same-size squares and count to find the total number
• MAT-02.G.03 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. Recognize that identical wholes can be equally divided in different ways. Demonstrate understanding that partitioning shapes into more equal shares creates smaller shares.

### A Sample of What Your Child Will Be Working on in Grade 02

• Solving challenging addition and subtraction word problems with one or two steps (e.g., a “one-step” problem would be: “Lucy has 3 fewer apples than Julie. Julie has 47 apples. How many apples does Lucy have?”)
• Quickly and accurately adding with a sum of 20 or less (e.g., 11 + 8); quickly and accurately subtracting from a number 20 or less (e.g., 16 – 9); and knowing all sums of one-digit numbers from memory by the end of the year
• Understanding what the digits mean in three-digit numbers (place value)
• Using understanding of place value to add and subtract three-digit numbers (e.g., 811 – 367); adding and subtracting two-digit numbers quickly and accurately (e.g., 77 – 28)
• Measuring and estimating length in standard units
• Solving addition and subtraction word problems involving length (e.g., “The pen is 2 cm longer than the pencil. If the pencil is 7 cm long, how long is the pen?”)
• Building, drawing, and analyzing 2-D and 3-D shapes to develop foundations for area, volume, and geometry in later grades

"I can ... statements"

In 3rd grade, your child will learn important new ideas and gain important new skills. One of the most important topics this year is multiplication and division. Another is fractions. Multiplication, division, and fractions are the building blocks for many life skills that students will learn in later grades, such as percentages. Students also need to master these topics to be ready for algebra and advanced math, so it is essential to get a good start with these topics in 3rd grade.

### MAT-03.OA Domain:

• MAT-03.OA.01 Interpret and model products of whole numbers.
• MAT-03.OA.02 Interpret and model whole-number quotients of whole numbers, as the number in a group or the number of groups.
• MAT-03.OA.03 Using drawings and equations with a symbol for an unknown number, solve multiplication and division word problems within 100 in situations involving equal groups, arrays, and measurement quantities.
• MAT-03.OA.04 Determine the unknown whole number in a multiplication or division equation relating three whole numbers
• MAT-03.OA.05 Apply properties of operations as strategies to multiply and divide.
• MAT-03.OA.06 Understand division as an unknown-factor problem.
• MAT-03.OA.07 Using mental strategies, fluently multiply and divide within 100
• MAT-03.OA.08 Solve two-step word problems using the four operations. represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies
• MAT-03.OA.09 Identify arithmetic patterns, and explain them using properties of operations

### MAT-03.NBT Domain:

• MAT-03.NBT.01 Use place value understanding to round whole numbers to the nearest 10 or 100.
• MAT-03.NBT.02 Using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction, fluently add and subtract within 1000
• MAT-03.NBT.03 Using strategies based on place value and properties of operations, multiply one-digit whole numbers by multiples of 10 in the range 10-90.

### MAT-03.NF Domain:

• MAT-03.NF.01 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts. Understand a fraction a/b as the quantity formed by a parts of size 1/b.
• MAT-03.NF.02 Understand a fraction as a number on the number line; represent fractions on a number line diagram.
• MAT-03.NF.02.a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
• MAT-03.NF.02.b 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.
• MAT-03.NF.03 - Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
• MAT-03.NF.03.a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. MAT-03.NF.03.b Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent using a visual fraction model.
• MAT-03.NF.03.c Recognize fractions, a/1 or a/a, that are equivalent to whole numbers. Express whole numbers as fractions, a/1 or a/a.
• MAT-03.NF.03.d Compare two fractions with the same numerator or the same denominator by reasoning about their size.
• 03.NF.03.e Recognize that comparisons are valid only when the two fractions refer to the same whole.
• 03.NF.03.f Record the results of comparisons with the symbols >, =, or <, and justify the conclusions by using a visual fraction model.

### MAT-03.MD Domain:

• MAT-03.MD.01 Tell and Write time to the nearest minute and measure time intervals in minutes. solve elapsed time word problems on the hour and the half hour, using a variety of strategies.
• MAT-03.MD.02 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 solve one-step word problems involving masses or volumes that are given in the same units.
• MAT-03.MD.03 Draw scaled picture graphs and scaled bar graphs to represent data sets with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs.
• MAT-03.MD.04 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 in appropriate unitsùwhole numbers, halves, or quarters.
• MAT-03.MD.05 Recognize area as an attribute of plane figures and understand concepts of area measurement.
• MAT-03.MD.05.a A square with a side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area.
• MAT-03.MD.05.b A plane figure, which can be covered without gaps or overlaps by n unit squares, is said to have an area of n square units.
• MAT-03.MD.06 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
• MAT-03.MD.07 Relate area to the operations of multiplication and addition.
• MAT-03.MD.07.a 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.
• MAT-03.MD.07.b 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.
• MAT-03.MD.07.c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a ╫ b and a ╫ c. Use area models to represent the distributive property in mathematical reasoning.
• MAT-03.MD.07.d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems
• MAT-03.MD.08 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths. Find an unknown side length. Exhibit rectangles with the same perimeter and different area or with the same area and different perimeters

### MAT-03.G Domain:

• MAT-03.G.01 Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals. Draw examples of quadrilaterals that do not belong to any of these subcategories
• MAT-03.G.02 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

### A Sample of What Your Child Will Be Working on in Grade 03

• Multiplying and dividing up to 10 × 10 quickly and accurately, including knowing the times tables from memory
• Solving word problems using addition, subtraction, multiplication, and division
• Beginning to multiply numbers with more than one digit (e.g., multiplying 9 × 80)
• Understanding fractions and relating them to the familiar system of whole numbers (e.g., recognizing that 3⁄1 and 3 are the same number)
• Measuring and estimating weights and liquid volumes, and solving word problems involving these quantities
• Reasoning about shapes (e.g., all squares are rectangles but not all rectangles are squares)
• Finding areas of shapes, and relating area to multiplication (e.g., why is the number of square feet for a 9-foot by 7-foot room given by the product 9 × 7?)

"I can ... statements"

In 4th grade, your child will gain important new skills while continuing to build on what he or she learned the previous year. One of the main areas studied in 4th grade is arithmetic and applying it to solve problems. This is an important life skill, and your child should make significant strides in this area during the year. Your child will also build knowledge and skills with fractions to prepare for mastering this topic in 5th and 6th grades. These skills will help ensure your child is ready for algebra and advanced math.

### MAT-04.OA Domain:

• MAT-04.OA.01 Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.
• MAT-04.OA.02 Use drawings and equations with a symbol for the unknown number (variable) to represent the problem. Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison.
• MAT-04.OA.03 Solve multistep 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 equations with a letter standing for the unknown
• MAT-04.OA.04 Find all factor pairs for a whole number in the range 1-36. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-36 is a multiple of a given one-digit number or is prime or composite.
• MAT-04.OA.05 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

### MAT-04.NBT Domain:

• MAT-04.NBT.01 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right
• MAT-04.NBT.02 Read and write multi-digit whole numbers to the one millions place using base-ten numerals, word form, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of c
• MAT-04.NBT.03 Use place value and/or understanding of numbers to round multi-digit whole numbers to any place.
• MAT-04.NBT.04 Fluently add and subtract multi-digit whole numbers to the one millions place using strategies flexibly, including the standard algorithm.
• MAT-04.NBT.05 Using strategies based on place value and the properties of operations, multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers. Illustrate and Explain the calculation by using equations, rectangular arrays, and/or area models
• MAT-04.NBT.06 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using 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.

### MAT-04.NF Domain:

• MAT-04.NF.01 Using visual fraction models, explain why a fraction a/b is equivalent to a fraction (n X a)/(n X b). Use this principle to recognize and generate equivalent fractions.
• MAT-04.NF.02 By creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2, compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the
• MAT-04.NF.03 - Understand a fraction a/b with a > 1 as a sum of unit fractions 1/b.
• MAT-04.NF.03.a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
• MAT-04.NF.03.b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition with an equation. Justify decompositions by using a visual fraction model or other strategies.
• MAT-04.NF.03.c Add and subtract mixed numbers with like denominators.
• MAT-04.NF.03.d Using visual fraction models and equations, solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
• MAT-04.NF.04 - Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
• MAT-04.NF.04.a Understand a fraction a/b as a multiple of 1/b.
• MAT-04.NF.04.b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number
• MAT-04.NF.04.c Using visual fraction models and equations, solve word problems involving multiplication of a fraction by a whole number.
• MAT-04.NF.05 Express a fraction with denominator 10 as an equivalent fraction with denominator 100. Use this technique to add two fractions with respective denominators 10 and 100.
• MAT-04.NF.06 Use decimal notation for fractions with denominators 10 or 100.
• MAT-04.NF.07 - Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.

### MAT-04.MD Domain:

• MAT-04.MD.01 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
• MAT-04.MD.02 Use the four operations to solve word problems involving distances, time intervals, liquid volumes, objects masses, 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. Using diagrams such as number line diagrams that feature a measurement scale, to represent measurement quantities
• MAT-04.MD.03 Apply the area and perimeter formulas for rectangles in real world and mathematical problems
• MAT-04.MD.04 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
• MAT-04.MD.05 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. Understand concepts of angle measurement.
• MAT-04.MD.05.a 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.
• MAT-04.MD.05.b An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
• MAT-04.MD.06 Measure angles in whole-number degrees using a protractor. using a protractor and ruler, Draw angles of a specified measure.
• MAT-04.MD.07 Recognize angle measure as additive. 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. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.

### MAT-04.G Domain:

• MAT-04.G.01 Draw and label points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
• MAT-04.G.02 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of specified size. Recognize right triangles as a category, and Identify right triangles
• MAT-04.G.03 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures. Draw lines of symmetry.

### A Sample of What Your Child Will Be Working on in Grade 04

• Using whole-number arithmetic to solve word problems, including problems with remainders and problems with measurements
• Adding and subtracting whole numbers quickly and accurately (numbers up to 1 million)
• Multiplying and dividing multi-digit numbers in simple cases (e.g., multiplying 1,638 × 7 or 24 × 17, and dividing 6,966 by 6)
• Understanding and applying equivalent fractions (e.g., recognizing that 1⁄4 is less than 3⁄8 because 2⁄8 is less than 3⁄8)
• Adding, subtracting, and multiplying fractions in simple cases (such as 2 3⁄4 − 1 1⁄4 or 3 × 5⁄8), and solving related word problems
• Understanding simple decimals in terms of fractions (e.g., rewriting 0.62 as 62⁄100)
• Measuring angles and finding unknown angles in a diagram

"I can ... statements"

Fifth grade is a milestone and a pivot point for students. The classroom focus on arithmetic during the elementary grades will develop into a more formal study of algebra in middle school. To be ready for algebra, students must have an understanding of fractional arithmetic, in part because even simple equations cannot be solved without fractions. Because of this, whole-number arithmetic comes mostly to a close in 5th grade, while multiplying and dividing fractions becomes a major focus.

### MAT-05.OA Domain:

• MAT-05.OA.01 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
• MAT-05.OA.02 Write simple expressions that record calculations with numbers. Interpret numerical expressions without evaluating them.
• MAT-05.OA.03 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. Graph the ordered pairs on a coordinate plane. Use the Graph to verify relationships.
• MAT-05.OA.04 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

### MAT-05.NBT Domain:

• MAT-05.NBT.01 Recognize 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 1/10 of what it represents in the place to its left.
• MAT-05.NBT.02 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. 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.
• MAT-05.NBT.03 Read, Write, and compare decimals to thousandths.
• MAT-05.NBT.03.a Read and write decimals to thousandths using base-ten numerals, word form, and expanded form
• MAT-05.NBT.03.b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
• MAT-05.NBT.04 Use place value understanding to round decimals to any place.
• MAT-05.NBT.05 Fluently multiply multi-digit whole numbers using strategies flexibly, including the standard algorithm.
• MAT-05.NBT.06 Using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division, Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Illustrate and Explain the calculation by using equations, rectangular arrays, and/or area models.
• MAT-05.NBT.07 Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, add, subtract, multiply, and divide decimals to hundredths. Relate the strategy to a written method and Explain the reasoning used.

### MAT-05.NF Domain:

• MAT-05.NF.01 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators
• MAT-05.NF.02 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, by using visual fraction models and equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate Mentally and Assess the reasonableness of answers.
• MAT-05.NF.03 Interpret a fraction as division of the numerator by the denominator (a/b = a ≈ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models and equations to represent the problem
• MAT-05.NF.04 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
• MAT-05.NF.04.a Interpret the product (a/b) ╫ q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a ╫ q ≈ b.
• MAT-05.NF.04.b. 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. Represent fraction products as rectangular areas.
• MAT-05.NF.05 Interpret multiplication as scaling (resizing), by:
• MAT-05.NF.05.a 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.
• MAT-05.NF.05.b 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.
• MAT-05.NF.05.c Relating the principle of fraction equivalence a/b = (n╫a) / (n╫b) to the effect of multiplying a/b by 1.
• MAT-05.NF.06 Solve real world problems involving multiplication of fractions and mixed numbers using visual fraction models and equations to represent the problem.
• MAT-05.NF.07 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
• MAT-05.NF.07.a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
• MAT-05.NF.07.b Interpret division of a whole number by a unit fraction, and compute such quotients.
• MAT-05.NF.07.c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using visual fraction models and equations to represent the problem.

### MAT-05.MD Domain:

• MAT-05.MD.01 Convert among different-sized standard measurement units within a given measurement system. Use these conversions in solving multi-step, real world problems.
• MAT-05.MD.02 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.
• MAT-05.MD.03 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
• MAT-05.MD.03.a 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.
• MAT-05.MD.03.b 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.
• MAT-05.MD.04 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft., and improvised units.
• MAT-05.MD.05 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
• MAT-05.MD.05.a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes. 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.
• MAT-05.MD.05.b Represent threefold whole-number products as volumes to represent the associative property of multiplication.
• MAT-05.MD.05.c Apply the formulas V = l ╫ w ╫ h and V = b ╫ 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.
• MAT-05.MD.05.d 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 problem

### MAT-05.G Domain:

• MAT-05.G.01 Use a pair of axes, to define the coordinates of a given point in the plane
• MAT-05.G.02 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane. interpret coordinate values of points in the context of the situation.
• MAT-05.G.03 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
• MAT-05.G.04 Classify two-dimensional figures in a hierarchy based on properties.

### A Sample of What Your Child Will Be Working on in Grade 05

• Adding and subtracting fractions with unlike denominators (e.g., 21⁄4 – 11⁄3), and solving word problems of this kind
• Multiplying fractions; dividing fractions in simple cases; and solving related word problems (e.g., finding the area of a rectangle with fractional side lengths; determining how many 1⁄3-cup servings are in 2 cups of raisins; determining the size of a share if 9 people share a 50-pound sack of rice equally or if 3 people share 1⁄2 pound of chocolate equally)
• Generalizing the place-value system to include decimals, and calculating with decimals to the hundredths place (two places after the decimal)
• Understanding and applying equivalent fractions (e.g., recognizing that 1⁄4 is less than 3⁄8 because 2⁄8 is less than 3⁄8)
• Multiplying whole numbers quickly and accurately, for example 1,638 × 753, and dividing
whole numbers in simple cases, such as dividing 6,971 by 63
• Understanding the concept of volume, and solving word problems that involve volume
• Graphing points in the coordinate plane (two dimensions) to solve problems
• Analyzing mathematical patterns and relationships

"I can ... statements"

The skills and understanding that your child will gain during 6th grade are among the most important foundations for college and career readiness. These include working with ratios and rates and working with variables and variable expressions — the building blocks of algebra. Many of this year’s topics will remain a major emphasis throughout the middle school years and into high school.

### MAT-06.RP Domain:

• MAT-06.RP.01 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
• MAT-06.RP.02 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.
• MAT-06.RP.03 Use tables of equivalent ratios, tape diagrams, double number line diagrams, and equations to reason about ratios and rates in real world and mathematical problems.
• MAT-06.RP.03.abd Make tables of equivalent ratios, unit rate, measurement conversion.
• MAT-06.RP.03.c Find a percent of a quantity as a rate per 100. Solve problems involving finding the whole, given a part and the percent.

### MAT-06.NS Domain:

• MAT-06.NS.01 Use visual fraction models and equations to interpret and compute quotients of fractions. Use models and equations to solve word problems involving division of fractions by fractions.
• MAT-06.NS.02 Fluently divide multi-digit numbers using strategies flexibly, including the standard algorithm.
• MAT-06.NS.03 Fluently add, subtract, multiply, and divide multi-digit decimals using strategies flexibly, including the standard algorithm for each operation.
• MAT-06.NS.04 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 to 100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
• MAT-06.NS.05 Understand that rational numbers are used together to describe quantities having opposite directions or values. Use rational numbers to represent quantities in real world contexts, explaining the meaning of 0 in each situation.
• MAT-06.NS.06 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes from previous grades to represent points on the line and in the plane with negative number coordinates.
• MAT-06.NS.06.a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. Recognize that the opposite of the opposite of a number is the number itself, for example: -(-3)=3, and that 0 is its own opposite.
• MAT-06.NS.06.b 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.
• MAT-06.NS.06.c 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.
• MAT-06.NS.07 Understand ordering and absolute value of rational numbers.
• MAT-06.NS.07.a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram
• MAT-06.NS.07.b Write, interpret, and explain statements of order for rational numbers in real world contexts
• MAT-06.NS.07.c Understand the absolute value of a rational number as its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real world situation
• MAT-06.NS.07.d Distinguish comparisons of absolute value from statements about order.
• MAT-06.NS.08 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.

### MAT-06.EE Domain:

• MAT-06.EE.01 Write and evaluate numerical expressions involving whole-number exponents
• MAT-06.EE.02 Write, Read, and evaluate expressions in which letters stand for numbers.
• MAT-06.EE.02.a Write expressions that record operations with numbers and with letters standing for numbers.
• MAT-06.EE.02.b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient, difference, quantity, etc.); view one or more parts of an expression as a single entity.
• Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
• MAT-06.EE.03 Apply the properties of operations to generate equivalent expressions.
• MAT-06.EE.04 Identify when two expressions are equivalent.
• MAT-06.EE.05 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.
• MAT-06.EE.06 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.
• MAT-06.EE.07 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.
• MAT-06.EE.08 Write a statement of inequality of the form x > c or the form x < c to represent a constraint or condition in a real world or mathematical problem. Recognize that inequalities of the form x > c or the form x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
• MAT-06.EE.09 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 (dependent variable) in terms of the other quantity (independent variable). Analyze the relationship

### MAT-06.G Domain:

• MAT-06.G.01 Based on prior knowledge of area of rectangles, decompose or Compose triangles to Find the area of a triangle. using knowledge of area of triangles and rectangles, Compose and/or decompose triangles, special quadrilaterals, and polygons to Find their areas. Apply these techniques in the context of solving real world mathematical problems.
• MAT-06.G.02 Using cubes of an appropriate size, pack a right rectangular prism having fractional edge lengths to find its volume. Then show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = ℓwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real world and mathematical problems.
• MAT-06.G.03 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.
• MAT-06.G.04 Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Use the nets to find the surface area of these figures. Apply these techniques in the context of solving real world and mathematical problems.

### MAT-06.SP Domain:

• MAT-06.SP.01 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
• MAT-06.SP.02 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.
• MAT-06.SP.03 Recognize that a measure of center for a numerical data set summarizes all of its values using a single number, while a measure of spread (variation) describes how its values vary with a single number.
• MAT-06.SP.04 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
• MAT-06.SP.05 Summarize numerical data sets in relation to their context by:
• MAT-06.SP.05.a Reporting the number of observations.
• MAT-06.SP.05.b Describing the nature of the attribute being investigated, including how it was measured and its units of measurement.
• MAT-06.SP.05.c Calculating quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.
• MAT-06.SP.05.d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

### A Sample of What Your Child Will Be Working on in Grade 06

• Understanding ratios and rates, and solving problems involving proportional relationships (e.g., if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)
• Dividing fractions and solving related word problems (e.g., how wide is a rectangular strip of land with length 3⁄4 mile and area 1⁄2 square mile?)
• Using positive and negative numbers together to describe quantities; understanding the ordering and absolute values of positive and negative numbers
• Working with variables and expressions by generalizing the way numbers work (e.g., when adding numbers, the order doesn’t matter, so x + y = y + x; likewise, properties of addition and multiplication can be used to rewrite 24x + 18y as 6(4x + 3y), or y + y + y as 3y)
• Understanding the process of solving simple equations
• Writing equations to solve word problems and describe relationships between quantities (e.g., the distance D traveled by a train in time T might be expressed by an equation D = 85T, where D is in miles and T is in hours)
• Reasoning about relationships between shapes to determine area, surface area, and volume

"I can ... statements"

In 7th grade, your child will grow in skill and understanding as he or she continues the previous grade’s work in proportional relationships, equations, and positive and negative numbers. These topics will remain a major emphasis throughout the middle school years and into high school. A good command of rates and proportional relationships, including percentages, is also an important life skill.

### MAT-07.RP Domain:

• MAT-07.RP.01 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
• MAT-07.RP.02 Recognize and represent proportional relationships between quantities.
• MAT-07.RP.02.a Decide whether two quantities are in a proportional relationship by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
• MAT-07.RP.02.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
• MAT-07.RP.02.c Represent proportional relationships by equations
• MAT-07.RP.02.d Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate.
• MAT-07.RP.03 Use proportional relationships to solve multi-step ratio and percent problems.

### MAT-07.NS Domain:

• MAT-07.NS.01 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.
• MAT-07.NS.01.a Describe situations in which opposite quantities combine to make 0.
• MAT-07.NS.01.b Understand p + q as the number located a distance |q| from p on a number line, in the direction indicated by the sign of q. 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.
• MAT-07.NS.01.c 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.
• MAT-07.NS.01.d - Apply properties of operations as strategies to Fluently add and subtract rational numbers.
• MAT-07.NS.02 Apply and extend previous understandings of multiplication, division, and fractions to multiply and divide rational numbers.
• MAT-07.NS.02.a 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 rational numbers. Interpret products of rational numbers by describing real world contexts.
• MAT-07.NS.02.b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then ?(p/q) = ?p/q = p/?q. Interpret products of rational numbers by describing real world contexts.
• MAT-07.NS.02.c Apply properties of operations as strategies to Fluently multiply and divide rational numbers.
• MAT-07.NS.02.d Convert a rational number to a decimal using long division. Know that the decimal form of a rational number terminates or eventually repeats.
• MAT-07.NS.03 Solve real world and mathematical problems involving the four operations with rational numbers.

### MAT-07.EE Domain:

• MAT-07.EE.01 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients with an emphasis on writing equivalent expressions.
• MAT-07.EE.02 Understand that rewriting an expression in different forms in a problem context can clarify the problem and how the quantities in it are related.
• MAT-07.EE.03 Solve multi-step real-life and mathematical problems posed with rational numbers in any form, using tools strategically. Apply properties of operations to calculate with numbers in any form. Convert between forms as appropriate. Assess the reasonableness of answers using mental computation and estimation strategies.
• MAT-07.EE.04 Use variables to represent quantities in a real world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
• MAT-07.EE.04.a 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. Solve equations of these forms fluently. Compare the algebraic solution to an arithmetic solution, identifying the sequence
• MAT-07.EE.04.b 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 solution set of the inequality and interpret it in the context of the problem.

### MAT-07.G Domain:

• MAT-07.G.01 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.
• MAT-07.G.02 Draw geometric shapes from 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. Use a variety of methods such as freehand, with ruler and protractor, and with technology.
• MAT-07.G.03 Describe the cross-sections (two-dimensional figures that result from slicing three-dimensional figures, as in plane sections) of right rectangular prisms and right rectangular pyramids.
• MAT-07.G.04 Know the formulas for the area and circumference of a circle and use them to solve problems. Informally derive the relationship between the circumference and area of a circle.
• MAT-07.G.05 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.
• MAT-07.G.06 Solve real world and mathematical problems involving area of two-dimensional figures composed of polygons and/or circles, including composite figures. Use nets to solve real world and mathematical problems involving surface area of prisms and cylinders, including composite solids. Solve real world and mathematical problems involving volumes of right prisms, including composite solids.

### MAT-07.SP Domain:

• MAT-07.SP.01 Understand that statistics can be used to gain information about a population by examining a sample of the population. Understand that 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.
• MAT-07.SP.02 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.
• MAT-07.SP.03 Informally assess the degree of visual 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.
• MAT-07.SP.04 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
• MAT-07.SP.05 Understand that the probability of a chance event is a number from 0 through 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 ╜ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
• MAT-07.SP.06 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency. Predict the approximate relative frequency given the probability.
• MAT-07.SP.07 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies. If there is a discrepancy, explain possible sources.
• MAT-07.SP.07.a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
• MAT-07.SP.07.b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
• MAT-07.SP.08 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
• MAT-07.SP.08.a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
• MAT-07.SP.08.b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (such as rolling double sixes), identify the outcomes in the sample space which compose the event.
• MAT-07.SP.08.c Design and use a simulation to generate frequencies for compound events.

### A Sample of What Your Child Will Be Working on in Grade 07

• Analyzing proportional relationships (e.g., by graphing in the coordinate plane), and distinguishing proportional relationships from other kinds of mathematical relationships (e.g., buying 10 times as many items will cost you 10
times as much, but taking 10 times as many aspirin will not lower your fever 10 times as much)
• Solving percent problems (e.g., tax, tips, and markups and markdowns)
• Adding, subtracting, multiplying, and dividing positive and negative numbers, and solving related word problems
• Solving word problems that have a combination of whole numbers, fractions, and decimals (e.g., a woman making $25 per hour receives a 10% raise; she will make an additional 1⁄10 of her salary an hour, or$2.50, for a new salary of \$27.50)
• Solving equations such as 1⁄2 (x – 3) = 3⁄4 quickly and accurately, and writing equations of this kind to solve word problems (e.g., “I knocked over a carton of milk, and 3 cups were spilled before I set the carton upright again. When I poured out the remaining milk equally into two measuring cups, there was 3⁄4 of a cup of milk in each one. How much milk was originally in the carton?”)
• Solving problems involving scale drawings
• Using statistics to draw inferences and make comparisons (e.g., deciding which candidate is likely to win an election based on a survey)

"I can ... statements"

In 8th grade, your child will learn a number of skills and ideas that he or she must know and understand to be ready for college and career. Your child will continue to learn how to write and reason with algebraic expressions. Your child also will make a thorough study of linear equations with one and two variables. Building on previous work with relationships between quantities, your child will be introduced to the idea of a mathematical function. And your child will prepare for high school geometry by understanding congruence (same shape and size) and similarity of geometric figures.

### MAT-08.NS Domain:

• MAT-08.NS.01 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually. Convert a decimal expansion which repeats eventually into a rational number.
• MAT-08.NS.02 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 (such as pi).

### MAT-08.EE Domain:

• MAT-08.EE.01 Develop, know and Apply the properties of integer exponents to Generate equivalent numeric and algebraic expressions.
• MAT-08.EE.02 Use square root and cube root symbols to represent solutions to equations of the form x(squared) = p and x(cubed) = p, where p is a positive rational number. evaluate square roots of small perfect squares and cube roots of small perfect cubes. Classify radicals as rational or irrational.
• MAT-08.EE.03 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.
• MAT-08.EE.04 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 (such as use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
• MAT-08.EE.05 Graph proportional relationships, interpreting the unit rate as the slope of the graph. compare two different proportional relationships represented in different ways.
• MAT-08.EE.06 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.
• MAT-08.EE.07 Solve linear equations in one variable.
• MAT-08.EE.07.a 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).
• Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
• MAT-08.EE.08 Analyze and solve pairs of simultaneous linear equations.
• 08.EE.08.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
• 08.EE.08.b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection
• 08.EE.08.c Solve real world and mathematical problems leading to two linear equations in two variables

### MAT-08.F Domain:

• MAT-08.F.01 Understand that a function is a rule that assigns to each input exactly one output. Understand that the Graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
• MAT-08.F.02 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, and/or by verbal descriptions).
• MAT-08.F.03 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.
• MAT-08.F.04 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 reading these 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/table values
• MAT-08.F.05 Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

### MAT-08.G Domain:

• MAT-08.G.01 Understand the properties of rotations, reflections, and translations by experimentation:
• 08.G.01.a Lines are transformed onto lines, and line segments onto line segments of the same length.
• 08.G.01.b Angles are transformed onto angles of the same measure.
• 08.G.01.c Parallel lines are transformed onto parallel lines.
• MAT-08.G.02 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 of transformations that exhibits the congruence between them.
• MAT-08.G.03 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
• MAT-08.G.04 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 of transformations that exhibits the similarity between them.
• MAT-08.G.05 Use informal arguments to establish facts about:
• 08.G.05.a the angle sum and exterior angles of triangles
• 08.G.05.b the angles created when parallel lines are cut by a transversal
• 08.G.05.c the angle-angle criterion for similarity of triangles
• MAT-08.G.06 Explain a proof of the Pythagorean Theorem and its converse.
• MAT-08.G.07 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions
• MAT-08.G.08 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
• MAT-08.G.09 Know the formulas for the volume of cones, cylinders and spheres. Use the formulas to solve real world and mathematical problems.

### MAT-08.SP Domain:

• MAT-08.SP.01 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
• MAT-08.SP.02 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.
• MAT-08.SP.03 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept(s).
• MAT-08.SP.04 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.

### A Sample of What Your Child Will Be Working on in Grade 08

• Understanding slope, and relating linear equations in two variables to lines in the coordinate plane
• Solving linear equations (e.g., –x + 5(x + 1⁄3) = 2x – 8); solving pairs of linear equations (e.g., x + 6y = –1 and 2x – 2y = 12); and writing equations to solve related word problems
• Understanding functions as rules that assign a unique output number to each input number; using linear functions to model relationships
• Analyzing statistical relationships by using a bestfit line (a straight line that models an association between two quantities)
• Working with positive and negative exponents, square root and cube root symbols, and scientific notation (e.g., evaluating √36 + 64; estimating world population as 7 x 109)
• Understanding congruence and similarity using physical models, transparencies, or geometry software (e.g., given two congruent figures, show how to obtain one from the other by a sequence of rotations, translations, and/or reflections)
• Understanding and applying the Pythagorean Theorem (a2 + b2 = c2) to solve problems

## HS Math Concepts

The high school content standards specify the mathematics that all students should study in order to be college and career ready and listed in conceptual categories. This is different than the K-8 standards in that the standards are not grade-specific.

• N-RN The Real Number System
• N-Q Quantities
• N-CN Complex Numbers
• N-VM Vector and Matrix Quantities

• A-SSE Seeing Structures in Expressions
• A-APR Arithmetic with Polynomials and Rational Expressions
• A-CED Creating Equations
• A-REI Reasoning with Equations and Inequalities

• F-IF Interpreting Functions
• F-BF Building Functions
• F-LE Linear, Quadratic, and Exponential Models
• F-TF Trigonometric Functions

• G-CO Congruence
• G-SRT Similarity, Right Triangles, and Trigonometry
• G-C Circles
• G-GPE Expressing Geometric Properties with Equations
• G-GMD Geometric Measure and Dimension
• G-MG Modeling with Geometry

• S-ID Interpreting Categorical and Quantitative Data
• S-IC Making Inferences and Justifying Conclusions
• S-CP Conditional Probability and the Rules of Probability
• S-MD Using Probability to Make Decisions

## Math Learning Progressions

The Mathematics Standards are built on progressions describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics. These Math Learning Progressions are grouped together by domains and then separated into grade level standards to demonstrate the structure of mathematics and preserve the idea of building learning across grade levels.

# [N] Number and Quantity

Students’ prior knowledge includes:

• Students know that there are numbers that are not rational, and approximate them by rational numbers (grade 8)
• Students apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers (grade 7)
##### The Real Number System
• Extend the properties of exponents to rational exponents.
• Use properties of rational and irrational numbers.
##### Quantities
• Reason quantitatively and use units to solve problems
##### The Complex Number System
• Perform arithmetic operations with complex numbers.
• Represent complex numbers and their operations on the complex plane.
• Use complex numbers in polynomial identities and equations
##### Vector and Matrix Quantities
• Represent and model with vector quantities.
• Perform operations on vectors.
• Perform operations on matrices and use matrices in applications.

## MAT-HS.N Overview: [N] Number and Quantity

### MAT-HS.N-RN Domain: [N-RN] The Real Number System

• MAT-HS.N-RN.01 Explain how rational exponents are like integer exponents with radical notation
• MAT-HS.N-RN.02 Apply properties of exponents to expressions with radicals/rational exponents
• MAT-HS.N-RN.03 Explain which sums or products of two numbers are rational or irrational, why
• MAT-HS.N-RN.04 Perform basic operations on radicals and simplify radicals to write equivalent expressions

### MAT-HS.N-Q Domain: [N-Q] Quantities*

• MAT-HS.N-Q.01 Use units to understand and guide the solution of multi-step problems
• MAT-HS.N-Q.02 Define appropriate quantities for the purpose of modeling
• MAT-HS.N-Q.03 Report quantities at a level of accuracy reflecting limitations on measurement

### MAT-HS.N-CN Domain: [N-CN] The Complex Number System

• MAT-HS.N-CN.01 Know that every complex number has the form a + bi with a and b real
• MAT-HS.N-CN.02 Use the relation i^2 1 and commutative/associative/distributive properties
• MAT-HS.N-CN.03 Find the conjugate of a complex number
• MAT-HS.N-CN.04 Represent complex numbers on complex plane in rectangular and polar form
• MAT-HS.N-CN.05 Represent +, , x, and conjugation of complex numbers geometrically
• MAT-HS.N-CN.06 Calculate the distance between numbers in the complex plane
• MAT-HS.N-CN.07 Solve quadratic equations with real coefficients that have complex solutions
• MAT-HS.N-CN.08 Extend polynomial identities to the complex numbers
• MAT-HS.N-CN.09 Show the Fundamental Theorem of Algebra is true for quadratic polynomials

### MAT-HS.N-VM Domain: [N-VM] Vector and Matrix Quantities

• MAT-HS.N-VM.01 Recognize vector quantities as having both magnitude and direction
• MAT-HS.N-VM.02 Find the components of a vector by subtracting the coordinates
• MAT-HS.N-VM.03 Solve problems involving velocity that can be represented by vectors
• MAT-HS.N-VM.04 Add and subtract vectors
• N-VM.04.a Add vectors end-to-end, componentwise, and by the parallelogram rule
• N-VM.04.b Given two vectors, determine the magnitude and direction of their sum
• N-VM.04.c Understand vector subtraction
• MAT-HS.N-VM.05 Multiply a vector by a scalar
• N-VM.05.a Represent and perform scalar multiplication graphically by scaling vectors
• N-VM.05.b Compute the magnitude of a scalar multiple
• MAT-HS.N-VM.06 Use matrices to represent and manipulate data
• MAT-HS.N-VM.07 Multiply matrices by scalars to produce new matrices
• MAT-HS.N-VM.08 Add, subtract, and multiply matrices of appropriate dimensions
• MAT-HS.N-VM.09 Understand matrix multiplication for square matrices is not commutative
• MAT-HS.N-VM.10 Understand that the 0 and identity matrices play a role in matrix + and x
• MAT-HS.N-VM.11 Multiply a vector by a matrix to produce another vector
• MAT-HS.N-VM.12 Work with 2 x 2 matrices as transformations of the plane

### A Sample of HS Math Concept Number and Quantity to Become Ready for College and Career

#### The Real Number System

• Extend the properties of exponents to rational exponents.
• Use properties of rational and irrational numbers.

#### Quantities

• Reason quantitatively and use units to solve problems.

#### The Complex Number System

• Perform arithmetic operations with complex numbers.
• Represent complex numbers and their operations on the complex plane.
• Use complex numbers in polynomial identities and equations.

#### Vector and Matrix Quantities

• Represent and model with vector quantities.
• Perform operations on vectors.
• Perform operations on matrices and use matrices in applications.

# Counting and Cardinality

### MAT-00.CC Domain: [CC] Counting and Cardinality

#### Count to tell the number of objects.

• MAT-00.CC.04 Understand the relationship between numbers and quantities
• MAT-00.CC.05 Count to 20 to answer how many? questions

#### Compare number

• MAT-00.CC.06 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group
• MAT-00.CC.07 Compare two written numbers between 1 and 10

# Number and Operations in Base Ten

### MAT-01.NBT Domain: [NBT] Number and Operations in Base Ten

#### Extend the counting sequence.

• MAT-01.NBT.01 Count forward and backward within 120, starting at any given number.
Read and write numerals within 120.
Represent a number of objects up to 120 with a written numeral.

#### Understand place value.

• MAT-01.NBT.02 Understand that the two digits of a two-digit number represent amounts of tens and ones.
• MAT-01.NBT.03 Compare two-digit numbers

### MAT-02.NBT Domain: [NBT] Number and Operations in Base Ten

#### Understand place value.

• MAT-02.NBT.01 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones
• MAT-02.NBT.02 Count within 1000; skip-count by 5s, 10s, and 100s
• MAT-02.NBT.03 Read and write numbers to 1000
• MAT-02.NBT.04 Compare two three-digit numbers

### MAT-03.NBT Domain: [NBT] Number and Operations in Base Ten

#### Use place value understanding and properties of operations to per

• MAT-03.NBT.01 Round whole numbers to the nearest 10 or 100
• MAT-03.NBT.02 Using strategies, fluently add and subtract within 1000
• MAT-03.NBT.03 Multiply one-digit whole numbers by multiples of 10

### MAT-04.NBT Domain: [NBT] Number and Operations in Base Ten

#### Generalize place value understanding for multi-digit whole number

• MAT-04.NBT.01 Recognize that a digit is ten times greater than one place to the right
• MAT-04.NBT.02 Read, write and Compare multi-digit whole numbers
• MAT-04.NBT.03 Use place value to round multi-digit whole numbers to any place

#### Use place value understanding and properties of operations to per

• MAT-04.NBT.04 Fluently add and subtract whole numbers using the standard algorithm*
• MAT-04.NBT.05 multiply whole numbers up to two by two digits
• MAT-04.NBT.06 Find quotient and remainders with up to 4-digit dividends and 1-digit

### MAT-05.NBT Domain: [NBT] Number and Operations in Base Ten

#### Understand the place value system.

• MAT-05.NBT.01 Recognize a digit is 10X the digit to the right and 1/10 the digit to t
• MAT-05.NBT.02 Explain patterns in the number of zeros when multiplying by powers of 1
• MAT-05.NBT.03 Read, Write, and Compare decimals to thousandths*
• MAT-05.NBT.04 Use place value to round decimals to any place

#### Perform operations with multi-digit whole numbers and with decima

• MAT-05.NBT.05 Fluently multiply multi-digit whole numbers*
• MAT-05.NBT.06 Find quotients with up to 4-digit dividends and 2-digit divisors
• MAT-05.NBT.07 add, subtract, multiply, and divide decimals to hundredths

# Number and Operations - Fractions

### MAT-03.NF Domain: [NF] Number and Operations Fractions

#### Develop understanding of fractions as numbers.

• MAT-03.NF.01 Understand a fraction 1/b as the quantity formed by 1 part of b equal pa
• MAT-03.NF.02 Understand a fraction as a number on the number line
• MAT-03.NF.03 Explain equivalence and Compare fractions

### MAT-04.NF Domain: [NF] Number and Operations Fractions

#### Extend understanding of fraction equivalence and ordering.

• MAT-04.NF.01 Explain why a fraction A/B is equivalent to a fraction (n x A)/(n x B)
• MAT-04.NF.02 Compare fractions (unlike numerators and denominators)
• MAT-04.NF.03 Understands a fraction is the sum of smaller fractions
• MAT-04.NF.04 multiply a fraction by a whole number
• MAT-04.NF.05 Express equivalent fractions with denominators of 10 and 100
• MAT-04.NF.06 Use decimal notation for fractions with denominators 10 or 100
• MAT-04.NF.07 Compare two decimals to hundredths by reasoning about their size

### MAT-05.NF Domain: [NF] Number and Operations Fractions

#### Use equivalent fractions as a strategy to add and subtract fractions

• MAT-05.NF.01 add and subtract fractions with unlike denominators
• MAT-05.NF.02 Solve word problems involving addition and subtraction of fractions

#### Apply and extend previous understandings of multiplication and div

• MAT-05.NF.03 Interpret a fraction as division of the numerator by the denominator
• MAT-05.NF.04 Multiply a fraction or whole number by a fraction.
• MAT-05.NF.05 Interpret multiplication as scaling
• MAT-05.NF.06 Solve real world problems by multiplying fractions and mixed numbers
• MAT-05.NF.07 divide using unit fractions and whole numbers

# Ratios and Proportional Relationships

### MAT-06.RP Domain: [RP] Ratios and Proportional Relationships

#### (RP) Cluster: Use the four operations with whole numbers to solve problems.

• MAT-06.RP.01 Understand the concept of a ratio
• MAT-06.RP.02 Understand the concept of a unit rate
• MAT-06.RP.03 Use ratio and rate reasoning to Solve real-world mathematical problems

### MAT-07.RP Domain: [RP] Ratios and Proportional Relationships

#### (RP) Cluster: Use the four operations with whole numbers to solve problems.

• MAT-07.RP.01 compute unit rates associated with ratios of fractions
• MAT-07.RP.02 Recognize and represent proportional relationships between quantities
• MAT-07.RP.03 Use proportional relationships to Solve multistep ratio and percent pr

# The Number System

### MAT-06.NS Domain: [NS] The Number System

#### Compute fluently with multi-digit numbers and find common factors

• MAT-06.NS.02 Fluently divide multi-digit numbers
• MAT-06.NS.03 Fluently add, subtract, multiply, and divide multi-digit decimals
• MAT-06.NS.04 Find the GCF of numbers 100 and below and the LCM of numbers 12 and belo

#### Apply and extend previous understandings of numbers to the system

• MAT-06.NS.05 Understand that + and - numbers describe quantities with opposite valu
• MAT-06.NS.06 Understand a rational number as a point on the number line
• MAT-06.NS.07 Understand ordering and absolute value of rational numbers
• MAT-06.NS.08 Solve real-world mathematical problems by graphing

### MAT-07.NS Domain: [NS] The Number System

#### Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

• MAT-07.NS.01 add and subtract rational numbers
• MAT-07.NS.02 Apply multiplication and division and of fractions to rational numbers
• MAT-07.NS.03 Solve real-world mathematical problems using operations with rational numbers

# [A] Algebra

Students’ prior knowledge includes:

• Students understand the connections between proportional relationships, line, and linear equations (grade 8)
• Students analyze and solve linear equations and pairs of simultaneous linear equations (grade 8)
• Students analyze proportional relationships and use them to solve real-world and mathematical problems (grade 7)
• Students use properties of operations to generate equivalent expressions (grade 7)
• Students solve real-life and mathematical problems using numerical and algebraic expressions and equations (grade 7)
• Students reason about and solve one-variable equations and inequalities (grade 6)
##### Seeing Structure in Expressions
• Interpret the structure of expressions.
• Write expressions in equivalent forms to solve problems.
##### Arithmetic with Polynomials and Rational Functions
• Perform arithmetic operations on polynomials.
• Understand the relationship between zeros and factors of polynomials.
• Use polynomial identities to solve problems.
• Rewrite rational expressions.
##### Creating Equations and inequalities
• Create equations that describe numbers or relationships.
##### Reasoning with Equations and Inequalities
• Understand solving equations as a process of reasoning and explain the reasoning.
• Solve equations and inequalities in one variable.  Solve systems of equations.
• Represent and solve equations and inequalities graphically

## MAT-HS.A Overview: [A] Algebra

### MAT-HS.A-SSE Domain: [A-SSE] Seeing Structure in Expressions

• MAT-HS.A-SSE.01 Interpret expressions that represent a quantity in context
• SSE.01.a Interpret parts expressions, such as terms, factors, and coefficients
• SSE.01.b Interpret expressions by viewing one or more of their parts as a single entity
• MAT-HS.A-SSE.02 Use the structure of an expression to Identify ways to rewrite it
• MAT-HS.A-SSE.03 Choose and produce an equivalent form of an expression
• MAT-HS.A-SSE.03.a factor a quadratic expression to reveal the zeros of the function it define
• SSE.03.b Complete the square in a quadratic expression to reveal the maximum or mini
• SSE.03.c Use the properties of exponents to transform expressions for exponential fu
• MAT-HS.A-SSE.04 Derive the formula for the sum of a finite geometric series

### MAT-HS.A-APR Domain: [A-APR] Arithmetic with Polynomials and Rational Expressions

• MAT-HS.A-APR.01 Understand that polynomials form a system analogous to the integers
• MAT-HS.A-APR.02 Know and apply the Remainder Theorem
• MAT-HS.A-APR.03 Identify zeros of polynomials when suitable factorizations are available
• MAT-HS.A-APR.04 Prove polynomial identities and use them to describe numerical relationships
• MAT-HS.A-APR.05 Know and apply the Binomial Theorem for the expansion of (x + y)^n
• MAT-HS.A-APR.06 Rewrite simple rational expressions in different forms
• MAT-HS.A-APR.07 Understand rational expressions form a system analogous to rational numbers

### MAT-HS.A-REI Domain: [A-REI] Reasoning with Equations and Inequalities

• MAT-HS.A-REI.01 Explain each step in solving a simple equation
• MAT-HS.A-REI.02 Solve simple rational and radical equations in one variable
• A-REI.03.a Solve linear equations in one variable
• REI.03.b Solve linear inequalities in one variable
• MAT-HS.A-REI.03 Solve linear equations and inequalities in one variable
• MAT-HS.A-REI.04 Solve quadratic equations in one variable
• MAT-HS.A-REI.04.a Use the method of completing the square to transform any quadratic equation
• A-REI.04.b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square
• MAT-HS.A-REI.05 Prove a solution set for 2 variable equation A + N times 2 var equation B
• MAT-HS.A-REI.06 Solve systems of linear equations in two variables exactly and with graphs
• MAT-HS.A-REI.07 Solve and graph a system of a linear and a quadratic equation in 2 variables
• MAT-HS.A-REI.08 Represent a system of linear equations as a single matrix equation
• MAT-HS.A-REI.09 Find inverse of a matrix and use it to solve systems of linear equations
• MAT-HS.A-REI.10 Understand a graph is the set of an equation's solutions
• MAT-HS.A-REI.11 Explain why the xcoord. of where y=f(x) and y=g(x) intersect Solve f(x) = g(x)
• MAT-HS.A-REI.12 graph the solutions to a linear inequality in two variables as a half plane

### A Sample of HS Math Concept ALGEBRA to Become Ready for College and Career

#### Seeing Structure in Expressions

• Interpret the structure of expressions.
• Write expressions in equivalent forms to solve problems.

#### Creating Equations and inequalities

• Create equations that describe numbers or relationships.

#### Arithmetic with Polynomials and Rational Functions

• Perform arithmetic operations on polynomials.
• Understand the relationship between zeros and factors of polynomials.
• Use polynomial identities to solve problems.
• Rewrite rational expressions

#### Reasoning with Equations and Inequalities

• Understand solving equations as a process of reasoning and explain the reasoning.
• Solve equations and inequalities in one variable.
• Solve systems of equations.
• Represent and solve equations and inequalities graphically.

# Operations and Algebraic Thinking

### MAT-00.OA Domain: [OA] Operations and Algebraic Thinking

• MAT-00.OA.01 Represent addition and subtraction with objects
• MAT-00.OA.02 Solve addition and subtract word problems to 10
• MAT-00.OA.03 Decompose numbers less than or equal to 10 into pairs
• MAT-00.OA.04 Find the number that makes 10 when added to 1-9
• MAT-00.OA.05 Fluently add and subtract basic facts within 5

### MAT-01.OA Domain: [OA] Operations and Algebraic Thinking

#### Represent and solve problems involving addition and subtraction.

• MAT-01.OA.01 Solve addition and subtraction word problems within 20
• MAT-01.OA.02 Solve word problems of addition of three whole numbers whose sum <=20

#### Understand and apply properties of operations and the relationship

• MAT-01.OA.03 Apply properties of operations as strategies to add and subtract
• MAT-01.OA.04 Understand subtraction as an unknown-addend problem

#### Add and subtract within 20.

• MAT-01.OA.05 Relate counting to addition and subtraction
• MAT-01.OA.06 Add and subtract within 20, with fluency within 10

#### Work with addition and subtraction equations.

• MAT-01.OA.07 Understand the meaning of the equal sign
• MAT-01.OA.08 Determine the unknown number in addition or subtraction equations

### MAT-02.OA Domain: [OA] Operations and Algebraic Thinking

#### Represent and solve problems involving addition and subtraction.

• MAT-02.OA.01 Solve addition and subtraction word problems within 100

#### Work with equal groups of objects to gain foundations for multipli

• MAT-02.OA.03 Determine whether a group of objects has an odd or even number of member
• MAT-02.OA.04 Add to find the number of objects arranged in arrays

### MAT-03.OA Domain: [OA] Operations and Algebraic Thinking

#### Represent and solve problems involving multiplication and division

• MAT-03.OA.01 Interpret products of whole numbers
• MAT-03.OA.02 Interpret whole-number quotients of whole numbers
• MAT-03.OA.03 Use multiplication and division within 100 to solve word problems
• MAT-03.OA.04 Determine the unknown whole number in a multiplication or division equat

#### Understand properties of multiplication and the relationship betwe

• MAT-03.OA.05 Apply properties of operations as strategies to multiply and divide
• MAT-03.OA.06 Understand division as an unknown-factor problem

#### Multiply and divide within 100.

• MAT-03.OA.07 Fluently multiply and divide basic facts within 100*

#### Solve problems involving the four operations, and identify and exp

• MAT-03.OA.08 Solve two-step word problems using the four operations
• MAT-03.OA.09 Identify arithmetic patterns and explain them using properties of operations

### MAT-04.OA Domain: [OA] Operations and Algebraic Thinking

#### Use the four operations with whole numbers to solve problems.

• MAT-04.OA.01 Interpret a multiplication equation as a comparison
• MAT-04.OA.02 Multiply or divide to solve word problems involving multiplicative compa
• MAT-04.OA.03 Solve multistep word problems in all operations

#### Gain familiarity with factors and multiples.

• MAT-04.OA.04 Find all factor pairs for a whole number in the range 1-100

#### Generate and analyze patterns.

• MAT-04.OA.05 Generate a number or shape pattern that follows a given rule

### MAT-05.OA Domain: [OA] Operations and Algebraic Thinking

#### Write and interpret numerical expressions.

• MAT-05.OA.01 Use parentheses, brackets, or braces in numerical expressions
• MAT-05.OA.02 Write simple and interpret expressions

#### Analyze patterns and relationships.

• MAT-05.OA.03 Generate two numerical patterns using two given rules
• MAT-05.OA.04 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

# Expressions and Equations

### MAT-06.EE Domain: [EE] Expressions and Equations

#### Apply and extend previous understandings of arithmetic to algebrai

• MAT-06.EE.01 Evaluate numerical expressions involving whole-number exponents
• MAT-06.EE.02 Write, Read, and evaluate expressions in which letters stand for numbe
• MAT-06.EE.03 Apply the properties of operations to generate equivalent expressions
• MAT-06.EE.04 Identify when two expressions are equivalent

#### Reason about and solve one-variable equations and inequalities.

• MAT-06.EE.05 Understand solving an equation as a process of answering a question
• MAT-06.EE.06 Use variables to represent numbers in solving real-world mathematical pr
• MAT-06.EE.07 Solve real-world mathematical problems by writing and solving equation
• MAT-06.EE.08 Write inequalities to represent conditions in real-world mathematical pr

#### Represent and analyze quantitative relationships between dependent

• MAT-06.EE.09 Use variables as quantities that change in relationship to one another

### MAT-07.EE Domain: [EE] Expressions and Equations

#### Use properties of operations to generate equivalent expressions.

• MAT-07.EE.01 add, subtract, factor, and expand linear expressions with rational coe
• MAT-07.EE.02 Rewrite expressions in different forms to understand the problem

#### Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

• MAT-07.EE.03 Solve real-life mathematical problems posed with + and - rational numb
• MAT-07.EE.04 Use variables and simple equations to Solve real-world mathematical problems

# [F] Functions

Students’ prior knowledge includes:

• Students define, evaluate and compare functions (grade 8)
• Students use functions to model relationships between quantities (grade 8)
• Students solve real-life and mathematical problems using numerical and algebraic expressions and equations (grade 7)
• Students represent and analyze quantitative relationships between dependent and independent variables (grade 6)
##### Interpreting Functions
• Understand the concept of a function and use function notation.
• Interpret functions that arise in applications in terms of the context.
• Analyze functions using different representations.
##### Building Functions
• Build a function that models a relationship between two quantities.
• Build new functions from existing functions.
##### Linear, Quadratic, and Exponential Models
• Construct and compare linear, quadratic, and exponential models and solve problems.
• Interpret expressions for functions in terms of the situation they model.
##### Trigonometric Functions
• Extend the domain of trigonometric functions using the unit circle.
• Model periodic phenomena with trigonometric functions.
• Prove and apply trigonometric identities.

## MAT-HS.F [F] Overview: Function

### MAT-HS.F-IF Domain: [F-IF] Interpreting Functions

• MAT-HS.F-IF.01 Understand that each element of the domain is exactly one element of the range
• MAT-HS.F-IF.02 Use, evaluate, and interpret function notation in terms of a context
• MAT-HS.F-IF.03 Recognize that sequences are functions whose domain is a subset of the integers
• MAT-HS.F-IF.04 Interpret graphs of functions that model a relationship between 2 quantities
• MAT-HS.F-IF.05 Relate the domain of a function to its graph and the relationship it describes
• MAT-HS.F-IF.06 Calculate and interpret the average rate of change of a function
• MAT-HS.F-IF.07 graph Functions expressed symbolically and show key features of the graph
• MAT-HS.F-IF.07.a Graph linear functions and show intercepts.
• F-IF.07.b Graph square root, cube root, and piecewisedefined functions
• F-IF.07.c Graph polynomial functions
• F-IF.07.d Graph rational functions
• MAT-HS.F-IF.07.e Graph exponential and logarithmic functions
• MAT-HS.F-IF.07.f graph a quadratic function and show intercepts, maxima and minima.
• MAT-HS.F-IF.08 Write a function defined by an expression in different but equivalent forms
• F-IF.08.a Use factoring and completing the square to show zeros/extreme values/symmetry
• F-IF.08.b Use properties of exponents to interpret expressions for exponential functions
• MAT-HS.F-IF.09 Compare properties of two Functions each represented in a different way

### MAT-HS.F-BF Domain: [F-BF] Building Functions

• MAT-HS.F-BF.01 Write a function that describes a relationship between two quantities
• F-BF.01.a Determine an expression/recursive process/steps for calculation from context
• F-BF.01.b Combine standard function types using arithmetic operations
• F-BF.01.c Compose functions
• MAT-HS.F-BF.02 Write arithmetic and geometric sequences, and translate between the two
• MAT-HS.F-BF.03 Identify effects on a graph, replacing f(x) with f(x) + k, f(xk), k(fx), f(x+k)
• MAT-HS.F-BF.04 Find inverse functions
• F-BF.04.a Solve f(x)
• F-BF.04.b Verify by composition that one function is the inverse of another
• F-BF.04.c Read values of an inverse function from a graph or a table
• F-BF.04.d Produce an invertible function from a noninvertible function
• MAT-HS.F-BF.05 Understand the inverse relationship between exponents and logarithms

### MAT-HS.F-LE Domain: [F-LE] Linear, Quadratic and Exponential Models*

• MAT-HS.F-LE.01 Know when to use linear vs exponential functions
• F-LE.01.a Prove linear functions grow by differences & exponential functions by factors
• F-LE.01.b Recognize where a quantity changes at a constant rate relative to another
• F-LE.01.c Recognize where a quantity grows/decays by constant percent relative to another
• MAT-HS.F-LE.02 Construct linear and exponential functions given a graph/relationship/pairs
• MAT-HS.F-LE.03 Observe that exponential increases are greater than linear increases
• MAT-HS.F-LE.04 For exponential models, express as a logarithm the solution to ab^ct = d
• MAT-HS.F-LE.05 Interpret parameters in a linear or exponential function in a context

### MAT-HS.F-TF Domain: [F-TF] Trigonometric Functions

• MAT-HS.F-TF.01 Understand radian measure of an angle
• MAT-HS.F-TF.02 Explain how the unit circle enables trigonometric functions to all real numbers
• MAT-HS.F-TF.03 Use special triangles to determine geometrically the values of sine, cosine
• MAT-HS.F-TF.04 Use the unit circle to explain symmetry (odd and even)
• MAT-HS.F-TF.05 Choose trigonometric functions to model periodic phenomena
• MAT-HS.F-TF.06 Understand that restricting a trigonometric function to a domain on which i
• MAT-HS.F-TF.07 Use inverse functions to solve trigonometric equations that arise in modeli
• MAT-HS.F-TF.08 Prove the Pythagorean identity sin^2(?) + cos^2(?) = 1
• MAT-HS.F-TF.09 Prove the addition and subtraction formulas for sine, cosine, and tangent a

### A Sample of HS Math Concept Functions to Become Ready for College and Career

#### Interpreting Functions

• Understand the concept of a function and use function notation.
• Interpret functions that arise in applications in terms of the context.
• Analyze functions using different representations.

#### Building Functions

• Build a function that models a relationship between two quantities.
• Build new functions from existing functions.

#### Linear, Quadratic, and Exponential Models

• Construct and compare linear, quadratic, and exponential models and solve problems.
• Interpret expressions for functions in terms of the situation they model.

#### Trigonometric Functions

• Extend the domain of trigonometric functions using the unit circle.
• Model periodic phenomena with trigonometric functions.
• Prove and apply trigonometric identities.

# Operations and Algebraic Thinking

### MAT-00.OA Domain: [OA] Operations and Algebraic Thinking

• MAT-00.OA.01 Represent addition and subtraction with objects
• MAT-00.OA.02 Solve addition and subtract word problems to 10
• MAT-00.OA.03 Decompose numbers less than or equal to 10 into pairs
• MAT-00.OA.04 Find the number that makes 10 when added to 1-9
• MAT-00.OA.05 Fluently add and subtract basic facts within 5

### MAT-01.OA Domain: [OA] Operations and Algebraic Thinking

#### Represent and solve problems involving addition and subtraction.

• MAT-01.OA.01 Solve addition and subtraction word problems within 20
• MAT-01.OA.02 Solve word problems of addition of three whole numbers whose sum <=20

#### Understand and apply properties of operations and the relationship

• MAT-01.OA.03 Apply properties of operations as strategies to add and subtract
• MAT-01.OA.04 Understand subtraction as an unknown-addend problem

#### Add and subtract within 20.

• MAT-01.OA.05 Relate counting to addition and subtraction
• MAT-01.OA.06 Add and subtract within 20, with fluency within 10

#### Work with addition and subtraction equations.

• MAT-01.OA.07 Understand the meaning of the equal sign
• MAT-01.OA.08 Determine the unknown number in addition or subtraction equations

### MAT-02.OA Domain: [OA] Operations and Algebraic Thinking

#### Represent and solve problems involving addition and subtraction.

• MAT-02.OA.01 Solve addition and subtraction word problems within 100

#### Work with equal groups of objects to gain foundations for multipli

• MAT-02.OA.03 Determine whether a group of objects has an odd or even number of member
• MAT-02.OA.04 Add to find the number of objects arranged in arrays

### MAT-03.OA Domain: [OA] Operations and Algebraic Thinking

#### Represent and solve problems involving multiplication and division

• MAT-03.OA.01 Interpret products of whole numbers
• MAT-03.OA.02 Interpret whole-number quotients of whole numbers
• MAT-03.OA.03 Use multiplication and division within 100 to solve word problems
• MAT-03.OA.04 Determine the unknown whole number in a multiplication or division equat

#### Understand properties of multiplication and the relationship betwe

• MAT-03.OA.05 Apply properties of operations as strategies to multiply and divide
• MAT-03.OA.06 Understand division as an unknown-factor problem

#### Multiply and divide within 100.

• MAT-03.OA.07 Fluently multiply and divide basic facts within 100*

#### Solve problems involving the four operations, and identify and exp

• MAT-03.OA.08 Solve two-step word problems using the four operations
• MAT-03.OA.09 Identify arithmetic patterns and explain them using properties of operations

### MAT-04.OA Domain: [OA] Operations and Algebraic Thinking

#### Use the four operations with whole numbers to solve problems.

• MAT-04.OA.01 Interpret a multiplication equation as a comparison
• MAT-04.OA.02 Multiply or divide to solve word problems involving multiplicative compa
• MAT-04.OA.03 Solve multistep word problems in all operations

#### Gain familiarity with factors and multiples.

• MAT-04.OA.04 Find all factor pairs for a whole number in the range 1-100

#### Generate and analyze patterns.

• MAT-04.OA.05 Generate a number or shape pattern that follows a given rule

### MAT-05.OA Domain: [OA] Operations and Algebraic Thinking

#### Write and interpret numerical expressions.

• MAT-05.OA.01 Use parentheses, brackets, or braces in numerical expressions
• MAT-05.OA.02 Write simple and interpret expressions

#### Analyze patterns and relationships.

• MAT-05.OA.03 Generate two numerical patterns using two given rules
• MAT-05.OA.04 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

# [G] Geometry

Students’ prior knowledge includes:

• Students understand congruence and similarity using physical models, transparencies, or geometry software (grade 8)
• Students understand and apply the Pythagorean Theorem (grade 8)
• Student solve real-world and mathematical problems involving volume of cylinders, cones and spheres (grade 8)
• Students draw, construct and describe geometrical figures and describe the relationships between them (grade 7)
• Students solve real-life and mathematical problems involving angle measures, area, surface area, and volume (grade 7)
##### Congruence
• Experiment with transformations in the plane.
• Understand congruence in terms of rigid motions.
• Prove and apply geometric theorems.
• Make geometric constructions.
##### Similarity, Right Triangles, and Trigonometry
• Understand similarity.
• Prove theorems involving similarity.
• Define trigonometric ratios and solve problems involving right triangles.
• Apply trigonometry to general triangles.
##### Circles
• Understand and apply theorems involving circles.
• Find arc lengths and areas of sectors of circles.
##### Expressing Geometric Properties with Equations
• Understand and use conic sections.
• Use coordinates to verify simple geometric theorems algebraically
##### Geometric Measurement and Dimension
• Explain surface area and volume formulas and use them to solve problems.
• Visualize relationships between two-dimensional and three-dimensional objects.
##### Modeling with Geometry
• Apply geometric concepts in modeling situations

## MAT-HS.G [G] Overview: Geometry

### MAT-HS.G-SRT Domain: [G-SRT] Similarity, Right Triangles, and Trigonometry

• MAT-HS.G-SRT.01 Verify experimentally the properties of dilations
• G-SRT.01.a A line not passing through the center to a parallel line, center line unchanged
• G-SRT.01.b A line segment is longer or shorter in the ratio given by the scale factor
• MAT-HS.G-SRT.02 Use definition of similarity/transformations to see if 2 figures are similar
• MAT-HS.G-SRT.03 Use similarity transformations to establish the AA criterion for two triangles
• MAT-HS.G-SRT.04 Prove theorems about triangles
• MAT-HS.G-SRT.05 Use congruence/similarity criteria to solve problems and to prove relationships
• MAT-HS.G-SRT.06 Understand that side ratios in right triangles are properties of the angles
• MAT-HS.G-SRT.07 Explain the relationship between the sine and cosine of complementary angles
• MAT-HS.G-SRT.08 Apply trigonometric ratios and the Pythagorean Theorem to solve right triangles
• MAT-HS.G-SRT.08.a Apply trigonometric ratios and the Pythagorean Theorem to solve right triangles
• MAT-HS.G-SRT.08.b Apply trigonometric ratios and the Pythagorean Theorem to solve special triangles
• MAT-HS.G-SRT.09 Derive the formula A = 1/2 ab sin( C ) for the area of a triangle
• MAT-HS.G-SRT.10 Prove the Laws of Sines and Cosines and use them to solve problems
• MAT-HS.G-SRT.11 Apply the Law of Sines and the Law of Cosines to find unknown measurements

### MAT-HS.G-C Domain: [G-C] Circles

• MAT-HS.G-C.01 Prove all circles are similar
• MAT-HS.G-C.02 Identify and describe relationships among inscribed angles, radii, and chords
• MAT-HS.G-C.03 Construct the inscribed and circumscribed circles of a triangle
• MAT-HS.G-C.04 Construct a tangent line from a point outside a given circle to the circle
• MAT-HS.G-C.05 Show the length of the arc intercepted by an angle proportional to the radius

### MAT-HS.G-GPE Domain: [G-GPE] Expressing Geometric Properties with Equations

• MAT-HS.G-GPE.01 Use Pythagorean Theorem to derive the equation of a circle
• MAT-HS.G-GPE.02 Derive the equation of a parabola given a focus and directrix
• MAT-HS.G-GPE.03 Derive the equations of ellipses and hyperbolas given foci, using the fact
• MAT-HS.G-GPE.04 Use coordinates to prove simple geometric theorems algebraically
• MAT-HS.G-GPE.05 Prove the slope criteria for parallel and perpendicular lines
• MAT-HS.G-GPE.06 Find the point on a line between two points that partitions it in a given ratio
• MAT-HS.G-GPE.07 Use coordinates to compute perimeter of polygons, area of triangles/rectangles

### MAT-HS.G-GMD Domain: [G-GMD] Geometric Measurement and Dimension

• MAT-HS.G-GMD.01 Support formulas for circumference/area(circle) & volume(cylinder/pyramid/cone)
• MAT-HS.G-GMD.02 Give an informal argument using Cavalieri's principle for the formulas for
• MAT-HS.G-GMD.03 Use volume formulas for cylinders, pyramids, cones, and spheres
• MAT-HS.G-GMD.04 Identify the shapes of 2D cross-sections of 3D objects

### MAT-HS.G-MG Domain: [G-MG] Modeling with Geometry

• MAT-HS.G-MG.01 Use geometric shapes, measures, and properties to describe objects
• MAT-HS.G-MG.02 Apply concepts of density based on area and volume in modeling situations
• MAT-HS.G-MG.03 Apply geometric methods to solve design problems

### A Sample of HS Math Concept Geometry to Become Ready for College and Career

#### Congruence

• Experiment with transformations in the plane.
• Understand congruence in terms of rigid motions.
• Prove and apply geometric theorems.
• Make geometric constructions

#### Similarity, Right Triangles, and Trigonometry

• Understand similarity.
• Prove theorems involving similarity.
• Define trigonometric ratios and solve problems involving right triangles.
• Apply trigonometry to general triangles.

#### Circles

• Understand and apply theorems involving circles.
• Find arc lengths and areas of sectors of circles.

#### Expressing Geometric Properties with Equations

• Understand and use conic sections.
• Use coordinates to verify simple geometric theorems algebraically.

#### Geometric Measurement and Dimension

• Explain surface area and volume formulas and use them to solve problems.
• Visualize relationships between two-dimensional and three-dimensional objects.

#### Modeling with Geometry

• Apply geometric concepts in modeling situations

# Geometry

### MAT-00.G Domain: [G] Geometry

#### Identify and describe shapes (squares, circles, triangles, rectangl

• MAT-00.G.01 Describe objects using names of shapes
• MAT-00.G.02 Correctly name shapes regardless of their orientations or overall size.
• MAT-00.G.03 Identify shapes as 2D or 3D

### MAT-01.G Domain: [G] Geometry

#### Reason with shapes and their attributes.

• MAT-01.G.01 Distinguish defining attributes of shapes
• MAT-01.G.02 Compose two-dimensional and three-dimensional shapes
• MAT-01.G.03 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters

### MAT-02.G Domain: [G] Geometry

#### Reason with shapes and their attributes.

• MAT-02.G.01 Recognize and draw shapes having specified attributes
• MAT-02.G.02 Partition rectangles into rows and columns of same-size squares
• MAT-02.G.03 Partition circles and rectangles into two, three, or four equal shares

### MAT-04.G Domain: [G] Geometry

#### Draw and identify lines and angles, and classify shapes by properti

• MAT-04.G.01 Draw points, lines, segments, rays, and angles
• MAT-04.G.02 Classify 2-dimensional figures based on parallel or perpendicular lines
• MAT-04.G.03 Recognize a line of symmetry for a 2-dimensional figure

### MAT-05.G Domain: [G] Geometry

#### Graph points on the coordinate plane to solve real-world and mathem

• MAT-05.G.01 Use a pair of axes, to define the coordinates of a given point in the pla
• MAT-05.G.02 represent real-world math problems by graphing coordinate points

#### Classify two-dimensional figures into categories based on their pro

• MAT-05.G.03 Understand that attributes of a category also belong to all subcategories
• MAT-05.G.04 Classify two-dimensional figures in a hierarchy based on properties

### MAT-06.G Domain: [G] Geometry

#### Solve real-world and mathematical problems involving area, surface

• MAT-06.G.01 Find the area of triangles, quadrilaterals, and other polygons
• MAT-06.G.02 Find the volume of a right rectangular prism with fractional edge lengths
• MAT-06.G.03 Draw polygons in the coordinate plane given coordinates for the vertices
• MAT-06.G.04 Represent three-dimensional figures using nets of rectangles and triangle

### MAT-07.G Domain: [G] Geometry

#### Draw, construct, and describe geometrical figures and describe the relationships between them.

• MAT-07.G.01 Solve problems involving scale drawings of geometric figures
• MAT-07.G.02 Draw geometric shapes with given conditions
• MAT-07.G.03 Describe 2-dimensional figures that result from slicing 3-dimensional figures

#### Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

• MAT-07.G.04 Know the formulas for area and circumference of a circle
• MAT-07.G.05 Use supplementary, complementary, vertical, and adjacent angles in proble
• MAT-07.G.06 Solve real-world mathematical problems involving area, volume and surface

# [S] Statistics and Probability

Students’ prior knowledge includes:

• Students investigate patterns of association in bivariate data (grade 8)
• Students use random sampling to draw inferences about a population (grade 7)
• Students investigate chance processes and develop, use, and evaluate probability models (grade 7)
• Students develop an understanding of statistical variability (grade 6)
• Students summarize and describe distributions (grade 6)
##### Interpreting Categorical and Quantitative Data
• Summarize, represent, and interpret data on a single count or measurement variable.
• Summarize, represent, and interpret data on two categorical and quantitative variables.
• Interpret linear models.
##### Making Inferences and Justifying Conclusions
• Understand and evaluate random processes underlying statistical experiments.
• Make inferences and justify conclusions from sample surveys, experiments and observational studies.
##### Conditional Probability and the Rules of Probability
• Understand independence and conditional probability and use them to interpret data.
• Use the rules of probability to compute probabilities of compound events in a uniform probability model.
##### Using Probability to Make Decisions
• Calculate expected values and use them to solve problems.
• Use probability to evaluate outcomes of decisions.

## MAT-HS.S [S] Overview: Statistics and Probability

### MAT-HS.S-ID Domain: [S-ID] Interpreting Categorical and Quantitative Data

• MAT-HS.S-ID.01 Represent data with plots on the real number line
• MAT-HS.S-ID.02 Use statistics to compare center and spread of two or more data sets
• MAT-HS.S-ID.03 Interpret differences in shape/center/spread of data, accounting for outliers
• MAT-HS.S-ID.04 Use the mean and standard deviation of a data set for normal distribution
• MAT-HS.S-ID.05 Summarize categorical data for two categories in twoway frequency tables
• MAT-HS.S-ID.06 Represent data on two quantitative variables on a scatter plot
• S-ID.06.a Fit a function to the data to solve problems
• S-ID.06.b Informally assess the fit of a function by plotting and analyzing residuals
• S-ID.06.c Fit a linear function for a scatter plot that suggests a linear association
• MAT-HS.S-ID.07 interpret the Slope and the Intercept of a linear model in context of data
• MAT-HS.S-ID.08 Compute and interpret the correlation coefficient of a linear fit
• MAT-HS.S-ID.09 Distinguish between correlation and causation

### MAT-HS.S-IC Domain: [S-IC] Making Inferences and Justifying Conclusions

• MAT-HS.S-IC.01 Understand statistics as a process for making inferences based on random sample
• MAT-HS.S-IC.02 Decide if a model is consistent with results from a data-generating process
• MAT-HS.S-IC.03 Compare the purposes of surveys/experiments/observational studies
• MAT-HS.S-IC.04 Use data from a sample survey to estimate a population mean or proportion
• MAT-HS.S-IC.05 Use data from a randomized experiment to compare two treatments
• MAT-HS.S-IC.06 Evaluate reports based on data

### MAT-HS.S-CP Domain: [S-CP] Conditional Probability and the Rules of Probability

• MAT-HS.S-CP.01 Describe events as subsets of a sample space using characteristics
• MAT-HS.S-CP.02 Using probabilities, understand and show that two events are independent
• MAT-HS.S-CP.03 Understand the conditional probability of A given B as P(A and B)/P(B
• MAT-HS.S-CP.04 Construct and interpret two-way frequency tables of data
• MAT-HS.S-CP.05 Recognize and explain the concepts of conditional probability and independence
• MAT-HS.S-CP.06 Find the probability of A given B as the fraction of B??s outcomes belong to A
• MAT-HS.S-CP.07 Apply and interpret the Addition Rule of probability
• MAT-HS.S-CP.08 Apply the general Multiplication Rule in a uniform probability model
• MAT-HS.S-CP.09 Use permutations and combinations to compute probabilities

### MAT-HS.S-MD Domain: [S-MD] Using Probability to Make Decisions

• MAT-HS.S-MD.01 Define a random variable for a quantity of interest by assigning a numerica
• MAT-HS.S-MD.02 Calculate the expected value of a random variable; interpret it as the mean
• MAT-HS.S-MD.03 Develop a probability distribution for a random variable defined for a samp
• MAT-HS.S-MD.04 Develop a probability distribution for a random variable defined for a samp
• MAT-HS.S-MD.05 Weigh outcomes of a decision by assigning probabilities to payoff values
• S-MD.05.a Find the expected payoff for a game of chance
• S-MD.05.b Evaluate and compare strategies on the basis of expected values
• MAT-HS.S-MD.06 Use probabilities to make fair decisions
• MAT-HS.S-MD.07 Analyze decisions and strategies using probability concepts

### A Sample of HS Math Concept Statistics and Probability your child will be learning

#### Interpreting Categorical and Quantitative Data

• Summarize, represent, and interpret data on a single count or measurement variable.
• Summarize, represent, and interpret data on two categorical and quantitative variables.
• Interpret linear models.

#### Making Inferences and Justifying Conclusions

• Understand and evaluate random processes underlying statistical experiments.
• Make inferences and justify conclusions from sample surveys, experiments and observational studies.

#### Conditional Probability and the Rules of Probability

• Understand independence and conditional probability and use them to interpret data.
• Use the rules of probability to compute probabilities of compound events in a uniform probability model.

#### Using Probability to Make Decisions

• Calculate expected values and use them to solve problems.
• Use probability to evaluate outcomes of decisions.

# Measurement and Data

### MAT-01.MD Domain: [MD] Measurement and Data

#### Measure lengths indirectly and by iterating length units.

• MAT-01.MD.01 Order three objects by length
• MAT-01.MD.02 Express the length of an object as a whole number of length units

#### Tell and write time.

• MAT-01.MD.03 Tell and write time in hours and half-hours using analog and digital clocks.

#### Represent and interpret data.

• MAT-01.MD.04 Organize, represent, and interpret data with up to three categories

### MAT-02.MD Domain: [MD] Measurement and Data

#### Measure and estimate lengths in standard units.

• MAT-02.MD.01 Measure the length using appropriate tools
• MAT-02.MD.02 Measure the length of an object twice, using different length units
• MAT-02.MD.03 Estimate lengths
• MAT-02.MD.04 Measure to determine how much longer one object is than another

#### Relate addition and subtraction to length.

• MAT-02.MD.05 Add and subtract within 100 to solve word problems involving lengths
• MAT-02.MD.06 Represent whole numbers as lengths from 0 on a number line

#### Work with time and money.

• MAT-02.MD.07 Tell and write time from analog and digital clocks
• MAT-02.MD.08 Solve word problems involving dollar bills, quarters, dimes, nickels,

### MAT-03.MD Domain: [MD] Measurement and Data

#### Solve problems involving measurement and estimation of intervals o

• MAT-03.MD.01 Tell time to the nearest minute and elapsed time
• MAT-03.MD.02 Measure and estimate liquid volumes and masses of objects

#### Represent and interpret data.

• MAT-03.MD.03 Draw a picture/bar graph to represent data and Solve problem
• MAT-03.MD.04 Generate measurement data by measuring with rulers

#### Geometric measurement: understand concepts of area and relate area

• MAT-03.MD.05 Recognize area as an attribute of plane figures
• MAT-03.MD.06 Measure areas by counting unit squares
• MAT-03.MD.07 Relate area to the operations of multiplication and addition

#### Geometric measurement: recognize perimeter as an attribute of plan

• MAT-03.MD.08 Solve real-world math problems involving perimeters of polygons

### MAT-04.MD Domain: [MD] Measurement and Data

#### Solve problems involving measurement and conversion of measurement

• MAT-04.MD.01 Know relative sizes of units within one system of measurement
• MAT-04.MD.02 Solve word problems involving distance, time, volume, mass, and money
• MAT-04.MD.03 Apply the area and perimeter formulas for rectangles in real-world pr

#### Represent and interpret data.

• MAT-04.MD.04 Make a line plot to display data of measurements in fractions of a un

#### Geometric measurement: understand concepts of angle and measure an

• MAT-04.MD.05 Recognize angles as shapes formed where two rays share a common endpo
• MAT-04.MD.06 Measure angles in whole-number degrees using a protractor
• MAT-04.MD.07 Recognize angle measure as additive

### MAT-05.MD Domain: [MD] Measurement and Data

#### Convert like measurement units within a given measurement system.

• MAT-05.MD.01 Convert among different-sized standard measurement units

#### Represent and interpret data.

• MAT-05.MD.02 Make a line plot to display measurements in fractions of a unit

#### Geometric measurement: understand concepts of volume and relate vo

• MAT-05.MD.03 Understand concepts of volume measurement
• MAT-05.MD.04 Measure volumes using cubic cm, cubic in, cubic ft, and improvised un
• MAT-05.MD.05 multiply and add to Solve real-world math problems involving volume

# Statistics and Probability

### MAT-06.SP Domain: [SP] Statistics and Probability

#### Develop understanding of statistical variability.

• MAT-06.SP.01 Recognize that statistical questions anticipate variability and account
• MAT-06.SP.02 Understand that a set of statistical data has a distribution
• MAT-06.SP.03 Recognize measures of center and variation for numerical data

#### Summarize and describe distributions.

• MAT-06.SP.04 Display numerical data in plots on a number line
• MAT-06.SP.05 Summarize numerical data sets in relation to their context

### MAT-07.SP Domain: [SP] Statistics and Probability

#### Use random sampling to draw inferences about a population.

• MAT-07.SP.01 Understand statistics used to gain information about a population by sam
• MAT-07.SP.02 Use data from a random sample to draw inferences about a population
• MAT-07.SP.03 Assess overlap of two distributions, measuring the difference of the cen
• MAT-07.SP.04 Use measures of center and variability to compare two populations

#### Investigate chance processes and develop, use, and evaluate probability models.

• MAT-07.SP.05 Understand that the probability of a chance event is a number between 0
• MAT-07.SP.06 Approximate the probability of a chance event
• MAT-07.SP.07 Develop a probability model and Use it to Find probabilities of events
• MAT-07.SP.08 Find probabilities of events using lists, tables, tree diagrams, and sim
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