# State Standards

## Kindergarten State Standards

**Counting and Cardinality (CC)**

- Know number names and the count sequence.
- Count to 100
- Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

- Count to tell the number of objects.
- Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

- Compare numbers.
- Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

**Operations and Algebraic Thinking (OA)**

- Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

- Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
- Fluently add and subtract within 5.

**Number and Operations in Base Ten (NBT)**

- Work with numbers 11–19 to gain foundations for place value.
- Group numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation

**Measurement and Data (MD)**

- Describe and compare measurable attributes.
- Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

- Classify objects and count the number of objects in categories.
- Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

- Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

**Geometry (G)**

- Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
- Correctly name shapes regardless of their orientations or overall size.

- Analyze, compare, create, and compose shapes.
- Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

## 1st Grade State Standards

**Operations and Algebraic Thinking (OA)**

- Represent and solve problems involving addition and subtraction.
- Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

- Understand and apply properties of operations and the relationship between addition and subtraction.
- Understand subtraction as an unknown-addend problem.
*For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.*

- Understand subtraction as an unknown-addend problem.
- Add and subtract within 20.
- Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

- Work with addition and subtraction equations.
- Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.
*For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.*

- Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

**Number and Operations in Base Ten (NBT)**

- Extend the counting sequence.
- Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

- Understand place value.
- Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

- Use place value understanding and properties of operations to add and subtract.

- Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

**Measurement and Data (MD)**

- Tell and write time.
- Tell and write time in hours and half-hours using analog and digital clocks.

- Represent and interpret data.

**Geometry (G)**

- Reason with shapes and their attributes.

Partition circles and rectangles into two and four equal shares, describe the shares using the words *halves*, *fourths*, and *quarters*, and use the phrases *half of*, *fourth of*, and *quarter of*. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

## 2nd Grade State Standards

**Operations and Algebraic Thinking (OA)**

- Represent and solve problems involving addition and subtraction.
- Take-from example: David had 63 stickers. He gave 37 to Susan. How many stickers does David have now? 63 – 37 = ?
- Add to example: David had $37. His grandpa gave him some money for his birthday. Now he has $63. How much money did David’s grandpa give him? $37 + ? = $63

- Add and subtract within 20.
- Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers

**Number and Operations in Base Ten (NBT)**

- Understand place value.
- Count within 1000; skip-count by 5s, 10s, and 100s.

- Use place value understanding and properties of operations to add and subtract.
- Add up to four two-digit numbers using strategies based on place value and properties of operations.

**Measurement and Data (MD)**

- Measure and estimate lengths in standard units.

- Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

- Work with time and money.
- Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.
*Example: If you have 2 dimes and 3 pennies, how many cents do you have?*

- Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.
- Represent and interpret data.

**Geometry (G)**

- Reason with shapes and their attributes.
- Cut a rectangle into rows and columns of same-size squares and count to find the total number of them.

## 3rd Grade State Standards

**Operations and Algebraic Thinking (OA)**

- Represent and solve problems involving multiplication and division.
- Understand properties of multiplication and the relationship between multiplication and division.
- Multiply and divide within 100.
- Solve problems involving the four operations, and identify and explain patterns in arithmetic.

**Number and Operations in Base Ten (NBT)**

- Use place value understanding and properties of operations to perform multi-digit arithmetic.

**Number and Operations—Fractions (NF)**

- Develop understanding of fractions as numbers.

**Measurement and Data (MD)**

- Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
- Represent and interpret data.
- Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
- Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

**Geometry (G)**

Reason with shapes and their attributes.

**Mathematical Practices (MP)**

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

## 4th Grade State Standards

**Operations and Algebraic Thinking (OA)**

- Use the four operations with whole numbers to solve problems.
- Gain familiarity with factors and multiples.
- Generate and analyze patterns.

**Number and Operations in Base Ten (NBT)**

- Generalize place value understanding for multidigit whole numbers.
- Use place value understanding and properties of operations to perform multi-digit arithmetic.

**Number and Operations—Fractions (NF)**

- Extend understanding of fraction equivalence and ordering.
- Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
- Understand decimal notation for fractions, and compare decimal fractions.

**Measurement and Data (MD)**

- Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
- Represent and interpret data.
- Geometric measurement: understand concepts of angle and measure angles.

**Geometry (G)**

- Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

**Mathematical Practices (MP)**

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

## 5th Grade State Standards

**Operations and Algebraic Thinking (OA)**

- Write and interpret numerical expressions.
- Analyze patterns and relationships.

**Number and Operations in Base Ten (NBT)**

- Understand the place value system.
- Perform operations with multi-digit whole numbers and with decimals to hundredths.

**Number and Operations—Fractions (NF)**

- Use equivalent fractions as a strategy to add and subtract fractions.
- Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

**Measurement and Data (MD)**

- Convert like measurement units within a given measurement system.
- Represent and interpret data.
- Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

**Geometry (G)**

- Graph points on the coordinate plane to solve real-world and mathematical problems.
- Classify two-dimensional figures into categories based on their properties.

**Mathematical Practices (MP)**

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

## 6th Grade State Standards

**Ratios and Proportional Relationships (RP)**

- Understand ratio concepts and use ratio reasoning to solve problems.

**The Number System (NS)**

- Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- Compute fluently with multi-digit numbers and find common factors and multiples.
- Apply and extend previous understandings of numbers to the system of rational numbers.

**Expressions and Equations (EE)**

- Apply and extend previous understandings of arithmetic to algebraic expressions.
- Reason about and solve one-variable equations and inequalities.
- Represent and analyze quantitative relationships between dependent and independent variables.

**Geometry (G)**

- Solve real-world and mathematical problems involving area, surface area, and volume.

**Statistics and Probability (SP)**

- Develop understanding of statistical variability.
- Summarize and describe distributions.

**Mathematical Practices (MP)**

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

## 7th Grade State Standards

**Ratios and Proportional Relationships (RP)**

- Analyze proportional relationships and use them to solve real-world and mathematical problems.

**The Number System (NS)**

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

**Expressions and Equations (EE)**

- Use properties of operations to generate equivalent expressions.
- Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

**Geometry (G)**

- Draw, construct and describe geometrical figures and describe the relationships between them.
- Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

**Statistics and Probability (SP)**

- Use random sampling to draw inferences about a population.
- Draw informal comparative inferences about two populations.
- Investigate chance processes and develop, use, and evaluate probability models.

**Mathematical Practices (MP)**

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

## 8th Grade State Standards

**The Number System (NS)**

- Know that there are numbers that are not rational, and approximate them by rational numbers.

**Expressions and Equations (EE)**

- Work with radicals and integer exponents.
- Understand the connections between proportional relationships, lines, and linear equations.
- Analyze and solve linear equations and pairs of simultaneous linear equations.

**Functions (F)**

- Define, evaluate, and compare functions.
- Use functions to model relationships between quantities.

**Geometry (G)**

- Understand congruence and similarity using physical models, transparencies, or geometry software.
- Understand and apply the Pythagorean Theorem.
- Solve real-world and mathematical problems involving volume of cylinders, cones and spheres.

**Statistics and Probability (SP)**

- Investigate patterns of association in bivariate data

**Mathematical Practices (MP)**

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

## High School State Standards

**Number and Quantity**

- The Real Number System (N-RN)
- Quantities (N-Q)
- The Complex Number System (N-CN)
- Vector and Matrix Quantities (N-VM)

**Algebra**

- Seeing Structure in Expressions (A-SSE)
- Arithmetic with Polynomials and Rational Expressions (A-APR)
- Creating Equations (A-CED)
- Reasoning with Equations and Inequalities (A-REI)

**Functions**

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

**Geometry**

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

**Modeling**

**Statistics and Probability**

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

**Contemporary Mathematics**

- Discrete Mathematics (CM-DM)

**Mathematical Practices (MP)**

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.