Home  →  Academic Standards 2023-24  →  Mathematics

# Mathematics

### Mathematics practices

#### Students will:

• make sense of problems and persevere in solving them;
• reason abstractly and quantitatively;
• construct viable arguments, and appreciate 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.

### Mathematics contents

#### Kindergarten

• Counting and Cardinality
• Know number names and the count sequence.
• Tell the number of objects.
• Compare numbers.
• Operations and Algebraic Thinking
• Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
• Number and Operations in Base Ten
• Work with numbers 11-19 to gain foundations for place value.
• Measurement and Data
• Describe and compare measurable attributes.
• Classify objects and count the number of objects in each category.
• Geometry
• Identify and describe shapes.
• Analyze, compare, create, and compose shapes.

• Operations and Algebraic Thinking
• Represent and solve problems involving addition and subtraction.
• Understand and apply properties of operations and the relationship between addition and subtraction.
• Add and subtract within 20.
• Work with addition and subtraction equations.
• Number and Operations in Base Ten
• Extend the counting sequence.
• Understand place value.
• Use place value understanding and properties of operations to add and subtract.
• Measurement and Data
• Measure lengths indirectly and by iterating length units.
• Tell and write time.
• Represent and interpret data.
• Geometry
• Reason with shapes and their attributes.

• Operations and Algebraic Thinking
• Represent and solve problems involving addition and subtraction.
• Add and subtract within 20.
• Work with equal groups of objects to gain foundations for multiplication.
• Number and Operations in Base Ten
• Understand place value.
• Use place value understanding and properties of operations to add and subtract.
• Measurement and Data
• Measure and estimate lengths in standard units.
• Relate addition and subtraction to length.
• Work with time and money.
• Represent and interpret data.
• Geometry
• Reason with shapes and their attributes.

• Operations and Algebraic Thinking
• 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
• Use place value understanding and properties of operations to perform multi-digit arithmetic.
• Number and Operations—Fractions
• Develop understanding of fractions as numbers.
• Measurement and Data
• 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
• Reason with shapes and their attributes.

• Operations and Algebraic Thinking
• Use the four operations with whole numbers to solve problems.
• Gain familiarity with factors and multiples.
• Generate and analyze patterns.
• Multiply and divide within 100.
• Number and Operations in Base Ten
• Generalize place value understanding for multi-digit whole numbers.
• Use place value understanding and properties of operations to perform multi-digit arithmetic.
• Number and Operations—Fractions
• 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
• 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
• Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

• Operations and Algebraic Thinking
• Write and interpret numerical expressions.
• Analyze patterns and relationships.
• Number and Operations in Base Ten
• Understand the place value system.
• Perform operations with multi-digit whole numbers and with decimals to hundredths.
• Number and Operations—Fractions
• 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
• 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
• Graph points on the coordinate plane to solve real-world and mathematical problems.
• Classify two-dimensional figures into categories based on their properties.

• Ratios and Proportional Relationships
• Understand ratio concepts and use ratio reasoning to solve problems.
• The Number System
• Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
• Flexibly and efficiently compute 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
• 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
• Solve real-world and mathematical problems involving area, surface area, and volume.
• Statistics and Probability
• Develop understanding of statistical variability.
• Summarize and describe distributions.

• Ratios and Proportional Relationships
• Analyze proportional relationships and use them to solve real-world and mathematical problems.
• The Number System
• Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
• Expressions and Equations
• Use properties of operations to generate equivalent expressions.
• Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
• Geometry
• 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
• 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.

• The Number System
• Know that there are numbers that are not rational, and approximate them by rational numbers.
• Expressions and Equations
• 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
• Define, evaluate, and compare functions.
• Use functions to model relationships between quantities.
• Geometry
• 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
• Investigate patterns of association in bivariate data.

#### Grades 9-12 – Number and Quantity Overview

• 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.

• Seeing Structure in Expressions
• Interpret the structure of expressions.
• Write expressions in equivalent forms to solve problems.
• Arithmetic with Polynomials and Rational Expressions
• 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
• 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.

• Interpreting Functions
• Understand the concept of a function and use function notation.
• Intercept 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.

• Congruence
• Experiment with transformations in the plane.
• Understand congruence in terms of rigid motions.
• Prove geometric theorems.
• Make geometric constructions.
• Similarity, Right Triangles, and Trigonometry
• Understand similarity in terms of similarity transformations.
• Prove theorems involving similarity.
• Define trigonometric ratios and solve problems involving right triangles.
• Apply trigonometry to general triangles.
• Circles
• Understand and apply theorems about circles.
• Find arc lengths and areas of sectors of circles.
• Expressing Geometric Properties with Equations
• Translate between the geometric description and the equation for a conic section.
• Use coordinates to prove simple geometric theorems algebraically.
• Geometric Measurement and Dimension
• Explain 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.

#### Grades 9-12 – Statistics and Probability

• 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.