# Math Standards

Our trimester home reports indicate a student’s progress toward mastery of the standards identified as benchmarks for each grade level.  This progress is reported under topic headings called “power standards.”

Listed below are some sub-domains in Mathematics that help explain what is assessed under each of those power standards.  For more detailed information, please consult with your child’s homeroom teacher.

Mathematical Practices

• 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.

Counting and Cardinality

• Know number names and the count sequence.
• Count to 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.

Mathematical Practices

• 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.

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.

Mathematical Practices

• 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.

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.

Mathematical Practices

• 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.

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.

Mathematical Practices

• 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.

Operations and Algebraic Thinking

• 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

• 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.

Mathematical Practices

• 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.

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.

Mathematical Practices

• 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.

Geometry

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

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.
• Multiply and divide 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.

Statistics and Probability

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

Mathematical Practices

• 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.

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.

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.

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.

Mathematical Practices

• 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.

The Number System

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

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.

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.

Statistics and Probability

• Investigate patterns of association in bivariate data.