Kindergarten

Deliverable Skills

  • Know number names and the count sequence.
  • Count to tell the number of objects.
  • Compare numbers.
  • Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
  • Work with numbers 11–19 to gain foundations for place value.
  • Describe and compare measurable attributes.
  • Classify objects and count the number of objects in categories.
  • Identify and describe shapes. 
  • Analyze, compare, create, and compose shapes.

1st Grade

Deliverable Skills

  • 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.
  • Extend the counting sequence.
  • Understand place value. 
  • Use place value understanding and properties of operations to add and subtract.
  • Measure lengths indirectly and by iterating length units.
  • Tell and write time.
  • Represent and interpret data.
  • Reason with shapes and their attributes.

2nd Grade

Deliverable Skills

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

3rd Grade

Deliverable Skills

  • 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.
  • Use place value understanding and properties of operations to perform multi-digit arithmetic.
  • Develop understanding of fractions as numbers.
  • 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.
  • Reason with shapes and their attributes

4th Grade

Deliverable Skills

  • Use the four operations with whole numbers to solve problems.
  • Gain familiarity with factors and multiples.
  • Generate and analyze patterns. 
  • Generalize place value understanding for multi-digit whole numbers.
  • Use place value understanding and properties of operations to perform multi-digit arithmetic.
  • 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.
  • 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.
  • Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

5th Grade

Deliverable Skills

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

6th Grade

Deliverable Skills

  • Understand ratio concepts and use ratio reasoning to solve problems.
  • 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.
  • 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.
  • Solve real-world and mathematical problems involving area, surface area, and volume.
  • Develop understanding of statistical variability.
  • Summarize and describe distributions.

7th Grade

Deliverable Skills

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

8th Grade

Deliverable Skills

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