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Number Operations
Kindergarten

Core Ideas

  • Understand the meanings of operations and how they relate to each other, make reasonable estimates, and compute fluently.
  • Develop an understanding of the different meanings of addition and subtraction of whole numbers.
  • Understand the effects of adding and subtracting whole numbers.
  • Develop relationships within addition and subtraction combinations.
  • Develop and use strategies to estimate.
 
1st Grade

Core Ideas

  • Understand the meanings of operations and how they relate to each other, make reasonable estimates, and compute fluently.
  • Develop an understanding of the different meanings of addition and subtraction of whole numbers and the relationship between the two operations.
  • Develop fluency in adding and subtracting whole numbers within 20.
  • Develop and use strategies to estimate and calculate.
  • Begin to develop an understanding of the concepts of multiplication and division through situations such as equal groupings of objects and equal sharing.
 
2nd Grade

Core Ideas

  • Understand the meanings of operations and how they relate to each other, make reasonable estimates, and compute fluently.
  • Demonstrate fluency in adding and subtracting whole numbers.
  • Use strategies to estimate and judge the reasonableness of results.
  • Understand situations that entail multiplication and division such as equal groupings of objects and equal sharing.

MARS Tasks

Apple Farm Field Trip

  • See Related Classroom Video Visit: Word Problem Clues
    Tracy Lewis leads a re-engagement lesson on the language of word problems, helping students to use word clues to identify mathematical operations. Students explore errors and strategies as they look together at student work. In addition to the lesson, the multimedia documentation of Tracy Lewis's teaching includes a pre-teaching planning conversation with Anthony Rogers, Leslie Thornley, and Camille Paris, and a follow-up faculty debrief with observing teachers. VIDEO >>

Pocket Money

Carol's Numbers

 
3rd Grade

Core Ideas

  • Understand the meanings of operations and how they relate to each other, make reasonable estimates, and compute fluently.
  • Understand different meanings of addition and subtraction of whole numbers and the relationship between the two operations.
  • Understand the effects of adding and subtracting whole numbers.
  • Understand multiplication as repeated addition, an area model, an array, and an operation on scale.
  • Develop fluency in adding and subtracting whole numbers.
  • Develop and use strategies to estimate and judge the reasonableness of results.
  • Solve problems involving dollars and cents.

MARS Tasks

The Pet Shop

 
4th Grade

Core Ideas

  • Understand the meanings of operations and how they relate to each other, make reasonable estimates, and compute fluently.
  • Understand division as the inverse operation of multiplication, the operation of sharing (partitive), partitioning (measurement), repeated subtraction, and an operation to determine rates.
  • Develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems.
  • Develop fluency in multiplying whole numbers.

MARS Tasks

Winning Lines

 
5th Grade

Core Ideas

  • Understand the meanings of operations and how they relate to each other, make reasonable estimates, and compute fluently.
  • Develop fluency in dividing whole numbers.
  • Understand the meaning of remainders by modeling division problems.
  • Reason about and solve problem situations that involve more than one operation in multi-step problems.
  • Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals.
  • Develop and use strategies to solve problems involving number operations with fractions and decimals relevant to students’ experience.

MARS Tasks

Candies

  • See Related Classroom Video Visit: Proportions & Ratios
    Hillary Lewis-Wolfsen leads students through a re-engagement activity identifying strong strategies for approaching a "candies" assessment created by the Mathematics Assessment Resource Service (MARS). In addition to an hour-long lesson, the multimedia documentation of Lewis-Wolfsen's teaching includes a pre-teaching planning conversation with Carolyn Dobson and Linda Fisher, and a follow-up faculty debrief with observing teachers. VIDEO >>

 
6th Grade

Core Ideas

  • Understand number systems, the meanings of operations, and ways of representing numbers, relationships, and number systems.
  • Understand fractions, decimals, and percents as parts of whole units and as parts of a collection.
  • Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.
  • Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line.
  • Understand the meaning and effects of operations with fractions and decimals.
  • Use factors, multiples, prime factorization, and relatively prime numbers to solve problems.
  • Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators, and paper-and-pencil, depending on the situation, and apply selected methods.
  • Develop and analyze algorithms for operations on fractions and decimals, and develop fluency in their use.
  • Understand and use proportional reasoning to represent quantitative relationships.
  • Understand and use the associative and commutative properties of addition to simplify computations with fractions, decimals, and whole numbers.

MARS Tasks

Gym

 
7th Grade

Core Ideas

  • Understand number systems, the meanings of operations, and ways of representing numbers, relationships, and number systems.
  • Develop, analyze, and explain methods for solving problems involving proportional reasoning, such as scaling and finding equivalent ratios.
  • Develop meaning of integers and represent and compare quantities with them.
  • Understand the meaning and effects of operations with rational numbers.
  • Understand and use the inverse relationships of a series of operations to simplify computations and solve problems.
  • Develop and analyze algorithms for computing with rational numbers.
  • Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with rational numbers.
  • Develop and use strategies to estimate the results of rational number computations, and judge the reasonableness of results.
  • Work flexibly with fractions, decimals, and percents to solve problems.
 
8th Grade

Core Ideas

  • Understand number systems, the meanings of operations, and ways of representing numbers, relationships, and number systems.
  • Develop meaning for percents greater than 100 and less than 1.
  • Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation.
  • Understand and use the inverse relationships of squaring and finding square roots to simplify computations and solve problems.
  • Demonstrate how and when to use the operations of exponents and roots.
  • Compare and contrast the properties of rational and irrational numbers.
 


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