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Standards-based assessment and Instruction

Summative Assessment Task: Grade K




Two Bowls


Michael has two bowls. Michael has five apples. Michael wants to put the five apples in the two bowls. Michael finds two different ways to put the five apples in the two bowls. What are two different ways Michael could have put the five apples in the two bowls? Show and tell how you know.


Composing and Decomposing Numbers Unit

The Composing and Decomposing Numbers Unit involves conceptualizing whole numbers in terms of their parts which builds flexible thinking, number sense and the foundation for addition and subtraction. Questions to answer might include–

  • How many different ways can you show five with the fingers on both hands?
  • How will you know when you have found all the ways?
  • Why is it important to find different combinations (ways) to build ten?
  • Did you see any patterns when you showed the combinations for ___?

Math Concepts and Skills Covered

The student develops strategies for whole number addition and subtraction in order to solve problems.

  • The student composes and decomposes numbers up to 10 with objects and pictures.

Exemplars Task-Specific Evidence

This task requires students to decompose numbers equal to five into pairs in more than one way.

Underlying Mathematical Concepts

  • Number sense to 5
  • Decomposing with 5s Combinations/Commutative Property
  • Counting on/Addition

Possible Problem-Solving Strategies

  • Model (manipulatives: bowls/apples, blocks/grid paper)
  • Diagram/Key
  • Tally chart
  • Ten frame (can be provided)
  • Table
  • Organized list

Formal Mathematical Language and Symbolic Notation

  • Model
  • Diagram/Key
  • Tally chart
  • Organized list
  • Combinations
  • Commutative Property
  • Equation
  • More than (>)/Greater than (>)/Less than (<)
  • Equivalent/Equal to
  • Odd/EvenTotal/Sum
  • Equal shares
  • Amount
  • Sets
  • Per
  • Pattern
  • Column
  • Rule

Possible Solutions

Student shows 2 combinations of 5, but not 0 + 5, 5 + 0.

Scoring Rationales and Corresponding Anchor Papers




Possible Connections

Below are some examples of mathematical connections. Your students may discover some that are not on this list.

  • All 4 combinations are found.
  • Can not use 0 + 5, 5 + 0 because apples must be in both bowls.
  • This is the Commutative Property: 2 + 3 = 3 + 2 or 4 + 1 = 1 + 4.
  • There are no equal amount of apples per bowl, 5 is an odd number.
  • Each combination has 1 bowl of odd number of apples/1 bowl even number of apples.
  • Increasing/decreasing pattern in table columns and diagrams is shown.
  • Relate to a similar task and state a math link.
  • Solve more than one way to verify the answer.
  • First combination: 3 less apples in bowl 1 than 2, 1 + 4 = 5, etc.
  • Rule: Odd + Even = Odd and Even + Odd = Odd.

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Here's What People Are Saying

The Exemplars program is designed to assess students' problem-solving and mathematical-communication skills. It also supports higher-level thinking and extension of mathematical reasoning.

S. Dement

Converse, TX

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