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Standards-based assessment and Instruction

Instructional Task: Grade K

Markers and Cans

Task

Nick has seven markers. Nick has two cans. Nick wants to put all the markers in two cans. What are four ways Nick could put the seven markers in the two cans? Show and tell how you know.

Alternative Versions of Task

More Accessible Version

Nick has seven markers. Nick has two cans. Nick wants to put all the markers in two cans. What are two ways Nick could put the seven markers in the two cans? Show and tell how you know.

More Challenging Version

Nick has seven markers. Nick has two cans. Nick wants to put all the markers in two cans. What are all the different ways Nick could put the seven markers in the two cans? 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 seven into pairs in more than one way. Students also need to recognize the meaning of a "pair."

Underlying Mathematical Concepts

  • Number sense to 7
  • Decomposing with 7, Combinations (Commutative Property)
  • Counting on/Addition

Possible Problem-Solving Strategies

  • Model (manipulatives: blocks on grid paper/markers + cans)
  • Diagram/Key
  • Tally chartTable
  • Organized list

Possible Mathematical Vocabulary/Symbolic Representation

  • Model
  • Diagram/Key
  • Tally chart
  • Table
  • Organized list
  • Combination
  • Group/Set
  • Commutative Property
  • Odd/Even
  • Total/Sum
  • Amount
  • Equal shares
  • Equation
  • Pattern
  • More than (>)/Greater than (>)/Less than (<)
  • Equivalent/Equal to
  • Set
  • Per
  • Columns

Possible Solutions

Student correctly shows any 4 of the 6 possible combinations.

More Accessible Version Solution

See solutions to original task.

More Challenging Version Solution

See solutions to original task.

Possible Connections

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

  • There are 6 possible combinations for Nick to make.
  • No combination has an equal amount in each can.
  • You can not use 0 markers in either can.
  • Each combination has an even number of markers in a can and an odd number in a can.
  • Relate to a similar task and state a math link.
  • Solve more than one way to verify the answer.
  • There are 5 more markers in can 2 than can 1, etc.
  • Student notes increasing/decreasing pattern in table columns and in diagram of cans.

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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
Teacher

Converse, TX

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