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Standards-based assessment and Instruction

Instructional Task: Grade 3

 

 

 

 

Pom-Poms

Task

Amy is in a craft store looking at packages of pom-poms. Amy sees packages of four red pom-poms. Amy sees packages of seven red pom-poms. Amy says she can buy seven packages of four pom-poms or four packages of seven pom-poms because she will get the same total of pom-poms. Is Amy correct? Show all your mathematical thinking.

Alternative Versions of Task

More Accessible Version

Amy is in a craft store looking at packages of pom-poms. Amy sees packages of four red pom-poms. Amy sees packages of three red pom-poms. Amy says she can buy three packages of four pom-poms or four packages of three pom-poms because she will get the same amount of pom-poms. Is Amy correct? Show all your mathematical thinking.

More Challenging Version

Amy is in a craft store looking at packages of pom-poms. Amy sees packages of four red pom-poms for fifty cents. Amy sees packages of seven red pom-poms for seventy-five cents. Amy says she can buy seven packages of four pom-poms or four packages of seven pom-poms because she will get the same amount of pom-poms. Is Amy correct? Which packages of pom-poms would be the better buy? Show all your mathematical thinking.

Multiplication Unit

The Multiplication Unit involves identifying a variety of models to represent the process of multiplication in order to learn how to use it to solve problems. Questions to answer may include:

  • How do multiplication situations differ from addition situations?
  • How do equal-sized groups model multiplication situations in the world outside of the classroom? What real-world examples of equal-sized groups can you think of?
  • How do arrays and area models represent multiplication situations in the world outside of the classroom? What real-world examples of arrays can you think of?
  • Given a multiplication equation, how can you create a situation to match it?

Math Concepts and Skills Covered

The student develops and uses strategies for multiplying whole numbers in order to solve problems. The student:

  • Finds the total number of objects when equal-sized groups of objects are joined or arranged in arrays up to 10 by 10.
  • Represents multiplication facts using a variety of methods.
  • Uses a variety of strategies to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties.

Exemplars Task-Specific Evidence

This task requires the students to know that multiplication involves finding the whole when they know the number of equal parts and the number in each part. Students must also be familiar with a variety of models to represent multiplication situations such as equal groups, rectangular arrays and/or equal jumps on a number line.

Underlying Mathematical Concepts

  • Creating multiplication situations to match an expression
  • Finding the product when both factors are known
  • Commutative Property
  • Number sense to 28

Possible Problem-Solving Strategies

  • Model (manipulatives)
  • Diagram/Key
  • Tally chart
  • Table
  • Arrays
  • Number line

Possible Mathematical Vocabulary/Symbolic Representation

  • Model
  • Diagram/Key
  • Tally chart
  • Table
  • Number line
  • Array
  • Product
  • Factor
  • Set
  • Total/Sum 
  • Dozen
  • Greater than (>)/Less than (<)
  • Equivalent/Equal to
  • Odd/Even
  • Equation
  • Expression
  • Row/Column
  • Rule
  • Variable

Possible Solutions

Amy is correct because 4 x 7 = 7 x 4.

More Accessible Version Solution

Amy is correct because 4 x 3 = 3 x 4.

More Challenging Version Solution

Amy is correct. 4 packages of 7 pom-poms is a better buy because they cost $3.00. 7 packages of 4 pom-poms will cost $3.50.

Possible Connections

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

  • Patterns in table: Packages +1, Pom-poms +7 or +4.
  • The +4 pom-pom pattern is always even.
  • The +7 pom-pom pattern is odd, even, odd, even ...
  • When you add equal groups on a number line, you jump over the same number of spaces each time moving to the right, away from 0.
  • The number of equal sets of 4 is extended beyond 7.
  • The number of equal sets of 7 is extended beyond 4.
  • Solve more than one way to verify the answer.
  • Relate to a similar task and state a math link.
  • 4 is an even number. 7 is an odd number. An even number times an odd number is an even number.

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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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