A Number Sense Game for 5.NF.5

So, I am the project manager for a special task force commissioned by the GA Department of Education.  In short, our job is to create and produce videos that will help K-12 math teachers better understand and teach particular math standards.  The specific standards for each grade level were identified by GA teachers themselves.

One of the standards identified in Grade 5 is 5.NF.5, which states, “Interpret multiplication as scaling (resizing).”  Basically, students need to understand that multiplication is not just about repeated addition, but that it can also be represented as comparison, in terms of scaling.

What I love about the actual language of the standard most is this line: “[Compare] the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication (italics added).”

So, in other words, use number sense and estimation – not recall of a procedure.

Recently, Jason D’arcangelo, one of the 5th grade video producers, asked me if I knew of any fun, engaging, and novel resources for this standard.  The first thing that came to mind is this gem from NCTM Illuminations.  However, it also integrates the other 3 operations, and decimals too.

So, I started searching.  And I found nothing.

Plan B?  Stand on the shoulders of a giant.  Marilyn Burns, to be exact.

I went to her book, Lesson for Multiplying and Dividing Fractions, Grades 5-6, which is part of the Teaching Arithmetic series.  And I found a game called “The Multiplying Game”.  This game is essentially like “war”, but the objective is to create a fraction multiplication expression that yields a smaller product than your opponent.  Not exactly what I wanted.  But, my wheels were spinning.

I started brainstorming how I could modify this to capture the spirit of 5.NF.5, and this is what I came up with.

Full disclaimer, though – I haven’t “piloted” it with real kids in real classrooms.  So, this is where I’d love your help.

Give this a try with your students and let me know how to make it better.

Materials Needed:
Deck of Playing Cards (J, Q, K removed)
Spinner (homemade with pencil and paper clip)

Calculator (preferably one that allows the user to enter fractions) optional

1. Player 1 chooses 5 cards from the deck at one time, and then spins the spinner below.


2. Player 1 must choose 4 of the 5 numbers on the cards to enter into the expression template on the gamemat.  The objective is to create an equation that matches the condition selected on the spinner.

  • For example, Player 1 draws the following: 5, 6, 4, Ace (1), 6
  • Player 1 spins and lands on “The product is GREATER than both factors”.
  • Player 1 chooses to “reject” one of the 6s, and uses the following numbers: 5, 6, 4, 1 in the following way:Example
  • Player 2 verifies that Player 1 is correct.  Calculator may be used at this step.
  • Players alternate taking turns, repeating these steps.

    Alternate Rule

  • Player 2 draws only 4 cards and must use Player 1’s rejected card.  This rule continues with every turn.

Special thanks to Mike Wiernicki for providing input and making this game better!



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