Gain Some, Lose Some – fraction multiplication as scaling game and printables

Rogue Algorithm
Grade Levels
4th - 6th
Resource Type
Formats Included
  • PDF
13 pages
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Rogue Algorithm


Multiplying makes things bigger, right? This is what my kids always think – as I’m sure yours do as well. Of course, this causes quite a problem when they start to work with multiplying fractions, where the “rules” they have learned for multiplication don’t seem to apply!

This set, including a game and printables, focuses on how the size of factors determines the size of the product. The game will keep your kids engaged while providing them valuable practice with reasoning about the size of a product when multiplying with fractions and whole numbers. Reference sheets and assessments allow you to reinforce, maintain, and assess your students’ understanding of this key fraction concept.

NOTE: This product is also available in my Scaling Fractions bundle with two other products that focus on fraction multiplication as well as a bonus ppt quiz only available in the bundle. Save 20% by purchasing all of the products in the bundle!

Common Core State Standards for Mathematics addressed:
Numbers and Operations – Fractions (5.NF)
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Interpret multiplication as scaling (resizing), by:
• Comparing 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. (5.NF.5a)
• Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by 
a fraction less than 1 results in a product less than the given number; and relating the principle of fraction equivalence a/b = (n x a)/(n x b) to the effect of multiplying a/b by 1. (5.NF.5b)


Fraction concepts are a major focus of the Common Core State Standards for Math in intermediate grades, and the expectations of elementary students in terms of what they understand about fractions is (in many instances) significantly more advanced than what was expected of them pre-Common Core. By the end of fifth grade, students are expected to have mastered multiplication and division of fractions, concepts that, before now, many students were not even exposed to until middle school.

One of the challenges I have found with helping students master fraction concepts is that some rules and procedures for analyzing and working with fractions are the same as those used with whole numbers, and others are different. Bigger numbers mean bigger value, right? Not when they are the denominators! My students faced another example of the counter-intuitive nature of fractions when we began working with fraction multiplication. For years, they have been told that when you multiply two numbers, you get a bigger number. [Of course, this is not technically true even of all whole numbers, but that’s a math misconception for another day!] Welcome to multiplication with fractions and mixed numbers, where sometimes the product is greater than both factors, sometimes the product is greater than just one factor, and sometimes the product is actually less than both factors. Throw in the fact that you can multiply by a fraction and have a number equal to one of the factors, and you have a recipe for some confused students.

• 2 reference sheets (full sheet and flipbook versions)
• game & recording sheet
• 3 assessment activities and scoring guide/rubric

Introducing the Concept

Included among the printables are a full-page graphic reference sheet and a foldable reference sheet. These references can be the starting point for an introduction or a review of the concepts addressed by the game.

The full-page reference sheet presents an overview of how the size of a product relates to the size of the factors used. It provides examples of equations in which the product is less than both factors, greater than both factors, less than one factor and equal to the other, and equal to one factor.

The foldable, like the full-page reference sheet, is designed to be glued in your students’ journals. The students will end up with four flaps, each of which can be lifted to reveal to describe the results of multiplying with fractions less than one, fractions equal to one, and numbers greater than one. My students love it when I use these flipbook-style journal inserts, and I think your students will as well!

The flipbook contains the same examples and descriptions as the full-page sheet, so you can choose whether to give your students the flipbook or non-flipbook versions of the reference sheet. Have your students use either of the journal inserts as a guide while they play the game, as well as when they complete other tasks that relate to fraction multiplication.

If you are looking for resources to introduce the concept of fraction multiplication as scaling, check out my Growing & Shrinking ppt, task cards, and printables set.

Practicing the Concept

I designed this game to provide my students with quick, repeated, and fun practice with identifying how the size of a product will compare to the size of the factors. The game requires few materials – chips or tokens and a paper clip or plastic spinner. The directions for the game are printed on the board itself, so all you need is the one sheet. My kids really enjoyed playing the game – especially because of the element of being able to have an opponent lose chips – and the variety of numbers on the spinners (whole numbers, improper fractions and proper fractions) forced my students to consider all of the “rules” that govern multiplication with fractions. With four different spinners and eight numbers on each spinner, your kids can play this again and again without repeating combinations of factors.

To play, you will need to provide each player with 10 chips or tokens as well as a cup of more tokens that will be the “pot.” A player spins twice to get two factors. Then, they gain or lose chips based on whether the product of the two factors would be less than both factors, greater than both factors, greater than one factor and less than the other, or equal to one factor. The way that players gain and lose chips matches the relationship between the factors and products. If the factors are both less than one, for instance, the player will lose two chips, reinforcing the idea that the product is less than both factors. If the factors are both greater than one, however, the player will gaintwo chips, reinforcing the idea that the product is greater than both factors.

The students do not need to be able to actually multiply the numbers to determine the size of the product. In fact, the standard itself requires students to be able to identify and explain how a product compares to the size of factors without calculating the numbers. When I taught this standard and used these materials, I had not yet taught students how to multiply fractions. I think that was actually helpful because lacking a knowledge of the procedure, the students couldn’t just multiply the numbers and compare – they had to actually use reasoning.

Included with the game is a recording sheet that you can have your students fill out as they play to show the factors they spun and their “prediction” about the size of the product.

For more practice with the concept of fraction multiplication as scaling, check out my Predicting Products task cards and printables set.

Assessing Student Understanding

Once your students have had an opportunity to practice the concept, use any of the three different assessment tasks to evaluate their understanding of product/factor relationships when multiplying with fractions. Each of the tasks requires students to evaluate multiplication expressions, equations, and/or inequalities based on how the size of their products compare to the size of their factors. For each activity, the students are asked to explain their thinking in writing, providing an opportunity to evaluate your students’ ability to communicate clearly and effectively using math vocabulary. Of course, these tasks needn’t be used simply as assessments. You can use them as guided review, paired practice, homework assignments – any way that suits your students’ needs! Keys and a rubric are provided for each of the tasks, and each assessment has a total of 10 points, making for easy conversion to a percentage grade.

For more practice with multiplying fractions as scaling, please check out the other related resources I have available –

Predicting Products - fraction multiplication as scaling task cards + printables

Growing & Shrinking – scaling fractions ppt, task cards, and printables

Looking for more fraction resources?

Name That Equation - fraction multiplication task cards + printables set

Foxy Fractions - adding/subtracting unlike denominators task cards + printables

Find the Fraction - fraction of a number task cards + printables (set a)

Stealthy Simplifying - all-in-one simplifying fractions bundle

In and Around - area and perimeter task cards + printables (set C)

I hope your students enjoy these resources and are able to build their proficiency with fractions. – Dennis McDonald
Total Pages
13 pages
Answer Key
Included with rubric
Teaching Duration
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