Multiplying makes things bigger, right? That's 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 of task cards and printables focuses on how the size of factors determines the size of the product, and it provides everything you need in one “print-and-go” package. The 32 task cards, 2 graphic reference sheets, and 2 assessment activities are the perfect resource for building your students’ understanding of fraction multiplication as scaling.
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
• 32 task cards
• 8 self-checking “answer cards”
• task card answer sheet and key
• 2 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 cards.
The first graphic reference sheet provides an overview of how whole number multiplication compares to fraction multiplication. It provides examples of equations in which the product is less than both factors, equations in which the product is less than one factor and equal to the other, and equations in which the product is equal to one factor. This reference sheet includes a couple open-ended questions, directed at the students, which can be an excellent jumping off point for a classroom conversation and/or a written reflection about the size relationship between factors in products in multiplication equations.
The foldable, like the full-page reference sheet, is designed to be glued in your students’ journals. The students will end up with three 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! Have your students use the journal inserts as guides while they work on the cards, as well as when they complete other tasks that relate to fraction multiplication.
Practicing the Concept
I designed these materials to help my students practice using the size of factors to identify the size of the product of those factors. Each card presents the students with a multiplication equation with an unknown product. The equations use proper fractions, improper fractions, and whole numbers as factors. The types of factors used in the equations are limited to: a) proper fraction x proper fraction; b) whole number x proper fraction; c) proper fraction x improper fraction equal to one: and, d) proper fraction x improper fraction greater than one. Students are asked to decide whether the product is less than both factors, the product is less than one factor and greater than the other factor, or the product is equal to one of the 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 in this set are eight “answer cards” that can serve as a resource if you use a self-paced structure for implementing the task cards. Often, I would have kids work in pairs on cards while I circulated to spot check and give feedback to pairs of students. Naturally, I would get backed up and not be able to reach as many kids until after they had already made many mistakes. I designed these answer cards so that the students could check themselves: catching errors, figuring out for themselves what they did wrong, and (hopefully) avoiding the same mistake on later cards.
There are lots of ways in which you can implement the task cards. You can have the students work on them independently, working through the task cards on their own. The students can work on them in pairs or small groups, completing all the task cards in one session. You can use them in centers, having the students complete 6-8 task cards a day over the course of the week. You can even use them as a variation of “problem of the day”, giving each student 1 sheet of 4 cards to glue in their journals and solve, one sheet per day for eight days.
Assessing Student Understanding
The two provided assessment activities can be used to evaluate student understanding of the size relationship between factors & products in multiplication equations that use fractions as factors. Both activities are a mix of multiple-choice questions, open-ended questions that have more than one answer, and an opportunity for students to explain their thinking in writing. These activities are formatted similarly, and have similar types of questions, though the numbers on each are different. I designed them this way so they could be easily used as a pre/post assessment. However, you can use these activity pages in a variety of ways – guided practice, paired work, homework, center assignments, or any other purpose that fits your teaching style or classroom routines.
Extending Student Understanding
For more practice with fraction multiplication as scaling, please check out the other related resources I have available –
Growing & Shrinking – scaling fractions ppt, task cards, and printables
Gain Some, Lose Some – fraction multiplication as scaling game and printables
Need 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