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 an instructional ppt, 32 task cards, reference sheets, and assessment activities – is the perfect introduction to the concept of multiplication as scaling, and it provides everything you need in one “print-and-go” package. After you have used these materials with your kids, they will have a much better understanding of how multiplication can both increase and decrease the value of a number.
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.
• 20-slide powerpoint presentation
• 2 reference sheets
• 32 task cards
• 8 self-checking “answer cards”
• task card answer sheet and key
• 2 assessment activities and scoring guide/rubric
This product is a ZIP file containing a PPTX file and a PDF. For directions about how to “unzip” the files, TpT provides instructions here
Introducing the Concept
All of the materials in this set use the metaphor of a “sizing potion”, some of which increase the size of an object (x 3, x 6) and some of which decrease the size of an object (x 1/2 , x 3/4). The goal was for my students to understand that when you multiply a given amount by a number greater than 1, the resulting product is larger (because it has “grown”), and when you multiply the same amount by a number less than 1, the resulting product is smaller (because it has “shrunk”).
Begin with the powerpoint, which uses graphics and animations to bring to life the concept of multiplication as scaling. The animations illustrate objects (in this case, dinosaurs) growing when given a potion that uses a whole number and shrinks with given a potion that uses a fraction less than one. All of the animations are timed to appear automatically, with arrows appearing on each slide when the slide needs to be advanced. A number of the slides present discussion questions that will allow your class to have a small-group and/or whole-group conversation about the concepts presented.
Follow-up the powerpoint by providing your students with one or both of the included reference sheets: a full-page reference and a foldable “flip book” reference. The first graphic reference sheet is full-page size and provides an overview of how multiplication can change a given number. It shows the result of multiplying a whole number by a whole number, a fraction by a whole number, and a fraction by a fraction. 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 show how multiplication can cause a number to “grow” or “shrink”. 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 multiplication as scaling.
Practicing the Concept
Once you have introduced the concept, your students can practice applying their understanding by working through the 32 task cards. The task cards use the same metaphor of “sizing potions”, continuing where the powerpoint leaves off. Each card presents the students with a given potion and a description of the size of a hypothetical pet (for example, a snake that is ¾ of a foot long). The students have to figure out from the label on the potion whether it is a growing potion or a shrinking potion and identify whether the animal’s new size will be greater than its original size or less than its original size.
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 provided assessment activities can be used to evaluate student understanding of multiplication as scaling. Each of the two-page activities uses a mix of multiple-choice, open-ended, and written response questions. The two 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.
For more practice with fractions, please check out the other related resources I have available –
Predicting Products - fraction multiplication as scaling task cards + printables
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