After students have ample experience developing fraction number sense, they will come to the realization that some fractions have different names but are the same size. As we work with fractions, I introduce the term equivalent fractions, even though I am not currently teaching equivalent fractions for mastery. It’s important to use UNLABELED fraction pieces for this, actually most, of these fraction lessons. Here are links to the ones I used: circles, squares, and rectangles. You can also find the lessons and printables from this post here.
I don’t initially teach students to multiply the number and denominator by the same number at the very beginning of my equivalent fraction lessons, because that strategy is often meaningless to my students at that point of instruction. To help my students create an understanding of equivalent fractions, I have them use models to find different names for fractions. One way to teach this is to give students outlines of different fractions and have students use their fraction pieces to find as many single fraction names for the region as possible. You can download that lesson below!
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After working with models, I extend this lesson the following day moving from concrete models to picture models by using grid paper and drawing the outline of a region and designated it as one whole. I lightly shade part of the region within the whole and students use different parts of the whole to determine multiple names for the part.
As I transition into more challenging equivalent fraction lessons, I like to have students continue to explore equivalent fractions through literature that moves students into problem solving situations. I prefer using real literature for this, but everything I found was a bit too young for my students and focused only on the size of fractional parts, rather than fraction equivalencies. I finally took a chance and wrote my own “book”. This was unlike anything I had ever created before, but I have to say that I’m pretty proud of the end result. The book takes students through various situations that require the reader to think about fraction size and equivalent fractions. You can download that book for free here.
At this point in the unit, I have not yet introduced students to a rule for finding equivalent fractions. I use the following lesson to begin transitioning students into discovering that rule. I give students an equation showing equivalent fractions, but one of the numbers is missing. I allow students to use any model or method they want to solve these problems. After the activity is complete, we meet together to look for a patterns and anything else that stands out to students. It’s always so tempted for me to tell students how to solve the problem, but I know that giving students time to explore will benefit them in the long-run.
My goal is for my students to see that if they multiply the top and bottom numbers by the same number, they will generate an equivalent fraction. One way to teach this is through an area model approach. I give students a worksheet with four squares in a row. I have students shade in the same fraction in each square using vertical dividing lines. Then, students slice each square into an equal number of horizontal slices. For each square, students write an equation showing the equivalent fraction. I follow this lesson with a class discussion on the rule for generating equivalent fractions. The discussion is important, because many students will only count the squares without thinking about the connection to multiplication.
Once students have been explicitly taught how to multiply the numerator and denominator by the same number, I continue to have students complete problems solving tasks where they apply their understanding of equivalent fractions. I particularly like this pattern block lesson, where the size of a whole is TWO hexagons. It requires students to change the way they look at the whole, because most students identify one hexagon as a whole.
After teaching equivalent fractions for mastery, I review as needed through some of the games and worksheets in my No Prep Fractions.