Dividing Fractions

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In this activity, students use rectangle manipulatives to gain a visual understanding of dividing fractions first by whole numbers and then by fractions. Print Settings Printer Brand: MakerBot Printer: MakerBot Replicator Rafts: Yes Supports: No Resolution: standard Infill: 20% How I Designed This To create this model, I used Tinkercad to get rectangles of different shapes. The original "whole" square is 50 mm by 50 mm. Then, I made a half, a fourth, an eighth, and a sixteenth of that whole. If you'd like to use examples with fractions other than these, you can do similar steps with different size fractions. Standards CCSS Overview and Background This activity is for sixth-grade students learning how to divide fractions. It satisfies the following standard: CCSS.Math.Content.6.NS.A.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Lesson Plan and Activity Depending on the examples students are figuring out will determine how many shapes you'll need to give them. For my examples, I needed 4 halves, 6 fourths, and 4 eighths. The first example we'll look at is (1⁄2)/4. You can talk students through this first example, then give them additional problems to try in groups. Start with the ½ rectangle and think of dividing it into 4 equal parts. We want to know how big one of those parts is. You can figure out that four of the 1/8ths will fit on the ½ [see Figure 1]. This means (1⁄2)/4=1/8. Once students are comfortable using a model to divide fractions by whole numbers, you can move on to dividing fractions by fractions. Similarly, you can talk students through the first example and then give them additional problems to try in groups. We will look at (1⁄2)/(1⁄4). I'll start with the ½ piece. Then we want to think about how big the shape needs to be so that this half is one fourth of the whole. So, we can put together 4 halves, which is equivalent to 2. Thus, (1⁄2)/(1⁄4)=2 [see Figure 2]. I'll go through one more example. We want to find (3⁄4)/(1⁄2). Take 3 fourth rectangles and think about what this is one half of. You can add another 3 fourths. Add them to get three halves. Thus, (3⁄4)/(1⁄2)=3/2 [see Figures 3 & 4]. Skills Learned Dividing fractions Duration of Lesson one class Preparation You should print these fraction shapes before giving the lesson.