Area Model (bold)
The area model is somewhat similar to an array model in multiplication. It is assumed that students are familiar with array models prior to instruction of fractions using the area model. I will use rectangles to introduce the model. Rectangles are easier than circles to draw freehand for myself and my students and are extendable. Students will show unit fractions using the area models. Usually in an area model, the unit is a rectangle. Students must understand that the rectangle is to be one whole. They then will divide the rectangle to find their unit fractions. In Figure 8, the unit rectangle is partitioned into 4 equal parts. Each sub-rectangle is one-fourth of the whole. It takes four one-fourths to make the whole.
The unit fraction is 1/d, with d being any number. Here d = 4. In figure 9, one part is shaded. Since there are four equal parts total, students would say ¼ is shaded. One-fourth is the unit fraction.
Students will need to practice this method naming different unit fractions. At this stage I will introduce the vocabulary of numerator and denominator. The denominator, the bottom digit, is the total parts needed to equal the one whole. The numerator, the top digit, is the number of copies. Once students divide the same whole into different equal parts (d), they can compare the different unit fractions and then conclude that the larger the d, the smaller 1/d will be for a fixed whole.
Once students become comfortable with using the area model to show unit fractions, they can progress to showing a general fraction. This will reinforce the idea of a general fraction being copies of a unit fraction. This practice will support the understanding of the unit fraction. To show the fraction "two-thirds" you would begin with one whole. Since the digit in the denominator is a three then you would partition the rectangle in three equal parts. Now we can see that that one part of the whole will be the unit fraction. Since 3 equal sub-rectangles are making the whole, each one is considered to be 1/3. With the area model it is clear that it takes three copies of the unit fraction to equal one whole. Then 2 of the 1/3's makes 2/3: (See Figure 10).
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