MMD#1: Fraction Addition

Dear Math for Mom & Dad,

     My son is struggling with fraction addition.  Rules by themselves make no sense to him.  Any suggestions?

Parent of a 4^th grader

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Dear Parent of a 4^th grader,

Area models provide a nice context for thinking about the meaning of fraction operations.  We’ll use that approach to model the sum 1/2 + 1/3.  First, take a rectangular sheet of paper and fold it in half the long way (i.e., a Hog Dog fold).  Then open the paper and fold it in thirds the other direction (i.e., a Letter fold).  This divides the sheet into 6 smaller rectangles, each of which has an area 1/6^th of the entire sheet (See Step 1).  Next, shade half of the sheet horizontally (See Step 2) and a third of the sheet vertically (See Step 3).  Finally, count the shaded rectangles, taking double shading into account.  You may also rearrange the shaded cells as seen in Figure 4 to avoid double shading.  Since 5 out of 6 rectangles are shaded, 1/2 + 1/3 = 5/6.  Alternatively, rectangles may be drawn on large cell graph paper and shaded to illustrate fraction operations.  

Use this approach to model the following sums.  Let me know how it goes!

·         1/4  + 1/3

·         1/3 + 3/8

For additional resources and ideas, visit my website math-ed.com 

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