For this lesson, fraction fringe was used. Fraction fringe is a die-cut manipulative available from Ellison. Click here for more information.
It is important when introducing a concept such as dividing fractions to place the mathematics in context. Ms. Grier's class considered making meatballs.
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The context: You have a 1/2 pound of meat. Each meatball is 1/16 pound of meat. How many meatballs can you make. The students identify 1/2 pound with the fraction fringe (in green). They then place the halves together with the sixteenths (purple). The students verbalize that you are dividing 1/2 pound of meat into 1/16 lb. portions. The students mark on the fringe each of the meatballs that can be made. They realize that each sixteenth represents a meatball. The equation in context makes more sense:
1/2 ÷ 1/16 = 8 meatballs
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In this example, there is 2/8 (in context, it can be described as 2/8 lb. of meat). Each meatball is 1/12 of a pound. How many meatballs can be made?
2/8 is represented on the brown fringe. Each twelfth is represented on the red fringe. Students can easily determine that 3 is the answer. Students will often give 3/12 as the answer. But bringing the problem back to the context of the meatballs allows students to see that there are three meatballs, each with a weight of 1/12 lb.
2/8 ÷ 1/12 = 3 meatballs
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Before students are introduced to the algorithm of finding the reciprocal of the divisor and multiplying, they should have plenty of practice considering what it means to divide one fraction by another fraction using manipulatives.
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In this example, the students' concept of dividing fractions is stretched. Here, there is 6/8 lb. of meat. The meatballs are now each 3/16 of a pound. The fraction fringe helps the students to visualize that now, each meatball is 3/16 of a pound. Therefore, you can make 4 meatballs with 6/8 of a pound.
6/8 ÷ 3/16 = 4 meatballs
This problem would be tricky to do at this point computationally. But using the manipulatives, students are able to explore the concept of dividing fractions without also being overwhelmed with the computation. Students would be ready after ample practice with the manipulatives to learn the computation. |
2/3 ÷ 1/12 = 8 |
3/4 ÷ 2/16 = 6 |
Indicator: 6.6.5.1
add, subtract, multiply, and divide with decimals and fractions, including mixed numbers, expressing answers in simplest form.
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