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Post date: Nov 2, 2011 3:14:54 PM
Sixth grade students need to develop a deep understanding of operations with rational numbers. Many students already know an algorithm for adding and subtracting fractions, but do not have the depth of understanding to make sense of their answers. Here are a few things we are using in class to help students understand addition and subtraction with fractions.
1. Estimation. Student can compare fractions to benchmarks like 0, 1/2, 1, etc. to make an estimate of their answer before they add or subtract. For example, 5/9 + 11/10 is close to 1/2 + 1 = 1 1/2 since half of 9 is 4.5 and 10/10 = 1.
2. Modeling. Students have used circles to model addition and subtraction. Addition can be thought of as "combining" or "putting together," while subtraction can be interpreted as "taking away." For an addition problem students shade in both addends (numbers being added) on a circle, leaving no blank space, and the sum is the combined shaded area. For a subtraction problem students shade in the first number and "cross out" the number being subtracted. The difference, or answer, is the area that is left uncrossed. This method is good for helping students visualize the problem and it also forces them to think about common denominators, because they have to make same size pieces to determine their result.
3. Fact families. An addition/subtraction fact family is made up of 3 numbers configured into 2 addition problems and 2 subtraction problems. A fact family can be created given any one of the four number sentences that make it up. Fact families allow students to check their answers and make sense of their answers by turning the problem into something with which they are more familiar. An example of a fact family:
1/2 + 1/3 = 5/6
1/3 + 1/2 = 5/6
5/6 - 1/2 = 1/3
5/6 - 1/3 = 1/2
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