Lately, the class has been involved in answering questions involving the addition and subtraction of fractional amounts.Some of the typical equations might look like:
2 1/4 + (1 1/3 -5/6) or
4 3/10 - (2 3/5 + 7/10) or
(3 3/4 + 2 1/8) - 2 2/7
While you might expect for me to be interested in the correct answer as my primary goal, I am actually much more concerned that kids are looking at the amounts and using appropriate strategies based on each unique circumstance.
We have studied several models that allow students to quickly create common denominators by thinking of such things as equivalent fractions on a clock, equivalent percents, and/or a good old common denominator. The trick is to know when to use each model.
The first problem is a great opportunity to use a clock model as all of the fractional amounts can be expressed as twelfths. Students should be familiar with clock fractions from the game "Roll around the Clock". 2 3/12 + ( 1 4/12 - 10/12)
The second problem is perfect for using percents as all of the amounts are very easily converted into percents that are easily added and subtracted. 430% - (260% + 70%)
The third problem is probably best solved by finding a common denominator as the fraction 2/7 is not easily represented on a clock, because 12 hours and/or 60 minutes cannot evenly be split into seven whole number pieces. Also, without a calculator, finding and using the percent that is equivalent to 2/7 is not practical. (3 6/8 + 2 1/8) - 2 2/7.... 5 7/8 - 2 2/7... 5 49/56 - 2 16/56...= 3 33/56
Of course, this post leaves out many steps, but the most important step is choosing the best strategy with which to work.
2 comments:
Maybe that's why I never succeeded with fractions, percents and decimals. NO ONE ever told me which model to use to figure it out. Where were you when I was in 5th grade in 1972?
I was in third grade and did not know any better ;-}
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