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Step on How To Multiply Fractions
In the first step of this instructional process, kids use a model to find answers to some fractions-multiplication examples.
In the second step (which really happens concurrently with step one) the kids keep a record of the results from step one.
After enough examples have been completed the kids move to the third step. They look for a pattern that suggests how to do the multiplication without the model.
In the fourth step the kids hypothesize how to do the multiplication without the model.
This hypothesis really a first description of the fractions-multiplication algorithm (procedure).
The fifth step is to complete examples using the hypothesized procedure and then redo those examples with the model to check the correctness of the procedure.
Of course, this 5-step instructional process can only work if you have an effective (and believable) way to model the multiplication of fractions.
We will look at three procedures for modeling fractions multiplication that are found in the literature.
There are 3 approaches for modeling fractions multiplication
- A Fractions of a Fractions
- Length x Length = Area
- Cross Shading
We will now examine each of these 3 approaches.
We will think of multiplying fractions as finding a fractions of another fractions.




Modeling – Fractions of Fractions
Modeling multiplication of fractions using the fractions of a fractions approach requires that the kids understand the relationship of multiplication to the word “of.”
We can establish this understanding showing whole-number examples like: 6 threes is the same as 6 X 3.






Modeling – Length times Length equals Area
Modeling multiplication of fractions using the length times length equals area approach requires that the kids understand how to find the area of a rectangle.
A great advantage to this approach is that the area model is consistently used for multiplication of whole numbers and decimals. Its use for fractions, then is merely an extension of previous experience.




Modeling – Cross Shading
Modeling multiplication of fractions using the cross shading approach does produce correct answers. However, to kids, it is a “nonsense method.”
The rationale for the answer, “because it is shaded both directions” does not make sense. It would make as much sense to say that the answer is all the parts that are shaded only one direction or the part that is not shaded.
If the rationale for the answer does not make sense to the kids–if it is not meaningful–it is simply another rote rule. For this reason, THE CROSS SHADING METHOD IS NOT RECOMMENDED. Teachers should choose to use either the fractions of a fractions method or the length times length equals area method when modeling multiplication of fractions.
With your partner, practice using the fractions of a fractions method to model multiplication of fractions until you are both comfortable enough to make a presentation using the method.
Also, practice using the length times length equals area method to model multiplication of fractions until you are both comfortable enough to make a presentation using this method.
When you are ready, make an appointment with your instructor to demonstrate each method.
Above article was taken from Dr. Benny Tucker
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