### Classifying Multiplication Problems

On the Addition tab there is a link to an
explanation of my system for classifying
word problems. In brief, I first classify problems as examples of
either addition,
subtraction, multiplication, or division. Having done that, I further
classify
word problems by how I would teach children to solve them - that is, on
the basis of
what model I would help them to make.

In the case of multiplication, I only distinguish 3 models. Other
authors make further
distinctions. Consider for example these two problems.

- Eva has 3 fish tanks. Each fish tank has 2 fish in it. How many fish does Eva have?
- Eva bought 3 fish tanks. Each fish tank cost 2 dollars. How much do the 3 fish tanks cost altogether?

From my perspective, the only distinction is that in the first
example each fish tank **contains** 2 fish while in the second
example each fish tank **is associated with** 2 dollars. I might
model both problems using 3 cups to represent the fish tanks and 6
pennies to represent either the fish or the dollars. Whether the
pennies are in the cups or not does not seem significant.

Or consider this problem.

- I have a rug that is 3 feet long and 2 feet wide. What is it area?

From my perspective, this problem is yet another example of Easy Multiplication. As the diagram below makes clear, my rug is made up of 3 columns of squares, with each square having an area of 1 square foot. There are 2 of these squares in each column.

Of course, the
concept of area is one that needs to be taught. But once children
understand
the concept they are able to model area problems as above. They then
should see that the model for area problems is identical to the model
for Easy Multiplication problems.

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