I have taught upper grades for a long time. In all of that time, I am ashamed to admit that I have never taught multiplying fractions using a model <runs and hides in shame>. The algorithm just makes sense to me, so that is what I have always taught.
Well, the people who wrote the CCSS and SBAC think differently, so I am learning to adapt my craft this year and include far more models into my teaching.
Now, if you have been reading my blog for a bit, you know that this "using models" thing isn't always the easiest thing for me (re: multiplying decimals...remember that fiasco??!) but I am getting more and more adept at it, and I think I am getting into the patterns of it all!
So this week, when we were learning about multiplying fractions, I actually STARTED with the model. I know....shocking.
I started with multiplying whole numbers by fractions. I taught the kids that if you have 3 x 1/5, that means that you have 1/5 three different times. Just like regular multiplication! Using the visual model, I was able to show the students what multiplying fractions by whole numbers actually means. I drew three rectangles, each broken into 5 parts. Then, one part of the five was colored in on each rectangle. Putting them together, the answer became 3/5. What's more, I was able to show them how it lead right into repeated addition! 1/5 + 1/5 + 1/5 = 3/5
Then, using those models, we were able to make the connection to the actual algorithm.
It got a little complicated when we got to fraction by fraction multiplication. Drawing the fraction strips was relatively painless, but putting them together into an array was a bit more complicated. We remedied this by making sure that one fraction rectangle was drawn vertically, while the second one was drawn horizontally. After they were drawn, the two rectangles were set on top of each other, forming an array.
The algorithm just came naturally after that.
I created some task cards for the kids to practice the multiplying in context too. They LOVED these. Kids love task cards. Working in groups, they were able to talk about the math, discussing strategies, and applying what they had learned over the course of the week.
To practice how they will be tested on the big state test, I created a multiple choice AND a constructed response sheet. Boy, was that constructed response tricky for the kids! They were able to apply what they learned, but explaining it is going to take more time. :)
On a happy note though, when we went to the computer lab to do some practice test training, one of the questions asked the kids do actually show the multiplication model for a fraction problem. You should have seen the beams of light coming from the smiles on these kids. They just KNEW they had that one correct!
Multiplying Fractions in 5 Days pack. You can get it here. :)