As promised, we embarked on the good ship "multiplying fractions" today! And as I promised my students, the people who struggled the most with today's introduction are the people who know "the algorithm" for multiplying. It's not because their algorithm gives wrong answers, but because they are also responsible for understanding a mode (drawing method) for multiplying fractions.
Why Does Having a Model Matter?
- If you ask most people to multiply 2x2, they can give you 4. Or 10x10 they can give 100. In their minds, they know right away that when you multiply, things get bigger.
- Only, it doesn't always work that way. When I multiply 1/2 x 1/2, I get 1/4, which is smaller than the two numbers I am multiplying! Why on earth does this happen with fractions and decimals!?
- That is what we want kids to understand. Not only how to to the multiplication, but how to be self-aware of if their answer makes sense. The models help develop that number sense of multiplyign fractions.
So What's All This About Brownies?
- We started investigating fractions today by looking at square brownie pans and dividing those up.
- I have prepared a short video for you to describe what the lesson was showing and how students should be answering multiplications problems with fractions using a model.
- Here's the link: http://www.educreations.com/lesson/view/bp2-3-1/2485420/?s=5CDOGF&ref=app.
So we're not calculating fraction multiplication yet?
- That's exactly right. So far we are just using drawings to help us examine fractions and multiplication.
- For multiplication we are using the "groups of" language. So 1/2 x 1/2 means, "half of half of a pan of brownies." That is something the kids can draw and describe.
- We will be using the calculated fraction strategy that we all know and love by the end of the week. It is an elegant and powerful strategy that we will use all year long and into the future. But right now we want to start by building a visual representation of what it means.
Thank you for your patience in this long(ish) math-y email! :) I hope you a have a great Monday afternoon!
Sincerely,
Brian MacNevin
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