Wednesday, June 22, 2016

Multiplication Strategies: x2, x4, x8

Over the past week, my son and I have made tremendous progress with multiplication. (Intro post here.) Each day, we add to his fluency toolbox by looking at specific strategies. The (related) strategies for 2s, 4s, and 8s, have been especially fruitful. Let's look at why...

2s...Dare to DOUBLE!
Twos are easy-peasy. Just a matter of doubling. We can see an example in this array.

If you multiply something by 2, you only need to double. Instead of 1 group of 6, you have 2 groups of 6; you just double 6.

4s...Double-Double
In Bridges in Mathematics, the strategy for multiplying by 4s is called Double-Double. It's easy to see why.

We already doubled when we multiplied by 2. To go from 2x a number to 4x a number, we double. So we double, then double again.

6 is doubled to 12 (x2)
12 is doubled to 24 (x4)

I bet you can guess what's coming next!

8s...Double-Double-Double
We call the strategy for 8s Double-Double-Double.
For 8x, we double 3 times:

6 is doubled to 12 (x2)
12 is doubled to 24 (x4)
24 is doubled to 48 (x8)

Can you see it in the model?

This is not a multiplication "trick" but rather a strategy with meaning behind it. Children need to see the visual model and understand what "Double-Double-Double" means. Once they understand the concept, they can apply it in wonderful ways.

I asked my son (just developing fluency with single digit multiplication) to consider these problems.

8 x 15 = ?

He doubled 15 and got 30. He doubled 30 (60). And doubled once more to get 120. So 8 x 15 = 120.

4 x 13 = ?

Double 13 to get 26. Double 26 to get 52. (Of course he then wanted to keep going and figure out 8 x 13. Double 52 and get 104!)

25 x 8 = ?

50, 100, 200, done! This problem was also a great opportunity to talk about another strategy. Do you know what it is? Leave your ideas in the comments below to start a RICH exchange.

Hope you're having a double dose of summer fun!

Credits:
Little Girl Graphic from: www.mycutegraphics.com
Number Frames (free app) from: http://www.mathlearningcenter.org/web-apps/number-frames/