Training a Mathematical Mind Even If You Hated Math Series – Multiplication
Last time we looked at this picture we discussed addition. We worked our way through each line of equivalencies and read or said what we saw. For those who missed that post you can find it here.
Now, I assume everyone has out their trusty notebook because today we are going to transform those additions into multiplication AND instead of just comparing one line of blocks to the orange block at the top, we will look at the relationships of some blocks to other blocks.
When we talk about multiplication it is important that the children know we are talking about rapid addition. Reciting equivalencies like the ones in image 2 solidifies this in their mind.
You don't have to do a lot of teaching about 3 groups of 3 cookies or 5 groups of 2 shells. You should talk about those things, but the student is always looking for an easier way to work things out. If my 5-year-old looks at image 2 he will read the first two lines as: o is the same as 2y. We will write that 0=2y. He has said y + y many times. He is the one who asked, "I can just say 2y and not y plus y, right?" My answer to that was, "Of course, that is called multiplication." He knew about multiplication but didn't really have a use for it. I would constantly have to coach him about what I was looking for in his answers. Now I don't. He has a use for multiplication. It makes his schoolwork go much faster and it helps him communicate better. Before it was something I forced him into. Now he requires it if for no other reason than to communicate more efficiently.
We would read the second image as: o is the same as 2y is the same as 5r is the same as 10w.
In our notebook we write (without looking at the blocks if the child is able to write for him/herself): 0 = 2y = 5r = 10w.
We learn quite a few things about this particular set of blocks and how math works if we stay long enough and pay attention.
- Not only does 0 = 2y but 5r = 2y and 10w = 2y.
- If that is true then 5r = 10w and it is all the same as o.
Every child with a sibling knows what a half is. If o = 1 slice of pizza, what is y?
- y = 1/2 o, which we read: y is the same as 1/2 of o.
- 1/2 o is the same as y.
- 1/2 o = y = 5w
Wait, there's more!
- 1/2 o = 3r - w
- 1/2 of o is the same as 2r + w
- y = 3r - w = 2r + w
"What", you say," Where is that?" Well if you pull out your blocks, or enlarge the image, that 3r is the same as 6w. That is one w too many. So we can either add 2r and a w to get a y or we can add 3r and subtract a w to get a y. But I wasn't covering subtraction and I am getting ahead of myself. You see once you know what to look for, it is all sitting there staring back at you.
Assignment: In your handy dandy math notebook, you write down the relationships you can find either in the first image or the second. Second assignment. Put away the image, using your memory alone come up with as many patterns for the o block as you can think of. Let's just stick with addition, multiplication and fractions. Post your results below if you are brave! We'll be back at this on Friday