I am trying to teach my son a concept of positive whole numbers being made up of other, smaller, positive whole numbers. This has been a tough going so far, full of unexpected obstacles. There was, for example, the part where I tried to explain and show that although a larger number can be made up of smaller numbers, it doesn’t work in reverse and a smaller number cannot be made up of larger numbers.
An even more formidable obstacle was (and still is) showing that a larger number can be made out of various combinations of smaller numbers. Say, 5=2+3, but also =4+1 and even 1+2+2. And by showing I mean proving. And by proving, I mean having my son test the rule and prove (or disprove) it to himself.
That’s why I was very happy when I got a hold of Oleg Gleizer’s book Modern Math for Elementary School. By the way, the book is free to download and use. We’ve been building and drawing multi-story buildings (mostly Jedi academies with x number of training rooms) ever since. If this sounds cryptic, I urge you to download the book and go straight to page 12, Addition, Subtraction and Young Diagrams.
And just yesterday I found this very simple activity on Mrs. T’s First Grade Class blog, via Love2Learn2Day‘s Pinterest board. All you need for it is a Ziploc bag, draw a line across the middle with a permanent marker, then add x number of manipulatives. Took me like 2 minutes to put it together, mostly because I had to hunt for my permanent marker.
The way we played with it was I gave the bag to my son and asked him how many items were in the bag. He counted 8. I showed him that the bag was closed tight, so nothing could fall out of it or be added to it. I also put a card with a large 8 on it in front of him as a reminder. At this point all 8 items were on one side of the line. I showed him how to move items across the line and let him play. As he was moving the manipulatives, I would simply provide the narrative:
Ok, so you took 2 of these and moved them across to the other side. Now you have 2 on the left and how many on the right? Yes, six (after him counting). Two here and six here. Two plus six. And how many items do we have in this bag? Good remembering, there are 8. So two plus six is 8. Want to move a few more over?
It went on like this for a few minutes until he got bored with it. Overall, I thought it was a good way of teaching, especially for children who do not like or can’t draw very well yet. Plus upping the complexity is really easy – draw more than one line on the bag and create opportunities for discovering that a number can be made of more than two smaller numbers.