In the beginning of my teaching days, I was terrified of manipulatives. I thought that students would mess around with them, blocks and chips would be flying through the air and no one would be learning. I’ve learned the last few years that the opposite is true. Manipulatives have become a way for students to both play and discover math concepts in my classroom.
Today the learning target was: I can discover addition rules.
In the middle of the floor I put out cups and two color counting chips. I showed them two cups with a few chips in each one and asked them how I could find out how many chips I had. I had 4 chips in one cup and 5 in the other. Many students scoffed (exclaimed “this is easy!”) and told me to count them. So to get at the properties of addition naturally, I asked how many different ways I could count them. I asked them to write some number sentences in their math journals. The students came up with:
4 + 5
5 + 4
(3 + 2) +4
9 + 0 (They made me pour all the chips in one cup!)
It was awesome to see how they were thinking. In just a minute or two, they figured out the commutative, associative and identity properties of addition. I walked around to each student, dropped counters into their cups, and asked them to record as many number sentences as they could with their chips. I was able to differentiate easily by dropping a small number in the student’s cups who were struggling, and larger numbers in those gifted student’s cups. Some of them asked for 3 cups, others stuck with two. They were sorting and dumping the chips, writing number sentences as they went along.
After about 5 minutes I asked them to share some addition rules that they discovered. They reported to me (in kid language):
- In every number sentence I always had the same sum.
- No matter how many ways you break the numbers you still get the same sum. (This is the associative property!)
- It didn’t matter which cup I added first, I always got the same sum. (This is the commutative property!)
- If I had a cup with zero in it, the other cup was the sum! (This is the identity property!)
Tomorrow I will name these things for them. We will learn that those exact “rules” they came up with are actually properties of addition, which can then translate to multiplication later in the year.
I now know that purposeful play is an important part of the learning process. My goal is to integrate this more and more each day!