Posts tagged math manipulatives
We usually use a lot of manipulatives with my son. But not this week. It was interesting to see how a 5-year old deals with something very abstract, such as numbers.
Last week, while grocery shopping, I asked him what was bigger, 8 or 14. Without hesitation he responded that 14 was bigger. Distractedly, I asked him why did he think so. The answer was “14 is bigger because I can count to 8, but I can’t count to 14″. The reasoning sounded both unexpected and logical to me.
This week started with my son asking me to write down a story he made up about his collection of toy garbage trucks. It started with
At first Mark had 0 garbage trucks. Then he found out about them, started watching videos about them. Then he had 1 garbage truck. Then he had 2 garbage trucks because he got a gift from a store. Then he had 3 garbage trucks…
on and on it went like this until he got to 7 because that’s how many trucks are in his collection. So it was basically a counting story.
Then today he wanted to write down the same story again, but I approached it differently. Instead of writing it down, I gave him a pencil and paper and we worked out some basic equations:
0+1 = 1
1+1 = 2
2+1 = 3
3+1 = 4
4+ 3= 7
(because he found 3 trucks at a garage sale all in one day)
After he was done writing it all down, he reviewed his work, then looked at me with a puzzled expression and asked “I don’t understand, Mom. Where are all the words?” Which gave me a chance to explain a bit about how equations can tell a story. He seemed to be happy to discover a way of writing things down in as few signs as possible.
Both stories seem trivial when I re-tell them. But when they happened, I was reminded of how abstract the concept of numbers and manipulating with numbers (as opposed to quantities) can be for a child. And for me, as an adult, it is a difficult one to relate to. It’s been a while since I was 5 years old. I simply don’t remember myself not knowing numbers. Do you?
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.
If you are looking for a simple and fun way of bringing more math into your child’s life, then here’s a solution for you. It costs little, takes no time to set up and is a great way to engage the whole family. I’m talking about playing a round or two of a board game.
If you read (or listened to) “Judy Moody Goes to College, you know what I’m talking about. The story revolves around Judy’s problems with math and how she overcomes them. Hint – her tutor, Chloe, starts off playing a round of “Life” with Judy.
Turns out, board games do help children acquire numerical knowledge. So if your child (and yourself) are bored to tears with worksheets and rote learning, board games such as Chutes and Ladders, the Candy Land, and the Ladybugs Game offer a great alternative.
After playing a few rounds of the Ladybug Game with my son I found out another unexpected benefit. If your child, like my son, has small motor difficulties that make work with manipulatives frustrating, board games offer a stress-free and enjoyable alternative.
But the benefits of board games go beyond simple counting (or addition and multiplication). There are games – board games, card games, computer games – that teach children mathematical thinking, including geometric, logical and probabilistic thinking. Here’s a great list, broken down by particular math skills, to get you started.
While right now our stack of board games is small – the Ladybug Game, Candy Land and Four-in-a-Row (which proved the most amazingly flexible so far), I am slowly adding more titles to my wish list.
As for Judy Moody, playing “Life” changes her attitude towards math. She learns that math is everywhere, that life is full of math and, as a result, acquires a new “mathtitude”.
Do you play board games with your child?