Odd and Even Numbers with Cuisenaire
This is the last post on chapter 2 of Gattegno Mathematics Textbook 1. I did the happy dance. I did. We’re covering activities 37-39, which are all about odd and even numbers. The next post will be a recap, and I’ll share some of the mistakes I’ve made and what I’ve learned since I started.
Odd and Even Numbers
One of the first math concepts I taught my son was odd and even. He could tell me if a number was odd or even when he was two. We played lots of games with odd and even because knowing if a number is odd or even is probably one of the most important things you can know about a number.
Even though P. could say which numbers were odd, and even though he had mentally attached a number to the rods, the exercises in this section still took him time to work out. Verbal regurgitation does not equal understanding. One of the fascinating things about this process is how often P. needs to use the rods to measure and gather information. There is an expression on his face when he knows exactly which rod he needs to solve the current challenge. But just because he has it for this activity, doesn’t mean he can take that understanding and apply it to a different activity. He wasn’t able to take the knowledge gained from rods of the same color and transfer it to odd and even numbers. It took some time to figure out which two rods of one color would be the same length as a single rod.
Gattegno defines odd numbers as those rods whose length can be formed by a white rod and 2 rods of the same color, or a white rod followed by two more white rods. Even numbers have a length which can be formed by two rods of the same color.
Gattegno uses three simple activities to work with odd and even numbers:
- Find all the rods that can be made into odd numbers by first placing a white rod and then 2 rods of the same color. Then we find the even ones. Those are the rods that are not odd.
- Next, we take a white rod and place it between a pair of rods of the same color. We should systematically work through all the rods and make these lengths. We have introduced the word pair here, by which we mean two of the same kind. This time, we placed a white rod in the center. Do the same rods come up odd and even, even though we moved the white rod’s location?
- Line up a pair of odd rods. When placed end to end, is the new length odd or even?
There are a couple of things I would add. We spent a lot more time on odd/even than Gattegno does. Or maybe not time, but we played a lot more games with it.
Place a pair of rods side by side with the white one on the top to the right. Are these odd or even? Do the same with another pair and a white rod, but this time put the white rod on the left. Join the two sets of rods. Are these joined rods odd or even? Does each rod make a pair?
Gattegno introduced the word pair in exercise two. We don’t want to gloss over that. Take a pair of dark green rods and add a white one. The dark green ones make a pair but the white one does not make a pair. It is the odd man out.
What happens if we add another white one? Now both the white ones and the dark green ones make a pair. What happens if we add another white one? We have a pair of dark green ones, a pair of white ones and one odd white one. What happens if we have a pair of red rods and take a red one away? Is this single rod odd? Why or why not? Can we make this rod out of any other rods? Are those rods a pair or a pair and a white rod?