Math Bites with Rods

Today we visited with 2 other homeschool families and Simonne showed a bit of what we are exploring with the cuisenaire rods. As we all talked, I realised that I haven't yet found any online resources for using implementing Gattegno's philosophy with rods. I was thinking to do a few posts on how we use Gattegno's method to explore mathematical concepts.

Let's start with getting familiar with the rods through play. I don't think the child needs to start with number symbols for the rods. Knowing that this rod is the 'red' rod, and that is the 'green' is sufficient representation as s/he plays with the rods and gets familiar with the relationships between them. Gattegno really teaches that teaching should be subordinated to learning. What I think that means is really letting the child explore, ask them what they are noticing, and letting the learning be it's own reward, vs celebrations, "good boy!" etc. He encourages us to just let the kids free play with the rods for a while, and in the process discuss the things we notice. Let them build whatever they want, arrange the rods in a variety of ways. All the while, they are internalizing important relationships between the rods.

Some activities to try:

• Make a ladder or stairs with the rods and notice that the size of the step is the size of the white rod. We can make stairs that are a little 'bigger' where the size of the step is the size of the red rod. Although the picture below has number associations for the rods, remember, that really isn't important right now.


• We can make trains of a particular length: e.g. how many trains can we make with length orange rod that only has one or 2 colors?


• We can play guessing games, taking out a white and a red rod, giving it to the child and asking him to close his eyes and give u back a particular one. That way, they become familiar with the rod by feel. You can add in the other rods (green, pink,...), as the child becomes familiar with them.

Have fun! Next time we will talk about exploring simple operations with the rods.

More Math with Rods

I've been sooo excited to be exploring math with rods. I'm sure I said it before but I really didn't understand much math through undergrad and grad school! I'm so grateful to be developing a strong core for myself (at 38!) and to be helping my kids at the same time. Take a look at these pictures and see how some simple rods illuminate important math principles.

The picture to the left is a wall exploring the number 20 (5 pink rods). We build as many trains with eh same length as we can and then look at what we can learn from the trains. So the yellow train tells us that 5 yellow rods gives us the same as 4 pink rods. We also learn that 2 dark greens and 4 reds give us 20. So if we convert to numbers, we know that 4 and 4 and 4 and 4 and 4 is 20, which is the same as saying that 5 groups of 4 is 20. I love sliding into multiplication without rote learning! Yippeee!

The picture of the church shows that kids can be pretty creative with the rods, and at the same time, be internalizing principles of symmetry, etc.

Play with Math using Rods and Gattegno!!!

Just a quick note about the wonderful method of exploring and internalising Mathematics that we recently found. I encourage you to investigate it for yourself. It was pioneered by Caleb Gattegno and uses Cuisenaire rods. I can't describe the experience, but I have done mathematics to the graduate level and taught it to the college level, and trust me, there is a lot that I do not understand. So much of mathematics seems to be the following of rules that you just don't 'get'. At my ripe old age, I'm just understanding what they meant when i was 'carrying the 1' in subtraction! So, as a homeschooler, I really want my kids to 'get'.

Gattegno's method helps the children to become familiar with mathematics in a very intuitive and visual way. More details on his methods later, maybe, but take a look at Simonne and Zachary exploring concepts that are become second nature (instead of rote learning math facts). So here is Simonne looking at all the ways to make rods of length 11 units. I think she was more excited about building the wall! She then wrote out that O+W = Bl + R and so on, also becoming familiar with algebraic notation.

Here is Zach building a ladder, which is just him becoming familiar with the order of the rods when there is only a difference of one unit. The visual piece is so important and leads to such wonderful realizations later on. They start to 'see' the mathematics.

Of course, we don't only have to build walls and ladders!!!

I'm excited about this because I've found the method to teach Jaedon math, when he is ready for it. I have heard that this works so well with special needs kids, who may not get the 'rules' of mathematics, but just start to 'see it'. Whatever you do, keep looking for methods and approaches that are right for your kids. If they aren't out there, you can create one!

Soap and Math

I really enjoy the times when learning happens and comes from a genuine desire from the child to really 'get' something. I really think all learning should be that way. Think about it. How many things did you learn because you 'should' and you just forgot afterwards? Even rudimentary things like ABC's and counting were done to music and using stuff we were interested in ("Johnny, do you want one cookie, or 2?")


I encouraged Simonne to start making soap for 2 reasons: so she could make some money to start attacking the list of toys she wants, and to help her make math practical. So here's a pic of the soaps. They are 50 cents each, so people often pay her in quarters. I asked her one night, what's 25 and 25? I was sure she knew, the amount of times we had done this. she said "About...45 cents?" and I figured she had no idea. A little testily, I explained in about 3 different ways, how to add 25 and 25. We used regular sum notation, base 10 blocks and counting by 5's on fingers. I wrote it up on the blackboard side of the easel. Some time later, I saw this on the white board side! She wrote out what I had on the board, expanded on it and added some annotations of her own! She said "Look Mommy, is this math?" I had an enthusiastic affirmative. Of course, I was suspicious. Did she really get it? Was she just copying what I did on the board? A few days later, I found out. We emptied the piggy bank, and started counting the money. She counted 2 quarters with no problem, then we moved on to the problem of 50 cents plus 50 cents. She got it!