We have been having a lot of fun with cuisenaire rods in Kindergarten! The last time I was with this class, they explored ways to build the orange rod using the other lengths. As the students worked, I heard a lot of “A white and a blue make an orange.” and “Two yellows make an orange.”
After reading the beginning portion of Marilyn Burn’s About Teaching Mathematics, I have equality and use of the equal sign on my mind a lot, especially when reflecting on these particular activities with cuisenaire rods. In the last activity, there was a lot of talk that seemed to be about “making” the orange more so than the two of them being the same as one another in length.
I wondered how we could shift that perspective a bit, or at least add another type of experience to the different rods being of equal length. I grabbed Balancing Act from my Math Reads kit and went to Kindergarten for another round!
After reading the book aloud, we did a notice and wonder. I was surprised at the ease of use of the word “balance” and the discussion about which different animals balanced one another out in the story.
My first direction to the students was to go back to their seats and find rods that would balance with one another. After looking around and seeing some rods on their ends with students creating their own teeter-totter, the teacher and I had to do a quick pause and redirection:)! She quickly grabbed rulers and we asked the students to pretend the ruler was the teeter-totter so that they rods could stay flat on the table, much better!
It was so interesting to see their different approaches! These two boys had different ideas. The one student liked to find rods the same length before putting them on the ruler, while the other put the longer rod on and kept adding smaller ones to the other side. He had to keep putting the longer one over the smaller ones each time, but his truly looked like balancing.
This was so interesting to see multiple rods balancing each side and I especially liked the red rod going vertical on the one ruler.
The student below was SO interesting because she was the only one balancing different sizes each time but the opposite sides were still staying balanced at the same time!
This table worked together so nicely, but started to have a great disagreement when I asked if all of the sides were balanced because the one side is shorter than the rest!
This group made the equal length rods but they was using the ruler to test that all of the sides were the same length:
I started thinking it may be a neat activity to ask students to take turns balancing out each other’s cuisenaire rods. For example Player 1 could put a rod or combination of rods on their side of the ruler and then Player 2 must balance out what they did, except using different rods. They could take turns being the first one to place the rod each time. If you wanted to be tricky, they could also remove rods on their turn instead of adding them.
I am wondering, however, how to incorporate notation into this? Would you ask the students to write equations for these rods during this activity?
I love idea of using the rods to identify equality. Illustrative Math
https://www.illustrativemathematics.org/content-standards/1/OA/D/7 has some great equality activities as well that help students see the true meaning of the equal signs. Thank you for your great ideas that really help illuminate the mathematics.
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Thinking about language. Balance is a weight concept. Do K’s transfer the weight to length? Or are they “following directions”? The connection may be obvious to us, but how do they understand it? What questions could you ask to dig deeper into what knowledge they are constructing? Other thoughts on =. What if you did a N/W with 10=5+5 and 2+3=4+1?
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I completely agree Becca and I should have mentioned that we did talk about the weight of rods the same length before they went back to their seats. That was part of the transition from book to table that was pretty important that I left out, thanks for the catch! I asked them if they thought two orange rods would balance each other and they said yes bc they are the same heaviness, so we played around with a couple others. Once we established same piece=same weight, the assumption was 1/2 as long, 1/2 the weight, but now I am not sure that was brought out clearly.
I’m loving following what you’re doing, Kristin! And it’s great to see all the ways the students made their balances! I think work with balances is a good idea all the way through. But I’ve also been impressed with my K students how they seem to understand the idea of equality really flexibly.
The usual kind of thing I say is something like, “Can you make a train with two rods, and another train with two rods? And then write down what you’ve done.” I think this has reinforced equals as “is the same as” or “is the same length as”, rather than the usual “and now here comes the answer”. There are a few children that sometimes confuse the + and the = sign, and a few that find writing a bit of a chore, but all the 43 students in the year group can do it. It seems like a really good start with the idea of equality and it’s been one of the things that have made the time we’ve given to it worth it.
I should have said there, what I say is, “Can you make a train with two rods, and another train with two rods *the same length*?”
Another thing: I love the way the book really helps to tune the class in. I did Graham’s 3-Act “Equally Balancing Numbers”
and I found the Ss were going off at tangents a bit, making perfume bottles with the pattern blocks and the like. I think that’s partly because I hadn’t given enough time to just play in the first place, but perhaps also because when they had the pattern blocks in front of them without the balance, they didn’t quite make the link to equal area strongly enough. Having read the book first, and talked about balancing and equality, would probably have tuned us in better! (Also of course experience with balances!)
I liked this post Kristin. You may like to know how Euclid might have used cuisenaire rods to explain multiplication. If so, the video is at https://youtu.be/_6Dvx526wZw?t=3m12s
BTW, with balance, it might to wise to use a pan balance rather than a teeter-totter see-saw diagram. Kids know that two kids of the same weight on either side of a teeter-totter will only balance if they are the same distance from the middle.
So an interesting connection between Balancing Act and the Cuisenaire Rods!
I’m wondering if another context might help them with that next step you described at the end of your blog. Recently a preschooler described the Cuisenaire rods to me as dinosaur mouthes and the other rods she was laying on top as teeth. She tried to figure out how many teeth would fit in the dinosaur mouth. It was fascinating. Were any of the kids imagining that the rods were different animals that could be balanced by different animals on the other sides a la Balancing Act? Wonder if there’s something to build on there!
Love this!!! Yes, I’d introduce symbolic and non-symbolic notation. I think ??? Simon Greg has posted on this. So, something like (drawing out the orange) = (whichever combos they have found). Then compare with friends’. List all combos that make orange. — Now here’s where I’m not sure how I’d proceed. Do you think sticking with just orange, naming it 10. Writing the symbolic (digit) under each rod. So this is mapping symbolic to non-symbolic. Then ask if we can use those same combos without the orange. In other words, should we build all combos of ten on both sides of the equation (other than orange) as non-symbolic; then translate to symbolic; or should we stick with just orange and 10 first. Ex:
10 = 8 + 2 and same as orange = ____ + ____
10 = 1 + 9
10 = 4 + 6 etc.
8+2 = 1 + 9
4+ 6 = 2 + 8
Does that make sense. Doing a notice & wonder they will figure out order doesn’t matter Ex: 2 + 8 = 8 + 2