“Notice and Wonder” with Cuisenaire Rods for Homeschool Math

Today for math we did one of my favorite activities, though I will admit, it is not always my children’s favorite. My daughter, now 10, build a structure with the Cuisinaire Rods, and then we did a “notice and wonder” activity. The structure that she build for today was a pyramid. I could have guessed this as it’s one of her favorite structures to build.

After building the structured, she stamped a side-view angle into her notebook with our stamps. (I reserved one set of rods, 1-10, for stamping that stay in our stamp kit. Here are the rods we use, and this is the stamp set that match perfectly with our rods.) We began with some easy observations. When doing a “notice and wonder” exercise, we just begin with simple observations. These are what she noticed:

  • It is not in rainbow order. (Have I mentioned rainbow order is important in this family?)
  • The squares decrease as you go up the pyramid.
  • Rough edges along the side (she’s talking about the steps here. They are not smooth as she images a pyramid’s side would be.)
  • Each layer is made of a square.
  • From the side, the shape is a triangle.

From this point we wrote in math language how each layer was expressed, we calculated the sum of each layer, and we calculated the difference between each of the layers. We talked about how 1, 4, 9, 16, 25, and the other totals listed were considered square numbers, because one could make a square of them. We also noticed that the difference between the squares was the series of odd numbers. We noted the sum of all the layers was 385.

Layer SquareTotalDifference
11 X 11
22 X 243
33 X 395
44 X 4167
55 X 5259
66 X 63611
77 X 74913
88 X 86415
99 X 9 8117
1010 X 1010019

Then we used the sums of each layer to calculated the fraction the top layer was to the bottom layer. This is what we found:

LayersFraction
1 of 21/4
2 of 34/9
3 of 49/16
4 of 516/25
5 of 625/36
6 of 736/49
7 of 849/64
8 of 964/81
9 of 1081/100

We noted that the fractions above did not appear to have the ability to be reduced.

That was the total of our math for yesterday. This enables us to do many things. An activity like this definitely teaches observation and mathematical thinking. It also breaks from the norm of math work, which provides for a nice break. It also uses many of the concepts that we’ve learned: multiplication, addition, subtraction and fractions. This is definitely not our everyday activity for math, but it does provide a nice break and a wonderful review.

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