... their relationship to one another, their sequence, even how to break down a number into two smaller numbers. We have done all this without ever actually having used a numeral system or saying a number by name. One or both of these questions might pop in your head: How? and Why?
Here in the Trees Class Blog, you'll find the answers to both these questions!
In the classroom, we used Cuisenaire rods, a math manipulative teaching tool. The children quickly discovered that there were ten different rods, each with their own length and color. We then learned that if you increase each rod by the length of the smallest white rod, you would find the correct rod to make the next step up.
Children completed a set of stairs to show their understanding. Upon completing the stairway, each child had built a model a three dimensional model of the numbers one through ten. We could see and feel the difference between different numerical qualities and how they related to each other. We could see and be excited by the beauty of a mathematical gold sequence being displayed visually.
By the next week, a number of children had noticed that you could line up many of the smallest white rods to match the length of the larger roads. In this way, they were learning that many “ones” go into larger numbers. The challenge was to see how many white blocks it took to match the length of the various other colored rods.
Next came the Bag Game challenge. This popular game challenged the children to identify the rod hidden inside a bag only by touch. They would name the color they thought was inside, open the bag, and see if they were right. In addition to being a lot of fun, this exercise brought our minds deeper into understanding quantity in three-dimensional space, this time by touch only.
This week, the challenge has been to find out how many ways to make an orange-length rod out of two other rods. It won't be long now before we circle back to the idea of the staircase and counting the steps from the smallest to the largest. The children will be challenged to come up with the new names for the rods, this time without using the colors as a reference point. It will be exciting to help them discover that each rod can be named for the number it represents. We can then make the connection that because we know that the yellow rod represents the number five, and we also see that two yellow rods together are the same length as an orange rod (10), that 5 and 5 together make 10.
So, why not simply start with actual numbers? Name them by name and write them out? In doing so, we would be starting with the abstraction of what a number actually is, and then we would have to work backwards with the children to discover the structure behind this system. Cuisenaire rods allow us to start tactilely with the physical and relational sense of what a number is before an abstract symbol it is assigned to it.
When asked, many four- and five-year-olds already know to say that 5+5 = 10, but the likelihood of them fully understanding what they are saying is quite low. So instead of starting there, or even with practicing writing numbers out, our work with the rods will help lead the children to a much more concrete understanding of what a number actually means.
