Numbers Up To 20 with Cuisenaire Rods

Gattegno's Textbook 1

We are nearing the end of the series on Gattegno's Textbook 1. This last chapter deals with numbers up to 20. You'll notice it isn't 11-20, given that we did 1-10 already. Nope, Gattegno, in perfect Gattegno fashion, introduces new information and circles back to old information to layer on the new understanding.

This is a fascinating aspect of Gattegno. Growing up, my thoughts about math were all very disconnected. It is still

taught in a disconnected way in most classrooms, including the homeschool classroom. Gattegno will have none of that. The first couple exercises in this last chapter involve making observations  and then applying those those observations to what we already know. 

Noticing The Orange Rod

We begin our study of numbers up to 20 by taking two rods of any color to find pairs of rods that are longer than an orange rod. 

Once the student has found a pair that is larger than the orange rod, ask the student to find which length must be added to the orange to make it equivalent with the pair she has just found.

Can the student find another pair? 

Questions to think about as we find pairs:

  • Is there a way to quickly tell if the rods are larger than an orange?
  • Which rods will create the most pairs of rods larger than an orange?
  • Which rods when combined together will not make pairs larger than an orange?

Measuring Against the Orange Rod

After this casual approach to find pairs, we want to help the student transition to a more systematic approach to finding 2 rods which are longer than an orange. This will help the student make preliminary connections with numbers up to 20.

Starting with the yellow rod and the dark green placed end to end, which rod do you need to place end to end with the orange to make the two lengths equivalent? What about a yellow and black? Yellow and tan? Yellow and blue? Yellow and orange?

Repeat this with the dark green rod, the black rod, tan rod and the blue rods for all the lengths that are larger than an orange.

Introducing Names For Numbers Up To 20

You'll notice in the video above, the my son is capable of stating the number names up to 20. He knows that orange and white make eleven. I didn't teach him this, he figured it out. If your child has not become aware of this by the time you reach this point, you will want to make sure that you state the number names of 11-20 and explain that an orange and one white is 11, and orange and a red is 12 and an orange and light green is 13. Gattegno stops, for now, at 13 and gives the student room to explore. 

We used something like this to play notice and wonder several months ago when we decided to build a staircase past 10. 

Noticing Patterns

I know how hard it is not to just go for number names and move on as this seems so simple to us. But there is a lot in this image to the left to observe.

What Do You Notice?

Here are some of the things we noticed:

  • These trains all have a common difference of one.
  • They form a staircase.
  • They all have a ten in them.
  • puzzle-piece
    This is the same staircase as a one through ten staircase but they all have a ten in front of them.
  • puzzle-piece
    P. says when he was younger he would wonder if you start over with one through nine after you reach two tens. If you do, is the next number three tens? And it is. But he is older, so he knows that.
  • puzzle-piece
     We both wonder why the teen numbers have such weird names. 

Taking Time To Notice

We all get busy and fall back into the habit of just getting the work done and ticking off our checklist. As if our child's education and development could be accurately tied to a checklist. 

One of the things I have learned from Gattegno is to attend to the situation at hand - to child in front of me. I generally notice more about P. than I do about his work. Being aware is not one of P's strong traits. He doesn't pay attention to social clues. And he is usually unaware of where he is in space. 

Part of his education is to help him learn to navigate the world he lives in. Intentionally noticing and wondering, in all areas, has affected not just math, but reading, relationships, and life in general. Noticing my child has led me to have more compassion for him. I am less trapped in my checklist and more focused on what is important. I am way more aware of how my presence affects him - for good and ill. 

You can download that PDF of that worksheet here.

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