One-Teen, Two-Teen…Place Value for Kinesthetic Learners

My second daughter has been my most academically challenging child to teach. School just isn’t a skill that is easy for her. She has to work hard for every good grade that she gets. In early elementary school, I despaired of just getting the basics down. It was a long slow trudge through simple things like counting. I learned that my daughter is a kinesthetic learner, meaning that she best absorbs information by doing things.

I had to harness this when I was teaching her to count. She could rattle off the numbers out loud, but when it came time to count objects or when she was reading a number out loud, it was typical for her to get things mixed up.

Twelve often was called twenty-one.  She frequently confused thirteen and thirty-one. And it really baffled her that there was no one-teen or two-teen. Her biggest problem was understanding place value and figuring out that you can’t interchange two digit numerals.

To solve this problem, I invented Popsicle stick math. I used Popsicle sticks because they are cheap, easy to handle, and I had a huge box of them lying around.

One day, we sat down and counted out bundles of ten Popsicle sticks. We piled them all around us and bundled them up with rubber bands. She knew that each bundle held ten sticks because she’d counted them out by herself.

Then we worked on counting by tens. Ten, twenty, thirty, etc. As we counted, I would write the numbers on a marker board to show her what they looked like. I’d ask questions like, “When you have thirty popsicle sticks, how many bundles do you have?”

She would answer, “Three.”

And I’d ask her, “Do you have any single sticks in thirty?”

She would answer, “No.”

And I would show her that the zero in the numeral 30 represented zero separate sticks and the three represented 3 bundles. Then I would write two numbers. A plain old 3 and the 30. We talked about how they were different and why we had to put that zero next to the three in thirty.

Once I felt that she clearly understood the multiples of ten and how to write and count out those multiples using our bundles. I would add in some different numbers. I started with the hated twelve and twenty one.

She figured out twenty and then I said, “Now, if we put one plain old Popsicle stick with the twenty, how many are there now?”

She could count consecutively, so she knew that the answer was twenty-one. Then we talked about how to write that. The two means two tens (two bundles) and the one meant one single stick. We couldn’t interchange them.

Then we demonstrated how twelve worked with one bundle and two singles.

If she got confused, we could take apart the bundles and count the individual sticks.

We worked out numbers like this for a long time. She finally understood how place value worked.

In the future, we were able to use these same Popsicle sticks to demonstrate addition and subtraction of two digit numbers, as well as tricky concepts like borrowing and carrying.

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1 Comment (+add yours?)

  1. Joshua
    Aug 07, 2015 @ 05:03:17

    Naming numbers, especially 10-20 is the area of math where students’ logical thinking leads them to the wrong answers. It is a bit unfair to the kids!

    Don’t feel that the need for concrete representations is a failure or weakness. Research supports the idea that including concrete, pictorial, and abstract representations is powerful for learning.


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