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Monday, March 3, 2014

Providing PROOF While Learning About Place Value

The First Grader I was working with  has a lot of experience with building numbers using base ten blocks using worksheets to show her understanding.

 But my goal was to have her PROVE that she knew her answer was correct.

I wanted her to verbalize her thinking.
So we began by having her count the number shown on the base ten blocks that I gave her and write down the number. In this photo you can see that she wrote down "52."
As you can see there are 12 ones. 
So when I ask her to prove to me that there were 5 tens and not just the 4 tens bars that I had given her, she placed the 10 ones on top of an empty tens bar to prove to me why she knew the number was 52.
"Oh, now I can see your thinking," I said.
Here is the problem that I gave her next.
You can see that I am guiding her to again form tens bars from the ones units because she knew that she was going to have to PROVE and EXPLAIN why she knew her answer was correct.
I increased the difficulty because I wanted to see what she knew about the hundreds place.  I also ask her to list her answer as a single number like 92, and also in an expanded form:____ tens _____ones.

This was her response:  11 tens and 6 ones  and 116.
That created the discussion about the fact that you can create one hundred out of the 11 tens with one ten left over.
"Let's do one with a thousand in it," she requested.

Of course, I explained one way to write out your proof for the final number calculated.
Because I wanted to see how she would react when there way no hundreds place amount.
Next problem
Solved and explained with ease.
The next twist was to give her the number to build and explain why she knew she had built it correctly.
And... while all this discussion was taking place, I was cooking spaghetti with homemade meat sauce and garlic bread too.

So... yes, I was working one on one with a learner, but this same discussion can be done with a small group or the whole group with a way to project an image of what is going on to the group.

We recorded our thinking by taking pictures on the I-Pad as we worked. When we were finished, we went back through the pictures and verbally summarized our thinking. 
 Your students could do the same thing, and record their thinking by making a video, and then giving it to you to listen to at a later time.


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