Break Those Numbers Apart!

I’m officially trading in my place value blocks for unifix cubes!

Today I was trying to teach a small group of students how to subtract with place value blocks. The problem came when I tried to show how to regroup! As soon as we traded a ten rod for ten ones, eyes glazed over and their minds left me. They couldn’t understand why we’d trade it in and pick up ten ones. I realized that is because it doesn’t really explain the concept, which is that we are breaking the ten into 10 ones, not trading. Instead I tried unifix cubes, which you can actually break apart.

So when I blasted apart a 10 pack of unifix cubes, the light bulbs switched on. The students were so excited to try it themselves, and then, when shown the algorithm next to it, I heard a lot of “OHHHH!!!”

It was the coolest thing. Here is how we did it.

Start with your problem, but only show the top number with the place value blocks.

photo 4 (4)

Decide if you can subtract seven from two.  As the numbers stand, you cannot. So…take a ten, and show it on the number below.  (The three tens become two tens.)

photo 1 (9)

Break that ten into ten tiny ones.

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Those ten ones are placed next to the two that were already there.

photo 2 (6)

Now we have 12 ones! We write it on the problem below to help us understand why we do that.

photo 1 (8)

Now we’re all situated, and we can subtract.  When you take seven ones away…

photo 5 (1)

You are left with five ones!

photo 3 (3)

Then, you can take one ten from the two tens.

photo 1 (7)

One ten and five ones remain!

photo 3 (2)

The best part is, teaching this way solidifies MY math and number sense.  When I grew up, were were taught how to “borrow and carry” but I had absolutely NO idea why. I learned how to do this as an adult, and it was very difficult to learn. I find that when I understand math more deeply, it is easier to think of different ways to teach these concepts to students who struggle!



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