Subtracting Across Zeros

The words "subtracting across zeros" can make a third or fourth grade teacher's hair stand on end. All of that crossing out and mess of nines and tens. How can we teach this skill (and the underlying concept) so that our students will truly understand?

Yesterday I tried something new. Each of my students was given four sheets of Kovich Class Cash (thousands, hundreds, tens, and ones), each with ten bills.

As they cut out their funny money, excitement grew. Comments like, "The bigger the bill, the more Mrs. Koviches you get," and "Can we keep it?" and "I'm rich!" could be heard.

Each child organized his/her money on the top of the desk to represent a place value chart.

Then the subtracting began. I explained that the money at the top of the desk was the bank. In the first problem, we began with the number 1000. Each child put a $1000 bill in the middle of his or her desk.

The problem was revealed on the screen in front of the class.

We discussed the fact that taking two hundred dollar bills, seven ten dollar bills, and six one dollar bills away from a single one thousand dollar bill would be impossible. Instead, we would need to go to the bank.

Each child exchanged one thousand dollar bill for ten hundred dollar bills. On the screen I showed how this appears in the common algorithm.

We established that we still had $1000. Ten hundreds equals one thousand. But could we take two hundreds, seven tens, and six ones away from ten hundreds? No. We had to go back to the bank.

The students took one hundred to the bank and exchanged it for ten tens. Then we looked at our algorithm again. 

Now we had nine hundreds and ten tens. Did this still equal 1000? Yes! Could we subtract two hundreds, seven tens, and six ones? No. Back to the bank.

One ten was exchanged for ten ones. Now we had nine hundreds, nine tens, and ten ones. Did this still equal 1000? Yes! And here's how our algorithm looked:

Could we subtract two hundreds, seven tens, and six ones? Yes! Yay! The students busily arranged their bills on their desks, taking 276 away from 1000.

When the flurry of activity was over, seven hundreds, two tens, and four ones were left. We again looked at the algorithm. Yep! 724. That's the same as seven hundreds, two tens, and four ones.

After this, we worked a half a dozen or so more problems, moving faster and faster. Eventually we moved to working the problems without the funny money. When the time came for each student to subtract using paper and pencil on their own, a few used their funny money to get started.

P.S. Due to popular demand, I have created a PowerPoint presentation and class cash templates that you can use in your classroom. Subtracting Across Zeros with Class Cash is now available in my Teachers pay Teachers store.