Three Digit Subtraction

Calfgrit8 had some homework that he couldn’t figure out. Cowgrit tried to help him with it, but she ended up coming to me: “Can you help CG8 with his homework?”

Cowgrit said she tried to help him, but she couldn’t figure out how to do it. I thought she was probably distracted by Calfgrit4, or maybe she was hurried with cooking dinner. I mean, it’s second grade homework, how difficult can it be?

The homework in question:

Pay the Bill

Solve.
Draw the coins to show the amount of change due.

A. Penny has $2.00. She buys an ice cream sundae for $1.89. How much change will she receive?

B. Percy has $1.00. He buys a small drink for $0.60. How much change will he receive?

C. Pip has $3.00. He buys a hamburger for $2.35. How much change will he receive?

. . . etc.

Looking over each problem, I immediately thought, “11 cents (a dime and a penny), 40 cents (four dimes), 65 cents (two quarters, a dime, and a nickel). . .” etc. Yeah, this isn’t complicated.

I sat down with Calfgrit8 and we talked through the problems a bit. “We haven’t learned how to subtract three-digit numbers, yet,” he explained.

“OK,” I said, “we can do it tonight.”

I wrote down
_200
-189

Then I sat there a minute looking at the equation.

“How do I do it, Dad?” CG8 asked.

“Um,” I answered, “well, ah, give me just a moment.”

I fiddled with the numbers a bit. I marked out the end zero and wrote “10” above it. Then I marked out the middle zero and wrote “9” above it. I thought that was it, but when I did the subtraction from right to left, I got 111 (instead of 011). How did this pattern change the beginning two to a one?

Wait a minute. I couldn’t remember actually how to do the borrowing from one digit to another. How many years has it been since I did subtraction on paper? Twenty years? Thirty years?

I took one of the other equations
_300
-235

I fiddled with the number again, but I couldn’t figure out how the old thing worked. I said to CG8, “You’ve done two-digit subtraction, right? I’ve seen you do that.”

“Yeah,” he confirmed.

“OK,” I said, “show me how you do that.”

He did 20 – 18.

“Great,” I said, “now lets use that to figure out how to do three-digit numbers.”

I wrote down the 200 – 189 equation again, and let him work it out, extrapolating what he knew for two-digit numbers. He did it correctly on his first try. And I saw how it was supposed to be done. Man, but that made me feel like an idiot.

CG8 quickly went through all six of his change problems, getting the right answer each time. Once he saw how it worked, it was all his. I wanted to give him some more three-digit numbers to subtract, but dinner was almost ready, and we still had another step to do on the homework.

I showed him how he could draw the change: I made a circle and wrote “1” in it for the penny, and then another circle with a “5” for the nickel. He got the pattern and used this for writing the change for each problem.

11 cents = circle-10, circle-1
40 cents = circle-10, circle-10, circle-10, circle-10
65 cents = circle-50, circle-5, circle-10
etc.

Afterward, Cowgrit and I talked about the homework. She, like me, could immediately tell the answer, but she couldn’t figure out how to explain it to CG8. “Yeah,” I agreed, “I ended up getting him to figure it out on his own.”

I wonder if helping with his homework will get easier or harder for me as his math problems get more advanced. I think I’m actually looking forward to him needing help balancing equations and solving for X.

Bullgrit