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Homeschool math, Grade 2, subtracting across zeros

Why is subtracting across zeros so hard for my child?

402 minus 178 answered 324 in pencil, a borrow across the zero gone wrong.

For example: 402 − 178 = 324

The right answer is 224. Your child wrote 324 or 234 because the borrow in 402 had to pass through the zero, and one step got dropped. Lots of kids do this. It's fixable, and you can start tonight. In LOOP we call it "Borrowed across a zero wrong."

Your child isn't being careless. A zero has nothing to lend, so the borrow has to go one more place to the left. That's several steps to hold in your head at once.

What they wrote402− 178324
Or this402− 178234
The right answer402− 178224
Here is what happened. In 402, the ones need to borrow (2 is too small to take 8 from), but the tens digit is 0. For 324, they got 12 − 8 = 4 and 9 − 7 = 2, but forgot to cross the 4 down to 3, so the hundreds were 4 − 1 = 3. For 234, they crossed the 4 down to 3 but left the 0 as a 10 after lending from it, so the tens were 10 − 7 = 3, and the hundreds came out 3 − 1 = 2.

Here is the right way. 402 is 4 hundreds, 0 tens and 2 ones. The 0 can't lend, so trade 1 hundred for 10 tens. Then trade 1 of those tens for 10 ones. Now you have 3 hundreds, 9 tens and 12 ones. 12 − 8 = 4, 9 − 7 = 2, and 3 − 1 = 2, so the answer is 224. Teachers call the trades "borrowing."

Is it this, or something else?

Before you fix anything, look at what they actually wrote.

324 or 234Borrowed across a zero wrong. This is the page you're on.
376Took the smaller digit from the bigger one. They did 8 − 2 = 6 in the ones instead of borrowing, then 7 − 0 and 4 − 1. That's a different mistake with its own fix.
223 or 225Their method is fine; one fact slipped. Check which fact: 12 − 8 is the usual one.

One wrong answer might just be a slip. If the same thing shows up again and again, it isn't. The sheet below will show you whether this is a pattern.

Free printable: 12 problems

Two of these (684−321 and 576−243) need no borrowing, so they are your check. If those two come back right and the other ten are all too big, this is probably the mistake. Check the key below for the exact wrong answers.

It prints on its own page.

Answer key

1. 224, 2. 138, 3. 268, 4. 363, 5. 345, 6. 358, 7. 335, 8. 333, 9. 327, 10. 159, 11. 337, 12. 218.

A child making this mistake will write one of these on each of the other ten: 1. 324 or 234, 2. 238 or 148, 3. 368 or 278, 5. 445 or 355, 6. 458 or 368, 7. 435 or 345, 9. 427 or 337, 10. 259 or 169, 11. 437 or 347, 12. 318 or 228. Every one is bigger than the true answer. Problems 4 and 8 stay correct.

Subtracting across zeros
Name ____________Date ________Subtract. Use a pencil.
1.402− 178
2.305− 167
3.506− 238
4.684− 321
5.704− 359
6.603− 245
7.801− 466
8.576− 243
9.902− 575
10.307− 148
11.800− 463
12.405− 187
looplearning.org

What to do this week

  1. Day 1: Use dimes and pennies, or base-ten blocks if you have them. Lay out 402 as 4 dollar bills, no dimes and 2 pennies (a dollar is 100 pennies), or 4 flats, no rods and 2 ones. Ask your child to take away 178, which is 1 dollar, 7 dimes and 8 pennies. They only have 2 pennies and no dimes, so they can't. Pause when they notice, and don't tell them the trade. If they get stuck, ask where a dime could come from. Once they trade a dollar for 10 dimes, then a dime for 10 pennies, they have 3 dollars, 9 dimes and 12 pennies, and the taking away works.
  2. Day 2: Same problems, now on paper. Before each column, have them say out loud: "Is the top number big enough?" In 402 − 178, is 2 big enough to take 8 from? No. Is 0 big enough to lend? No. Go left to the 4.
  3. Day 3: Do the printable again and count how many are still too big. If most of the ten are right now, you're good. If they're still getting the same wrong answer, do Day 1 again.

LOOP does this for every page. Your child does a printed page in pencil. You take a photo. LOOP tells you which mistake showed up on each problem and prints the next page. Your child works on paper the whole time.

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Tyler Judson, LOOP co-founder. Before LOOP I tutored math, one kid at a time. LOOP is my try at giving every kid that kind of attention without a tutor in the room.

The mistake names are the ones LOOP uses, examples checked by running LOOP's mistake-finder.

Know what your child is missing, on paper.

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