Why does my child forget the zero in two-digit multiplication?
For example: 34 × 12 = 102
The right answer is 408. Your kid wrote 102 because the second row of the problem was not moved over a place. They never put the zero down, so the tens row landed right under the ones row. Lots of kids do this. It's fixable, and you can start tonight. In LOOP we call it "Forgot the zero in the tens row."
Your kid isn't being careless. They know to multiply by the 2, and then by the 1. What they missed is that the 1 in 12 is really a 10. Its row has to start one place over.
What they wrote34× 126834102
The right answer34× 1268340408
Here is what happened. They did 34 × 2 = 68, which is right. Then they did 34 × 1 = 34 and wrote it straight under the 68, with nothing moved over. Adding 68 and 34 gave 102.
Here is the right way. The 1 in 12 is 1 ten, so the second row is 34 × 10 = 340. Put a 0 in the ones place first, then write 34 next to it. Now 68 + 340 = 408.
Is it this, or something else?
Before you fix anything, look at what they actually wrote.
102Forgot the zero in the tens row. This is the page you're on.
46Added instead of multiplied. They did 34 + 12 and never multiplied at all.
68Stopped after the ones row. They did only 34 × 2 and never started the tens row.
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 (47 × 6 and 126 × 4) have a one-digit bottom number, so there is no tens row to forget. They are your check. If those two come back right and the other ten are all too small, this is probably the mistake. Check the key below for the exact wrong answers.
A child making this mistake will write 102, 115, 180, 364, 108, 135, 288, 378, 675, 328 for problems 1, 2, 3, 5, 6, 7, 9, 10, 11, 12. Every one is smaller than the true answer. Problems 4 and 8 stay correct.
Multiplying by two-digit numbers
Name ____________Date ________Multiply. Use a pencil.
1.34× 12
2.23× 14
3.45× 13
4.47× 6
5.52× 16
6.36× 21
7.27× 32
8.126× 4
9.48× 15
10.63× 24
11.75× 18
12.41× 35
looplearning.org
What to do this week
Day 1: Use a grid of squares, or draw a rectangle 34 long and 12 wide. Split the 12 into 10 and 2. Ask your kid how many squares are in the 34 by 2 part, then in the 34 by 10 part. Don't tell them about the zero. If they get stuck, ask how many squares are in ten rows of 34. Once they count 340, point out the 0 on the end. That is the zero they were missing.
Day 2: Same problems, now on paper. Before the second row, have them say out loud: "Am I multiplying by ones or by tens?" In 34 × 12, the 1 is a ten, so the row starts with a 0.
Day 3: Do the printable again and count how many are still too small. 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 kid 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 kid works on paper the whole time.
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 for Grade 5 multiplication. The examples were checked by running LOOP's mistake-finder.