It’s the same multiplication. Just with nothing hidden.
If your kid’s multiplication homework has a bunch of numbers stacked up before the final answer, that’s partial products.
It usually shows up in 4th grade, and it’s honestly one of the more useful “new math” strategies once you see what it’s doing.
The idea
Break the numbers into tens and ones. Multiply each piece. Add the pieces together.
That’s it.
Start small: 34 × 6
34 is really 30 + 4. So:
- 30 × 6 = 180
- 4 × 6 = 24
- 180 + 24 = 204
Most adults already do this in their heads without realizing it. Partial products just writes it down.
Two-digit times two-digit: 36 × 24
Now both numbers get broken apart. 36 is 30 + 6, and 24 is 20 + 4. Every piece gets multiplied by every piece:
- 30 × 20 = 600
- 30 × 4 = 120
- 6 × 20 = 120
- 6 × 4 = 24
Add them up: 600 + 120 + 120 + 24 = 864.
Four multiplications, four pieces. If your kid only has three pieces on their paper, one is missing. It’s an easy one to skip.
How it connects to the way you learned
Here’s the same problem the “old way”:
- 36 × 4 = 144
- 36 × 20 = 720 (that’s the row where you put the 0 down first)
- 144 + 720 = 864
Look closely. 144 is just 120 + 24. And 720 is just 600 + 120.
The standard method does the exact same four multiplications. It just combines them as it goes, and hides the carrying. Partial products shows every step.
And remember that area model box from the last post? Those four pieces are the four boxes. Same math, different picture.
Why bother?
- It’s easier to check. Each piece is a simple problem. If the answer’s wrong, you can find exactly which piece broke.
- It builds mental math. Kids who get this can do 25 × 12 in their heads.
- It makes the old way make sense. When they move to the standard method, they’ll know why the 0 goes there.
How to help at home
- Ask “what is that digit really worth?” The 3 in 36 is really 30. A really common slip is multiplying by 3 instead of 30.
- Count the pieces. Two-digit times two-digit should always give four.
- Line up the pieces before adding. Messy columns cause a lot of wrong answers that have nothing to do with multiplying.
- Practice out loud. At the store, try “4 packs of 12, that’s 4 tens and 4 twos.” Short and casual works better than a worksheet fight.
The bottom line
Partial products isn’t a different kind of multiplication. It’s the same thing you learned, with the steps written out.
It takes a little longer at first. That’s normal. Once it clicks, kids usually get faster, not slower.
If your kid wants more practice, the free math worksheets are there anytime.
And if there’s a homework method you want me to break down next, feel free to ask me. I’d be glad to help!
