Partial products multiplication, explained for parents
Partial products multiplies each place-value part separately and adds the results. For 23 × 14 that's 12 + 80 + 30 + 200 = 322. It's the area model written as a list, and it shows every step the standard method hides.
Checked October 29, 2026 against the sources listed at the end.
What partial products are
Every multi-digit number is a sum of place-value parts: 23 is 20 + 3. Multiplying two such numbers means multiplying every part of one by every part of the other. Each of those small results is a partial product, and adding them gives the answer.
Children write the problem the usual way, top and bottom, then list each partial product underneath, often with a note beside it saying which two parts made it.
A worked example: 23 × 14
- 4 × 3 = 12
- 4 × 20 = 80
- 10 × 3 = 30
- 10 × 20 = 200
- Add them: 12 + 80 + 30 + 200 = 322.
One more: 347 × 6
With a one-digit number it's quick. 347 is 300 + 40 + 7, so the partial products are 6 × 7 = 42, 6 × 40 = 240, 6 × 300 = 1,800. Together: 42 + 240 + 1,800 = 2,082.
Why schools teach it
The Common Core doesn't name partial products. It asks fourth graders to multiply using strategies based on place value and the properties of operations, and to explain the calculation with equations, arrays or area models. Partial products is one such strategy, and many math programs teach it.
Its strength is that nothing is hidden: no carrying, no shifted rows. A child can see that 10 × 20 is 200 and why the answer is in the hundreds. It's also the same four numbers as the area model, so the picture and the list support each other.
Helping with homework
- Have your child say each line out loud: "four times twenty is eighty". Hearing "twenty" instead of "two" keeps the zeros in place.
- Count the lines before adding: a two-digit by two-digit problem always has four.
- Line the numbers up by place value when adding them, ones under ones.
- When the method feels easy, show how the standard algorithm adds some lines together as it goes. Our standard algorithm page walks through it.
- If your child's teacher uses different words or a different layout, use theirs. The point is that your child hears one way of explaining it, not two competing ones; a quick note to the teacher asking "how do you want this shown?" is always welcome.
Try it
Print two-digit by one-digit multiplication worksheets and two-digit by two-digit worksheets, each with an answer key, and check single-digit facts on the multiplication chart.
Questions parents ask
Is partial products the same as the area model?
They give the same numbers in a different layout. The area model draws them as boxes in a rectangle; partial products lists them under the problem.
Does the order of the lines matter?
No, since adding works in any order. Many classes start with the ones so the list matches the standard method later, but follow what the teacher shows.
Practice at your child's level
Peabody, our site for children, has free stories and learning games written at each reading level and math grade, with no sign-up. Start where your child is comfortable, not where the calendar says.
- Start reading on Peabody Peabody asks your child's grade, starts the stories a little under it, and moves the level as books run easy or hard.
- Reading levels and math by grade Where each grade starts, and a page for every level and math path.
- The free library Stories sorted by level, to read on screen.
- Decodable readers Stories built from the sounds a beginning reader has been taught.
Where this comes from
Written for parents, to use alongside your child's teacher, not instead of them. General information only, not professional, medical or legal advice. Checked on October 29, 2026. Something wrong or out of date? Write to hello@peabody.kids.