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What is the partial products method? A parent’s guide

If your child’s multiplication has more lines than you expect, each with a small product and a lot of zeros, that is the partial products method. It is the area model written as a column, and the step before the method most parents learned.

By The Kizupi team · Written · Updated

Key findings

  • Grade 4 standards ask children to multiply up to a four-digit number by a one-digit number, and two two-digit numbers, with strategies based on place value and the properties of operations [1]. Partial products is one of those strategies: every digit is multiplied at its full place value.
  • Each line of a partial products problem is one box of an area model, so the two methods always give the same list of numbers.
  • The standard algorithm is the Grade 5 expectation: “Fluently multiply multi-digit whole numbers using the standard algorithm” [2]. It adds the partial products as it goes, which is why it has fewer lines.

What partial products are

A partial product is the answer to one small piece of a bigger multiplication. Split each number by place value, multiply every piece of one number by every piece of the other, write each answer on its own line, then add the lines.

36× 25305 × 61505 × 3012020 × 660020 × 30900

For 36 × 25, 36 is 30 and 6, and 25 is 20 and 5. That makes four partial products: 5 × 6 = 30, 5 × 30 = 150, 20 × 6 = 120 and 20 × 30 = 600. Then 30 + 150 + 120 + 600 = 900.

How it matches the area model

Draw 36 × 25 as an area model and you get four boxes: 600, 120, 150 and 30. Those are the same four numbers. The area model shows them as parts of a rectangle; partial products lists them in a column so they are easy to add.

30620600120515030

If your child’s class draws the boxes first and then writes the column, that is why: one picture, then the same numbers in a form you can add.

Example 1: a one-digit multiplier, 7 × 248

248× 7567 × 82807 × 401,4007 × 2001,736

248 is 200, 40 and 8. Multiply each by 7: 7 × 8 = 56, 7 × 40 = 280 and 7 × 200 = 1,400. Add them: 56 + 280 + 1,400 = 1,736. Every line is a fact your child knows, with zeros for the place value.

From partial products to the standard algorithm

The standard algorithm for 36 × 25 writes two lines, not four: 180 and 720. Look back at the partial products. 30 + 150 = 180 is everything times 5. 120 + 600 = 720 is everything times 20. The standard algorithm adds each row as it goes, carrying the tens in the child’s head instead of writing them down.

36× 251805 × 3672020 × 36900

That is the Grade 5 step [2]. A child who can explain where 180 and 720 come from, using the four partial products, understands the algorithm rather than just following it.

The two mistakes to look for

  • Dropping the zeros. Writing 2 × 3 = 6 for 20 × 30 instead of 600. Ask your child to say the numbers aloud, “twenty times thirty”, and to check the size: 20 × 30 must be more than 20 × 10 = 200.
  • Missing a line. Two two-digit numbers always give four partial products, and a three-digit number times a one-digit number gives three. Count the lines before adding.

How to help at home

  1. Split numbers out loud. Say 248, and your child says “200, 40 and 8”. Every partial product depends on this.
  2. Practice multiplying by tens. 20 × 30, 7 × 40, 5 × 300. If 2 × 3 is quick, 20 × 30 is quick too.
  3. Write what each line is. A small note like “5 × 30” next to each partial product makes a missing line easy to spot.
  4. Estimate first. 36 × 25 is near 40 × 25 = 1,000, so 900 makes sense and 9,000 does not.

For practice with a hint on every problem, try the free Grade 4 multiplication and division word problem sheets, each with an answer key.

Questions parents ask

What grade learns partial products?

Usually Grade 4, where the standards ask for multi-digit multiplication with strategies based on place value [1]. The standard algorithm follows in Grade 5 [2].

Is partial products the same as the area model?

They use the same numbers. The area model draws each partial product as a box in a rectangle; the partial products method lists them in a column and adds them.

Why does partial products have so many lines?

It writes every piece separately: four lines for two two-digit numbers. The standard algorithm combines them into one line per digit of the bottom number, which is shorter but hides where the numbers come from.

What order should the partial products go in?

Any order gives the right answer, because addition can be done in any order. Many classes start with the ones, like the standard algorithm, so the habit carries over.

Keep going

Sources

  1. Common Core State Standards Initiative, Grade 4, Number and Operations in Base Ten (4.NBT). Read November 7, 2026.
  2. Common Core State Standards Initiative, Grade 5, Number and Operations in Base Ten (5.NBT). Read November 7, 2026.

Cite this page: The Kizupi team, “What is the partial products method? A parent’s guide,” Kizupi, updated November 8, 2026, https://kizupi.com/guides/partial-products-multiplication.

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