Area model multiplication, explained for parents
An area model turns a multiplication into a rectangle. Each number is split into tens and ones, the rectangle is split the same way, and each small box is an easy multiplication. Add the boxes and you have the answer: 23 × 14 is 200 + 30 + 80 + 12 = 322.
Checked October 29, 2026 against the sources listed at the end.
What an area model is
Think of multiplication as the area of a rectangle: 3 rows of 4 squares is 12 squares. For bigger numbers nobody draws every square. Instead the sides are split into place-value parts (tens and ones), which splits the rectangle into a few smaller boxes. Each box is a small multiplication a child can do in their head, and adding the boxes gives the whole.
Children often call it the box method. The rectangle doesn't need to be drawn to scale; a quick sketch with the right labels is all the homework needs.
A worked example: 23 × 14
- Split each number by place value: 23 = 20 + 3, and 14 = 10 + 4.
- Draw a rectangle with 2 columns and 2 rows, and label the sides with those parts.
- Multiply to fill each box: 10 × 20 = 200, 10 × 3 = 30, 4 × 20 = 80, 4 × 3 = 12.
- Add the boxes: 200 + 30 + 80 + 12 = 322.
- Check that it's sensible: 23 × 14 is a bit more than 20 × 15 = 300, so 322 fits.
Why schools teach it
The Common Core asks fourth graders to multiply bigger numbers using strategies based on place value, and to illustrate and explain the calculation with equations, rectangular arrays or area models. The area model makes the size of each part visible: here the 10 × 20 box is 200, most of the answer, which helps a child judge whether an answer is sensible.
It is a step on the way, not a replacement. The same standards expect children to multiply multi-digit numbers with the standard algorithm, the method most parents learned, by the end of fifth grade.
How it connects to the method you learned
In the method you probably learned, 23 × 14 has two rows: 23 × 4 = 92, and 23 × 10 = 230. Those rows are the area model's rows added up: 80 + 12 = 92, and 200 + 30 = 230. Then 92 + 230 = 322.
So when your child moves to the standard method, the area model is the reason it works. The "put a zero" on the second row is the 10 in the side of the rectangle.
Helping with homework
- Ask your child to talk you through one problem before you say anything. Explaining it is half the learning.
- Watch for lost zeros: 10 × 20 is 200, not 2. Saying "ten twenties" out loud helps.
- Check every box is filled. A forgotten box is the most common slip.
- Estimate first (round both numbers), then see if the answer is close.
- 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
Build it with base-ten blocks on screen: tens rods and ones cubes laid out in a rectangle show the same four boxes. For practice, print two-digit by two-digit multiplication worksheets with answer keys, and keep a multiplication chart handy for the single-digit facts.
Questions parents ask
Does the rectangle have to be drawn to scale?
No. A rough rectangle with the right labels is enough. Some teachers like the boxes roughly in proportion so children see that the tens box is the biggest, but it isn't required.
Will my child ever learn the regular way?
Yes. In the Common Core, multiplying multi-digit numbers with the standard algorithm is a fifth-grade expectation. The area model comes first because it shows why that method works.
Can the area model handle three-digit numbers?
Yes, with more boxes: a three-digit number splits into hundreds, tens and ones, so 234 × 56 is a rectangle three boxes wide and two tall.
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.