Multiplication using an area model

Part ofMathsMultiplying and dividingYear 6

What is an area model?

An area model is a rectangular grid that can help you solve multiplication problems. The process is similar to how you find the area of a rectangle.

Two-digit numbers can be partitioned into smaller parts to make them easier to multiply.

The area model below shows how the multiplication calculation 14 × 16 can be partitioned into a series of smaller multiplication calculations.

Two rectangles which are the same size. Inside the first is 16×14. On its left edge is 14 and on its top edge 16. An arrow points to the next rectangle, which is split 4 smaller rectangles. On its left edge are 10 at the top and then 4 below. On the top edge from left to right are 10 and 6. Inside the 4 smaller rectangles from left to right are the calculations 10×10, 10×6, 4×10 and 4×6.

First, find the answer to each of these smaller multiplication calculations:

10 × 10 = 100

10 × 6 = 60

4 × 10 = 40

4 × 6 = 24

Then you can add all the results together to find the answer:

100 + 60 + 40 + 24 = 224

Therefore:

16 × 14 = 224

Back to top

Activity: Multiplying using an area model

Complete this interactive activity to understand how to use an area model to multiply. Then put your knowledge to the test.

Back to top

Area models

You can use partitioning skills to start completing an area model.

Think about the multiplication calculation 27 × 48.

The number 27 can be partitioned into 20 and 7. The number 48 can be partitioned into 40 and 8.

Take a look at a completed area model for this calculation.

A rectangle is split 4 smaller rectangles. On its left edge numbers are written: 20 at the top and then 7 below. On the top edge from left to right are 40 and 8. Inside each smaller rectangle is a calculation. From left to right on each row are 40×20, 8×20, 40×7 and 8×7.

When the numbers are partitioned, you can work out the answers to the smaller multiplication calculations for each of the parts you have created.

Then you should add the results together to find the answer.

The results are:

40 × 20 = 800

8 × 20 = 160

40 × 7 = 280

8 × 7 = 56

All that's left to do is add together the results:

800 + 160 + 280 + 56 = 1296

So you now know that:

27 × 48 = 1,296

Back to top

Example 1

A rectangle is split 4 smaller rectangles. On its left edge numbers are written: 20 at the top and then 7 below. On the top edge from left to right are 30 and 2. Inside each smaller rectangle is a calculation or a question mark. From left to right on each row are 20×30, a question mark, 7×30 and 7×2.

What is missing from this area model?

Back to top

Example 2

Take a look at this area model and answer these two questions.

A rectangle is split horizontally into 2 smaller rectangles. On its left edge 24 is written and below it 30 is written. Inside each smaller rectangle is a question mark.
  • What are the two multiplication calculations missing from this area model?
  • What is 24 × 30?

Back to top

Example 3

Look at this area model and answer these questions.

A rectangle has been divided into 7 horizontal rectangles of equal height. The length of the main rectangle and those within it is 15. The height of each rectangle is 4. Within each of the 7 rectangles is a question mark.
  • What is missing from the rows?
  • What number has been partitioned?

Back to top

Use your times tables and more maths skills to defeat monsters and reclaim the Kingdom of Mathematica

Play our fun maths game Guardians: Defenders of Mathematica
Back to top

More on Multiplying and dividing

Find out more by working through a topic