Area model multiplication
Show products as rectangle areas before formal algorithms.
Quick answer
Area model multiplication is a way to multiply numbers by drawing rectangles and breaking them into smaller parts. It helps you understand how multiplication works and makes big multiplication problems easier to solve.Learning outcome
By the end of this page, you will be able to use area models to multiply two-digit numbers by breaking them into parts and drawing rectangles to show your work. Success signs:- You can draw a rectangle to show how two numbers multiply together
- You can split bigger numbers into tens and ones to make multiplication easier
- You can add up the areas of smaller rectangles to find the total area
- You can use this method to solve multiplication problems like 24 × 13
Why this matters
Area model multiplication helps you understand what multiplication really means. Instead of just memorising steps, you see how numbers fit together in space. This method is useful for:- Learning how multiplication works in real life, like when you share out items or plan a garden
- Preparing for more advanced maths like algebra and long multiplication
- Building confidence in solving bigger multiplication problems
- Using maths to solve everyday puzzles, like planning a party or buying toys
How it works
Area model multiplication uses rectangles to show how two numbers multiply together. Here’s how to do it:- Break one number into tens and ones (or hundreds, tens, and ones for bigger numbers)
- Draw a rectangle and split it into smaller rectangles based on those parts
- Write the parts of each number along the sides of the rectangle
- Multiply each small part to find the area of each small rectangle
- Add all the small areas together to get the final answer
Examples you can see
Let’s try a simple example: 12 × 13. Step 1: Break 12 into 10 and 2, and 13 into 10 and 3. Step 2: Draw a big rectangle and split it into four smaller rectangles. Step 3: Label the top with 10 and 2, and the side with 10 and 3.| 10 | 2 | |
|---|---|---|
| 10 | 100 | 20 |
| 3 | 30 | 6 |
- 10 × 10 = 100
- 10 × 2 = 20
- 3 × 10 = 30
- 3 × 2 = 6
Try it as a mini adventure
Imagine you are designing a garden. You want to plant flowers in a rectangular area that is 14 metres long and 12 metres wide. Adventure challenge: How much space do you need for your garden? Step 1: Break the numbers:- 14 = 10 + 4
- 12 = 10 + 2
- Top: 10 and 4
- Side: 10 and 2
- 10 × 10 = 100 square metres
- 10 × 2 = 20 square metres
- 4 × 10 = 40 square metres
- 4 × 2 = 8 square metres
Common mistakes
- Mistake: Forgetting to write the correct multiplication for each small rectangle.
Why it happens: Kids might mix up which numbers to multiply.
Fix: Always double-check that you multiply the top number by the side number for each small rectangle. - Mistake: Adding the small areas wrong.
Why it happens: Adding large numbers can be tricky.
Fix: Use a calculator or count carefully, or write down each addition step. - Mistake: Not splitting numbers correctly.
Why it happens: Some kids forget that 14 is 10 + 4, not 1 + 4.
Fix: Use base-10 blocks or drawings to help you see tens and ones clearly.
Parent and carer guide
You can help your child by:- Using base-10 blocks or drawing rectangles to show how numbers break apart
- Practising with simple problems like 12 × 11 or 15 × 13
- Letting your child explain their thinking as they work
- Using real-life examples like planning a room or a garden
- Not worrying if they make mistakes — it’s part of learning!
Practice questions
- What is 11 × 12 using the area model?
- Draw an area model for 13 × 14.
- Find 15 × 16 using area model multiplication.
- What is 21 × 13?
- Use the area model to solve 17 × 18.
- 11 × 12 = 132
- Draw a rectangle with sides 10 + 3 and 10 + 4. Areas: 100, 30, 40, 12. Total = 182
- 15 × 16 = 240
- 21 × 13 = 273
- 17 × 18 = 306
FAQ
What is area model multiplication?
Area model multiplication is a way to multiply numbers by drawing rectangles and splitting them into smaller parts. It helps show how multiplication works by using area.
Why do we use area models?
Area models help us understand how multiplication works, especially for larger numbers. They make it easier to break down a problem and solve it step by step.
Can I use area models for any multiplication?
Yes! You can use area models for any multiplication, but they work best for two-digit numbers. They are especially helpful when you are learning how to multiply bigger numbers.
Is area model multiplication the same as regular multiplication?
It gives the same answer, but area model multiplication shows the process more clearly. It helps you understand why multiplication works, not just how to do it.
How can I practice area model multiplication at home?
You can practice by drawing rectangles and breaking numbers into tens and ones. Try it with everyday numbers like your age or how many toys you have.