Area Model Multiplication - Grid Method, Examples, and Worksheets

What is area model multiplication?

Area model multiplication is a way to multiply by using a rectangle. The rectangle is split into smaller rectangles, and each smaller rectangle shows one partial product.

The method is friendly because it turns one big multiplication problem into smaller facts that are easier to see. You split by place value, multiply each part, and then add the parts together.

For example, 17 x 14 can become 10 x 10, 7 x 10, 10 x 4, and 7 x 4. Those four smaller answers add up to the full product.

Why the area model helps

The area model makes place value visible. Students can see tens, ones, hundreds, and partial products instead of only memorizing a vertical method.

It also helps students avoid a common mistake: forgetting that the 3 in 34 means 30, not just 3.

Once the area model makes sense, the standard multiplication algorithm feels less like a trick because students understand where the partial products come from.

Practice worksheets

After the examples, use the Grade 4 Area Model Multiplication Worksheets for printable practice. The worksheet page and this lesson are linked together so students can learn the method, then practice it on paper.

Each worksheet gives students area model boxes where they can write the partial products before finding the final answer.

The four steps

Step 1: Split each factor by place value. For 34 x 12, write 34 as 30 + 4 and 12 as 10 + 2.

Step 2: Draw a rectangle and split it into boxes. A 2-digit by 2-digit problem usually makes four boxes.

Step 3: Multiply to fill every box. Each box is one partial product.

Step 4: Add the partial products. The sum is the final answer.

Example 1: 17 x 14

Start with an easy grid. Split 17 into 10 + 7. Split 14 into 10 + 4.

Now multiply every top part by every side part: 10 x 10 = 100, 7 x 10 = 70, 10 x 4 = 40, and 7 x 4 = 28.

Add the four parts: 100 + 70 + 40 + 28 = 238. So, 17 x 14 = 238.

Area model grid showing 17 x 14 split into 10 plus 7 and 10 plus 4 — The first example uses a full grid so students can see the four rectangles clearly.

Example 2: 23 x 14

Split the factors: 23 = 20 + 3 and 14 = 10 + 4.

Fill the boxes: 20 x 10 = 200, 3 x 10 = 30, 20 x 4 = 80, and 3 x 4 = 12.

Add the partial products: 200 + 30 + 80 + 12 = 322. So, 23 x 14 = 322.

Area model diagram showing 23 x 14 with four partial products — Every part of 23 must multiply every part of 14.

Example 3: 36 x 18

Split the factors: 36 = 30 + 6 and 18 = 10 + 8.

The four boxes are 30 x 10 = 300, 6 x 10 = 60, 30 x 8 = 240, and 6 x 8 = 48.

Add: 300 + 60 + 240 + 48 = 648. So, 36 x 18 = 648.

Area model diagram showing 36 x 18 split into 30 plus 6 and 10 plus 8 — The model keeps the tens and ones visible while solving 36 x 18.

Example 4: 47 x 25

Split the factors: 47 = 40 + 7 and 25 = 20 + 5.

Fill the boxes: 40 x 20 = 800, 7 x 20 = 140, 40 x 5 = 200, and 7 x 5 = 35.

Add carefully: 800 + 140 + 200 + 35 = 1175. So, 47 x 25 = 1175.

Area model diagram showing 47 x 25 with partial products 800 140 200 and 35 — This example is tougher because both numbers have larger tens parts.

Example 5: 58 x 13

Split the factors: 58 = 50 + 8 and 13 = 10 + 3.

Partial products: 50 x 10 = 500, 8 x 10 = 80, 50 x 3 = 150, and 8 x 3 = 24.

Add: 500 + 80 + 150 + 24 = 754. So, 58 x 13 = 754.

Area model diagram showing 58 x 13 split into 50 plus 8 and 10 plus 3 — The small 3 still makes two partial products, so it cannot be skipped.

Example 6: 61 x 24

Split the factors: 61 = 60 + 1 and 24 = 20 + 4.

Partial products: 60 x 20 = 1200, 1 x 20 = 20, 60 x 4 = 240, and 1 x 4 = 4.

Add: 1200 + 20 + 240 + 4 = 1464. So, 61 x 24 = 1464.

Area model diagram showing 61 x 24 and the small 1 part in the model — Even a small ones part still creates real products in the model.

Example 7: 72 x 36

Split the factors: 72 = 70 + 2 and 36 = 30 + 6.

Partial products: 70 x 30 = 2100, 2 x 30 = 60, 70 x 6 = 420, and 2 x 6 = 12.

Add: 2100 + 60 + 420 + 12 = 2592. So, 72 x 36 = 2592.

Area model diagram showing 72 x 36 with four partial products — For a harder example, estimate first so the final answer feels reasonable.

Example 8: 124 x 6

Area models also work when one factor has only one digit.

Split 124 into 100 + 20 + 4. Keep 6 as one row.

Multiply each part by 6: 100 x 6 = 600, 20 x 6 = 120, and 4 x 6 = 24.

Add: 600 + 120 + 24 = 744. So, 124 x 6 = 744.

Area model diagram showing 124 x 6 split into 100 plus 20 plus 4 — A 3-digit by 1-digit problem becomes one row with three partial products.

Example 9: 132 x 14

Now try a larger model. Split 132 into 100 + 30 + 2. Split 14 into 10 + 4.

This model has six partial products: 100 x 10 = 1000, 30 x 10 = 300, 2 x 10 = 20, 100 x 4 = 400, 30 x 4 = 120, and 2 x 4 = 8.

Add them: 1000 + 300 + 20 + 400 + 120 + 8 = 1848. So, 132 x 14 = 1848.

Area model diagram showing 132 x 14 with six partial products — A 3-part by 2-part area model has six boxes, so check that all six are used.

How to check your answer

Use estimation before or after solving. For example, 47 x 25 is close to 50 x 25, which is 1250. The exact answer 1175 is close, so it makes sense.

Also check that every place-value part was used. In a 2-digit by 2-digit problem, you usually need four partial products.

If your answer is much too small, you may have forgotten a tens product. If it is much too large, you may have added an extra zero or multiplied the wrong parts.

Common mistakes

Mistake 1: Splitting 34 as 3 + 4 instead of 30 + 4. The 3 is really 3 tens, so it means 30.

Mistake 2: Filling only two boxes in a 2-digit by 2-digit problem. You need to multiply every part by every other part.

Mistake 3: Forgetting to add the partial products at the end. The boxes are pieces of the answer, not separate final answers.

Mistake 4: Writing the right numbers in the boxes but adding them carelessly. Always line up the place values when adding.

Quick practice

Try these with an area model: 24 x 13, 35 x 16, 42 x 27, 63 x 18, and 81 x 22.

Answers: 24 x 13 = 312, 35 x 16 = 560, 42 x 27 = 1134, 63 x 18 = 1134, and 81 x 22 = 1782.

When you finish, print the Area Model Multiplication Worksheets for more practice.