Short answer
The grid method (also called the area model) splits a multiplication into smaller, easier parts. You partition each number by place value, fill a grid with the products of each pair, and add all the partial products together to get the final answer.
At a glance
- Key stage
- Key Stage 3
- Subject
- Number
- Type
- How-to guide
- For
- Students
- Read time
- 4 min
- Last updated
- 21 October 2026
Where this fits
- Key Stage 3Years 7–9This article
- GCSEYears 10–11
Method at a glance
- Partition each number
- Draw the grid
- Fill each cell
- Add the partial products
- Check your answer
Why learn the grid method?
The grid method makes large multiplications manageable because each cell in the grid only requires simple multiplication of a number by a multiple of 10. It also shows clearly why multiplication works: multiplying 34 × 27 is the same as finding the area of a rectangle 34 units wide and 27 units tall — split into four smaller rectangles.
This visual understanding supports algebra later: expanding brackets such as (3x + 4)(2x + 7) uses exactly the same grid layout.
How do you set up the grid?
Method at a glance:
- Partition each number. Split each factor into its hundreds, tens, and units components (e.g. 47 = 40 + 7; 316 = 300 + 10 + 6).
- Draw the grid. Write one number's parts across the top and the other's parts down the left side.
- Fill each cell. Multiply the row heading by the column heading for each cell.
- Add the partial products. Sum all the values in the grid to find the total.
- Check your answer. Estimate first (e.g. 47 × 23 ≈ 50 × 20 = 1 000) to confirm the answer is in the right ballpark.
Worked example 1: two-digit × two-digit
Calculate 47 × 23.
Partition: 47 = 40 + 7; 23 = 20 + 3.
| 40 | 7 | |
|---|---|---|
| 20 | 800 | 140 |
| 3 | 120 | 21 |
Partial products: 800 + 140 + 120 + 21 = 1 081
Check: 50 × 20 = 1 000 — answer of 1 081 is reasonable. ✓
Worked example 2: three-digit × two-digit
Calculate 236 × 34.
Partition: 236 = 200 + 30 + 6; 34 = 30 + 4.
| 200 | 30 | 6 | |
|---|---|---|---|
| 30 | 6 000 | 900 | 180 |
| 4 | 800 | 120 | 24 |
Partial products: 6 000 + 900 + 180 + 800 + 120 + 24 = 8 024
Check: 240 × 30 = 7 200; 240 × 4 = 960; total ≈ 8 160 — close to 8 024. ✓
A handy shortcut: add each row separately first, then add the two row totals.
- Row 1 (×30): 6 000 + 900 + 180 = 7 080
- Row 2 (×4): 800 + 120 + 24 = 944
- Total: 7 080 + 944 = 8 024 ✓
Worked example 3: decimal numbers
Calculate 4.2 × 3.6.
Strategy: multiply 42 × 36 using the grid, then adjust for the decimal places.
42 × 36:
| 40 | 2 | |
|---|---|---|
| 30 | 1 200 | 60 |
| 6 | 240 | 12 |
Total = 1 200 + 60 + 240 + 12 = 1 512.
Both original numbers have one decimal place (total: 2 d.p.), so divide by 100: 1 512 ÷ 100 = 15.12
How does the grid method compare to long multiplication?
| Feature | Grid method | Long multiplication |
|---|---|---|
| Layout | Spread out; all parts visible | Compact; carries required |
| Error checking | Easy — each cell is independent | Harder — carries propagate errors |
| Speed | Slightly slower | Faster once fluent |
| Concept clarity | Shows the distributive law visually | Less obvious why it works |
Both methods give the same answer. Most students find the grid method less error-prone until they are fluent with long multiplication.
How does the grid method connect to algebra?
Expanding double brackets uses the same approach. For (x + 3)(x + 5):
| x | 3 | |
|---|---|---|
| x | x² | 3x |
| 5 | 5x | 15 |
Result: x² + 3x + 5x + 15 = x² + 8x + 15.
Mastering the number grid method now makes bracket expansion at GCSE feel familiar.
Frequently asked questions
Does the grid method work for multiplying three numbers together?
Multiply two of the numbers first using the grid, then multiply the result by the third number using a new grid. For 4 × 12 × 25, calculate 12 × 25 = 300 first, then 4 × 300 = 1 200. Alternatively, reorder the multiplication for easier arithmetic.
What if one of the numbers has a zero digit?
Include the zero as part of the partition but recognise the cell product is zero — you still write it in the grid for clarity. For example, 304 = 300 + 0 + 4: the "tens" row gives all zeros and you can skip it, but write 0 in those cells to avoid confusion.
How do I check for errors in my grid?
Estimate the answer before you start (round each number to 1 significant figure and multiply). After completing the grid, check that your total is close to the estimate. If it is wildly different, look for a cell where you multiplied incorrectly — a missing zero is the most common error.
Can I use the grid method in GCSE exams?
Yes — examiners accept any valid method. At GCSE, long multiplication is slightly more efficient, but the grid method is fully valid and many students continue to use it successfully throughout their studies.
Professor Pi helps you choose and master the best method for every calculation — add the AI Tutors connector at aitutors.me.
Key terms
- grid method
- Partition each number
- Draw the grid
- Fill each cell
- Add the partial products
- Check your answer