Year 5 · Mathematics · Number
Multiplication strategies
Multiply two- and three-digit numbers by one- and two-digit numbers by splitting numbers into parts, and use estimation to check answers.
Awaiting educator review. This material was drafted by our content team with AI assistance and is waiting for review by a qualified educator. Please check it suits your child before using it. Created 10 October 2026.
Learning goals
Learners will
- Multiply a two-digit number by a one-digit number using partitioning.
- Multiply a two-digit number by a two-digit number using an area model.
- Estimate products to check whether an answer is reasonable.
Success looks like
- I can split a number into tens and ones to make multiplying easier.
- I can draw an area model to multiply two two-digit numbers.
- I can round numbers to estimate an answer before I calculate.
The big idea
Big multiplications are easier when you break them into smaller pieces. This is called partitioning. To work out 47 × 6, split 47 into 40 and 7. Then multiply each part by 6 and add the results.
This works because 47 groups of 6 is the same as 40 groups of 6 plus 7 groups of 6. Nothing is lost or added; the multiplication is just organised into parts you already know how to do.
When both numbers have two digits, an area model keeps everything tidy. Draw a rectangle and split it into parts, one for each combination of tens and ones. Work out each part, then add them.
Multiplying by 10 is a handy step. Multiplying a whole number by 10 moves every digit one place to the left, so 23 × 10 = 230. Many problems can be split into a “times 10” part and a smaller part.
Always estimate first. Round each number to something easy, multiply, and use that as a check. For 49 × 21, estimate 50 × 20 = 1000. If your final answer is close to 1000 (it is 1029), it is reasonable. If you got 10 290, you would know something had gone wrong.
- Partition one number into tens and ones.
- Multiply each part.
- Add the partial products and compare with your estimate.
Worked examples
Two-digit by one-digit
Work out 47 × 6.
- Estimate: 50 × 6 = 300, so the answer should be a bit less than 300.
- Partition 47 into 40 + 7.
- 40 × 6 = 240.
- 7 × 6 = 42.
- Add: 240 + 42 = 282.
Answer: 47 × 6 = 282
Two-digit by two-digit using an area model
Work out 23 × 14.
- Estimate: 20 × 15 = 300.
- Partition 14 into 10 + 4 and draw a rectangle split into two parts.
- 23 × 10 = 230.
- 23 × 4 = 92 (because 20 × 4 = 80 and 3 × 4 = 12).
- Add: 230 + 92 = 322, which is close to the estimate of 300.
Answer: 23 × 14 = 322
A real-life problem
A homeschool group orders 18 boxes of pencils. Each box holds 24 pencils. How many pencils are there in total?
- The number sentence is 24 × 18.
- Estimate: 25 × 20 = 500.
- 24 × 10 = 240.
- 24 × 8 = 192 (because 20 × 8 = 160 and 4 × 8 = 32).
- Add: 240 + 192 = 432.
Answer: There are 432 pencils.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
What is 36 × 5?
180 — 30 × 5 = 150 and 6 × 5 = 30. 150 + 30 = 180.
Which of these correctly shows 64 × 3 split into parts?
60 × 3 + 4 × 3 — 64 = 60 + 4, and both parts must be multiplied by 3: 60 × 3 + 4 × 3 = 180 + 12 = 192.
What is 25 × 12?
300 — 25 × 10 = 250 and 25 × 2 = 50. 250 + 50 = 300.
Which is the best estimate for 49 × 21?
About 1000 — Round to 50 × 20 = 1000. The exact answer is 1029.
What is 58 × 4?
232 — 50 × 4 = 200 and 8 × 4 = 32. 200 + 32 = 232.
What is 32 × 15?
480 — 32 × 10 = 320 and 32 × 5 = 160. 320 + 160 = 480.
A cinema ticket costs $17. How many dollars do 6 tickets cost?
$102 — 17 × 6: 10 × 6 = 60 and 7 × 6 = 42. 60 + 42 = 102, so the tickets cost $102.
A bus seats 48 people. How many people can 13 full buses carry?
624 — 48 × 10 = 480 and 48 × 3 = 144. 480 + 144 = 624.
Watch out for
- Multiplying only one part of a partitioned number, for example 64 × 3 = 60 × 3 + 4 = 184. Remind the learner that every part must be multiplied.
- Forgetting the place value of a digit, such as treating the 4 in 47 as 4 rather than 40. Saying the parts aloud (“forty times six”) helps.
- Skipping the estimate. An estimate catches many mistakes, so make it a habit before every calculation.
Tips for parents
- Ask the learner to explain each step out loud. Explaining is one of the best ways to understand.
- Let them choose their own way to partition. There is often more than one good method, for example 25 × 12 as 25 × 10 + 25 × 2 or as 25 × 4 × 3.
- Check answers with a calculator only after the learner has estimated and calculated by hand.
Go further
- Use a supermarket catalogue to plan a party for 12 guests and work out the cost of buying several of each item.
- Investigate: what is 11 × 11, 11 × 12, 11 × 13? Look for a pattern and predict 11 × 15 before checking.
- Draw an area model for a three-digit number times a two-digit number, such as 124 × 15.