45-minute lesson
Primary 5 Mathematics: Multiplication strategies
Lesson objective
- 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 criteria:
- 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.
Materials
- Grid paper or plain paper and a ruler
- Pencil and eraser
- A shopping catalogue or receipt with prices (optional)
Introduction
5 minIntroduce today's words:
- Product: The answer to a multiplication.
- Partition: To split a number into parts, such as 47 = 40 + 7.
- Area model: A rectangle divided into parts, used to show and organise the parts of a multiplication.
- Estimate: A sensible approximate answer found using rounded numbers.
- Factor: A number that is multiplied by another number. In 6 × 4 = 24, 6 and 4 are factors.
Ask your child what they already know about multiplication strategies.
Explanation
9 minBig 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
7 minTwo-digit by one-digit
Work out 47 × 6.
Step 1: Estimate: 50 × 6 = 300, so the answer should be a bit less than 300.
Step 2: Partition 47 into 40 + 7.
Step 3: 40 × 6 = 240.
Step 4: 7 × 6 = 42.
Step 5: Add: 240 + 42 = 282.
Answer: 47 × 6 = 282
Two-digit by two-digit using an area model
Work out 23 × 14.
Step 1: Estimate: 20 × 15 = 300.
Step 2: Partition 14 into 10 + 4 and draw a rectangle split into two parts.
Step 3: 23 × 10 = 230.
Step 4: 23 × 4 = 92 (because 20 × 4 = 80 and 3 × 4 = 12).
Step 5: 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?
Step 1: The number sentence is 24 × 18.
Step 2: Estimate: 25 × 20 = 500.
Step 3: 24 × 10 = 240.
Step 4: 24 × 8 = 192 (because 20 × 8 = 160 and 4 × 8 = 32).
Step 5: Add: 240 + 192 = 432.
Answer: There are 432 pencils.
Guided practice (do together)
9 min1. What is 36 × 5?
(a) 150 (b) 180 (c) 185 (d) 306
2. Which of these correctly shows 64 × 3 split into parts?
(a) 60 × 3 + 4 × 3 (b) 60 + 4 × 3 (c) 64 + 3 (d) 6 × 3 + 4 × 3
3. What is 25 × 12?
(a) 250 (b) 275 (c) 325 (d) 300
4. Which is the best estimate for 49 × 21?
(a) About 100 (b) About 500 (c) About 1000 (d) About 10 000
Independent practice
11 min5. What is 58 × 4?
6. What is 32 × 15?
7. A cinema ticket costs $17. How many dollars do 6 tickets cost?
8. A bus seats 48 people. How many people can 13 full buses carry?
Questions to check understanding
- Can you split a number into tens and ones to make multiplying easier?
- Can you draw an area model to multiply two two-digit numbers?
- Can you round numbers to estimate an answer before I calculate?
- What was the trickiest part today?
Answer guide
1. 180 — 30 × 5 = 150 and 6 × 5 = 30. 150 + 30 = 180.
2. 60 × 3 + 4 × 3 — 64 = 60 + 4, and both parts must be multiplied by 3: 60 × 3 + 4 × 3 = 180 + 12 = 192.
3. 300 — 25 × 10 = 250 and 25 × 2 = 50. 250 + 50 = 300.
4. About 1000 — Round to 50 × 20 = 1000. The exact answer is 1029.
5. 232 — 50 × 4 = 200 and 8 × 4 = 32. 200 + 32 = 232.
6. 480 — 32 × 10 = 320 and 32 × 5 = 160. 320 + 160 = 480.
7. $102 — 17 × 6: 10 × 6 = 60 and 7 × 6 = 42. 60 + 42 = 102, so the tickets cost $102.
8. 624 — 48 × 10 = 480 and 48 × 3 = 144. 480 + 144 = 624.
Review
4 minRecap the success criteria together. Watch for these common misconceptions:
- 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.
Extension activities
- 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.
Suggested follow-up
- Revisit multiplication strategies tomorrow with two or three quick questions from memory.
- Try the online practice check for this topic and look at any questions that need another go.
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.