3B · Chapter 8 · Lesson 7
Multiplying by 8 and 9
Use known facts and properties to compute and explain products.
Today's mathematical question
Use two useful multiplication facts to work out 9 × 9. What is the product?
Learning target
Use known facts and properties to compute and explain products.
Before starting: Prior lesson: The Multiplication Table of 9. Try the warm-up independently.
Prerequisite · 3 questions
Check earlier skills first
These are earlier ideas you need for today; revisit them if they are difficult.
- P1
Find 9 groups of 6. Can you use 8 groups plus one more?
Reveal explanation
Answer: 54
9 groups of 6 make 9 × 6 = 54. Or find 8 × 6 and add 6.
9 rows of 6 dots = 54 dots. - P2
Compute 9 × 3. Explain a strategy using a known fact.
Reveal explanation
Answer: 27
9 groups of 3 make 9 × 3 = 27. Or find 8 × 3 and add 3.
9 rows of 3 dots = 27 dots. - P3
There are 9 equal trays with 3 counters on each tray. How many counters are there?
Reveal explanation
Answer: 27
9 groups of 3 make 9 × 3 = 27. Or find 8 × 3 and add 3.
9 rows of 3 dots = 27 dots.
Learn and understand
For 8 × n, double 4 × n. For 9 × n, find 10 × n and subtract one group. Both are examples of the distributive property, where you split a multiplication into simpler pieces. Choose the strategy that helps you explain the product clearly. When you calculate 8 × 6 as twice 4 × 6, compare that with finding 9 × 6 by subtracting one group from 10 × 6. Both strategies use groups of six.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Sketch eight or nine rows and mark the known part used in the calculation. Check by reversing the factor order.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- partial product
- smaller product used to find a larger one
- array
- equal rows and columns
- distributive property
- splitting multiplication over addition or subtraction
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
Use two useful multiplication facts to work out 9 × 9. What is the product?
- Identify the whole, the units, and what the question asks.
- 9 groups of 9 make 9 × 9 = 81. Or find 8 × 9 and add 9.
- Check that the answer uses the right units and makes sense.
Answer: 81
Check your understanding 1
An array has 8 rows, with 7 objects in each row. Split it into smaller arrays and find the total.
Reveal answer and explanation
56 — 8 groups of 7 make 8 × 7 = 56. Or find 7 × 7 and add 7.
Worked example 2
Explore, calculate, verify
An array has 8 rows, with 4 objects in each row. Split it into smaller arrays and find the total.
- Identify the whole, the units, and what the question asks.
- 8 groups of 4 make 8 × 4 = 32. Or find 7 × 4 and add 4.
- Check that the answer uses the right units and makes sense.
Answer: 32
Check your understanding 2
Explain how splitting 9 equal groups of 7 helps you find their total.
Reveal answer and explanation
63 — 9 groups of 7 make 9 × 7 = 63. Or find 8 × 7 and add 7.
Worked example 3
Explore, calculate, verify
Explain how splitting 8 equal groups of 7 helps you find their total.
- Identify the whole, the units, and what the question asks.
- 8 groups of 7 make 8 × 7 = 56. Or find 7 × 7 and add 7.
- Check that the answer uses the right units and makes sense.
Answer: 56
Check your understanding 3
Use two useful multiplication facts to work out 8 × 5. What is the product?
Reveal answer and explanation
40 — 8 groups of 5 make 8 × 5 = 40. Or find 7 × 5 and add 5.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
Use two useful multiplication facts to work out 8 × 9. What is the product?
Reveal explanation
Answer: 72
8 groups of 9 make 8 × 9 = 72. Or find 7 × 9 and add 9.
8 rows of 9 dots = 72 dots. - G2
Explain how splitting 8 equal groups of 8 helps you find their total.
Reveal explanation
Answer: 64
8 groups of 8 make 8 × 8 = 64. Or find 7 × 8 and add 8.
8 rows of 8 dots = 64 dots. - G3
Use two useful multiplication facts to work out 9 × 5. What is the product?
Reveal explanation
Answer: 45
9 groups of 5 make 9 × 5 = 45. Or find 8 × 5 and add 5.
9 rows of 5 dots = 45 dots. - G4
An array has 9 rows, with 7 objects in each row. Split it into smaller arrays and find the total.
Reveal explanation
Answer: 63
9 groups of 7 make 9 × 7 = 63. Or find 8 × 7 and add 7.
9 rows of 7 dots = 63 dots. - G5
Explain how splitting 9 equal groups of 8 helps you find their total.
Reveal explanation
Answer: 72
9 groups of 8 make 9 × 8 = 72. Or find 8 × 8 and add 8.
9 rows of 8 dots = 72 dots.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
An array has 8 rows, with 6 objects in each row. Split it into smaller arrays and find the total.
Reveal explanation
Answer: 48
8 groups of 6 make 8 × 6 = 48. Or find 7 × 6 and add 6.
8 rows of 6 dots = 48 dots. - I2
Explain how splitting 9 equal groups of 5 helps you find their total.
Reveal explanation
Answer: 45
9 groups of 5 make 9 × 5 = 45. Or find 8 × 5 and add 5.
9 rows of 5 dots = 45 dots. - I3
Use two useful multiplication facts to work out 9 × 4. What is the product?
Reveal explanation
Answer: 36
9 groups of 4 make 9 × 4 = 36. Or find 8 × 4 and add 4.
9 rows of 4 dots = 36 dots. - I4
An array has 9 rows, with 5 objects in each row. Split it into smaller arrays and find the total.
Reveal explanation
Answer: 45
9 groups of 5 make 9 × 5 = 45. Or find 8 × 5 and add 5.
9 rows of 5 dots = 45 dots. - I5
Explain how splitting 8 equal groups of 6 helps you find their total.
Reveal explanation
Answer: 48
8 groups of 6 make 8 × 6 = 48. Or find 7 × 6 and add 6.
8 rows of 6 dots = 48 dots. - I6
Explain how splitting 8 equal groups of 5 helps you find their total.
Reveal explanation
Answer: 40
8 groups of 5 make 8 × 5 = 40. Or find 7 × 5 and add 5.
8 rows of 5 dots = 40 dots. - I7
Use two useful multiplication facts to work out 8 × 7. What is the product?
Reveal explanation
Answer: 56
8 groups of 7 make 8 × 7 = 56. Or find 7 × 7 and add 7.
8 rows of 7 dots = 56 dots. - I8
An array has 8 rows, with 8 objects in each row. Split it into smaller arrays and find the total.
Reveal explanation
Answer: 64
8 groups of 8 make 8 × 8 = 64. Or find 7 × 8 and add 8.
8 rows of 8 dots = 64 dots.
Challenge · 2 questions
Challenge and error analysis
Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.
- C1
Without counting individual counters, show two different decompositions for 9 × 3, and explain why both work.
Reveal explanation
Answer: 27
One decomposition is (8 × 3) + (1 × 3) = 27. Another is (4 × 3) + (5 × 3) = 27. The partitions use different group splits but preserve the same product.
- C2
An array has 9 rows of 6 dots. A student says turning it creates 6 more dots. Explain the error and find the total.
Reveal explanation
Answer: 54
Turning an array swaps rows and columns but adds no dots. Both 9 × 6 and 6 × 9 equal 54.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
An array has 8 rows, with 9 objects in each row. Split it into smaller arrays and find the total.
Reveal explanation
Answer: 72
8 groups of 9 make 8 × 9 = 72. Or find 7 × 9 and add 9.
8 rows of 9 dots = 72 dots. - E2
Explain how splitting 8 equal groups of 9 helps you find their total.
Reveal explanation
Answer: 72
8 groups of 9 make 8 × 9 = 72. Or find 7 × 9 and add 9.
8 rows of 9 dots = 72 dots. - E3
Use two useful multiplication facts to work out 9 × 3. What is the product?
Reveal explanation
Answer: 27
9 groups of 3 make 9 × 3 = 27. Or find 8 × 3 and add 3.
9 rows of 3 dots = 27 dots.