3B · Chapter 8 · Lesson 5
The Multiplication Table of 8
Derive 8s by doubling, arrays, and known facts.
Today's mathematical question
Find 8 groups of 3. Can you use 7 groups plus one more?
Learning target
Derive 8s by doubling, arrays, and known facts.
Before starting: Prior lesson: Dividing by 6 and 7. 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
21 counters are shared equally into 7 groups. How many counters are in each group?
Reveal explanation
Answer: 3
Use inverse multiplication: 7 × 3 = 21; therefore 21 ÷ 7 = 3.
7 rows of 3 dots = 21 dots. - P2
Each tray holds 6 counters. How many full trays are required to arrange 30 counters?
Reveal explanation
Answer: 5
Find how many groups of 6 fit into 30: 30 ÷ 6 = 5.
6 rows of 5 dots = 30 dots. - P3
30 counters are shared equally into 6 groups. How many counters are in each group?
Reveal explanation
Answer: 5
Use inverse multiplication: 6 × 5 = 30; therefore 30 ÷ 6 = 5.
6 rows of 5 dots = 30 dots.
Learn and understand
Eight equal groups can be formed by doubling four groups. For instance, 8 × 6 is twice 4 × 6. You may also double 2 × 6 twice. The total does not change because each doubling copies the same set of equal groups. To see 8 × 7, first find 4 × 7 = 28 and double it to 56. In an array this means copying four equal rows, not doubling both dimensions.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Build four rows of equal dots, duplicate them, and compare the two arrays. Show 8 × n = 2 × (4 × n).
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- double
- twice a quantity
- factor
- number multiplied
- array
- equal rows of objects
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
Find 8 groups of 3. Can you use 7 groups plus one more?
- Identify the whole, the units, and what the question asks.
- 8 groups of 3 make 8 × 3 = 24. Or find 7 × 3 and add 3.
- Check that the answer uses the right units and makes sense.
Answer: 24
Check your understanding 1
Compute 8 × 9. Explain a strategy using a known fact.
Reveal answer and explanation
72 — 8 groups of 9 make 8 × 9 = 72. Or find 7 × 9 and add 9.
Worked example 2
Explore, calculate, verify
Compute 8 × 5. Explain a strategy using a known fact.
- Identify the whole, the units, and what the question asks.
- 8 groups of 5 make 8 × 5 = 40. Or find 7 × 5 and add 5.
- Check that the answer uses the right units and makes sense.
Answer: 40
Check your understanding 2
There are 8 equal trays with 4 counters on each tray. How many counters are there?
Reveal answer and explanation
32 — 8 groups of 4 make 8 × 4 = 32. Or find 7 × 4 and add 4.
Worked example 3
Explore, calculate, verify
There are 8 equal trays with 10 counters on each tray. How many counters are there?
- Identify the whole, the units, and what the question asks.
- 8 groups of 10 make 8 × 10 = 80. Or find 7 × 10 and add 10.
- Check that the answer uses the right units and makes sense.
Answer: 80
Check your understanding 3
Find 8 groups of 10. Can you use 7 groups plus one more?
Reveal answer and explanation
80 — 8 groups of 10 make 8 × 10 = 80. Or find 7 × 10 and add 10.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
There are 8 equal trays with 5 counters on each tray. How many counters are there?
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. - G2
Find 8 groups of 5. Can you use 7 groups plus one more?
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. - G3
Find 8 groups of 8. Can you use 7 groups plus one more?
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. - G4
Compute 8 × 6. Explain a strategy using a known fact.
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. - G5
There are 8 equal trays with 9 counters on each tray. How many counters are there?
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.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
There are 8 equal trays with 6 counters on each tray. How many counters are there?
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
Compute 8 × 4. Explain a strategy using a known fact.
Reveal explanation
Answer: 32
8 groups of 4 make 8 × 4 = 32. Or find 7 × 4 and add 4.
8 rows of 4 dots = 32 dots. - I3
There are 8 equal trays with 8 counters on each tray. How many counters are there?
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. - I4
Find 8 groups of 9. Can you use 7 groups plus one more?
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. - I5
Find 8 groups of 4. Can you use 7 groups plus one more?
Reveal explanation
Answer: 32
8 groups of 4 make 8 × 4 = 32. Or find 7 × 4 and add 4.
8 rows of 4 dots = 32 dots. - I6
Compute 8 × 8. Explain a strategy using a known fact.
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. - I7
Compute 8 × 10. Explain a strategy using a known fact.
Reveal explanation
Answer: 80
8 groups of 10 make 8 × 10 = 80. Or find 7 × 10 and add 10.
8 rows of 10 dots = 80 dots. - I8
Compute 8 × 3. Explain a strategy using a known fact.
Reveal explanation
Answer: 24
8 groups of 3 make 8 × 3 = 24. Or find 7 × 3 and add 3.
8 rows of 3 dots = 24 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 8 × 6, and explain why both work.
Reveal explanation
Answer: 48
One decomposition is (7 × 6) + (1 × 6) = 48. Another is (4 × 6) + (4 × 6) = 48. The partitions use different group splits but preserve the same product.
- C2
An array has 8 rows of 5 dots. A student says turning it creates 5 more dots. Explain the error and find the total.
Reveal explanation
Answer: 40
Turning an array swaps rows and columns but adds no dots. Both 8 × 5 and 5 × 8 equal 40.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
Find 8 groups of 7. Can you use 7 groups plus one more?
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. - E2
Compute 8 × 7. Explain a strategy using a known fact.
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. - E3
There are 8 equal trays with 7 counters on each tray. How many counters are there?
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.