3B · Chapter 8 · Lesson 6
The Multiplication Table of 9
Use ten-times-minus-one-group and place-value patterns.
Today's mathematical question
There are 9 equal trays with 10 counters on each tray. How many counters are there?
Learning target
Use ten-times-minus-one-group and place-value patterns.
Before starting: Prior lesson: The Multiplication Table of 8. 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
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. - P2
There are 8 equal trays with 3 counters on each tray. How many counters are there?
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. - P3
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.
Learn and understand
Nine groups are one fewer group than ten. To calculate 9 × 7, start with 10 × 7 = 70 and remove one group of 7. This method comes from an actual array: a ten-row array with one row crossed out. The product is 63, not 70 − 9. Try 9 × 8 using ten groups: 10 × 8 = 80. Remove one group of eight to get 72. Point to the removed row on your drawing.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Draw ten equal rows, cross out one row, and write the matching subtraction. Compare this to nine complete rows.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- compensation
- adjusting an easier calculation to obtain the original
- product
- answer to multiplication
- group
- equal collection
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
There are 9 equal trays with 10 counters on each tray. How many counters are there?
- Identify the whole, the units, and what the question asks.
- 9 groups of 10 make 9 × 10 = 90. Or find 8 × 10 and add 10.
- Check that the answer uses the right units and makes sense.
Answer: 90
Check your understanding 1
Find 9 groups of 5. Can you use 8 groups plus one more?
Reveal answer and explanation
45 — 9 groups of 5 make 9 × 5 = 45. Or find 8 × 5 and add 5.
Worked example 2
Explore, calculate, verify
Find 9 groups of 6. Can you use 8 groups plus one more?
- Identify the whole, the units, and what the question asks.
- 9 groups of 6 make 9 × 6 = 54. Or find 8 × 6 and add 6.
- Check that the answer uses the right units and makes sense.
Answer: 54
Check your understanding 2
Compute 9 × 5. Explain a strategy using a known fact.
Reveal answer and explanation
45 — 9 groups of 5 make 9 × 5 = 45. Or find 8 × 5 and add 5.
Worked example 3
Explore, calculate, verify
Compute 9 × 6. Explain a strategy using a known fact.
- Identify the whole, the units, and what the question asks.
- 9 groups of 6 make 9 × 6 = 54. Or find 8 × 6 and add 6.
- Check that the answer uses the right units and makes sense.
Answer: 54
Check your understanding 3
There are 9 equal trays with 8 counters on each tray. How many counters are there?
Reveal answer and explanation
72 — 9 groups of 8 make 9 × 8 = 72. Or find 8 × 8 and add 8.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
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. - G2
Find 9 groups of 4. Can you use 8 groups plus one more?
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. - G3
Compute 9 × 4. Explain a strategy using a known fact.
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. - G4
There are 9 equal trays with 7 counters on each tray. How many counters are there?
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
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.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
Find 9 groups of 8. Can you use 8 groups plus one more?
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. - I2
Compute 9 × 9. Explain a strategy using a known fact.
Reveal explanation
Answer: 81
9 groups of 9 make 9 × 9 = 81. Or find 8 × 9 and add 9.
9 rows of 9 dots = 81 dots. - I3
Compute 9 × 8. Explain a strategy using a known fact.
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. - I4
There are 9 equal trays with 9 counters on each tray. How many counters are there?
Reveal explanation
Answer: 81
9 groups of 9 make 9 × 9 = 81. Or find 8 × 9 and add 9.
9 rows of 9 dots = 81 dots. - I5
Find 9 groups of 7. Can you use 8 groups plus one more?
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. - I6
Find 9 groups of 9. Can you use 8 groups plus one more?
Reveal explanation
Answer: 81
9 groups of 9 make 9 × 9 = 81. Or find 8 × 9 and add 9.
9 rows of 9 dots = 81 dots. - I7
Find 9 groups of 10. Can you use 8 groups plus one more?
Reveal explanation
Answer: 90
9 groups of 10 make 9 × 10 = 90. Or find 8 × 10 and add 10.
9 rows of 10 dots = 90 dots. - I8
Compute 9 × 10. Explain a strategy using a known fact.
Reveal explanation
Answer: 90
9 groups of 10 make 9 × 10 = 90. Or find 8 × 10 and add 10.
9 rows of 10 dots = 90 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 × 7, and explain why both work.
Reveal explanation
Answer: 63
One decomposition is (8 × 7) + (1 × 7) = 63. Another is (4 × 7) + (5 × 7) = 63. 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
There are 9 equal trays with 6 counters on each tray. How many counters are there?
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. - E2
Find 9 groups of 3. Can you use 8 groups plus one more?
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. - E3
There are 9 equal trays with 5 counters on each tray. How many counters are there?
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.