3B · Chapter 8 · Lesson 1
The Multiplication Table of 6
Represent six equal groups, derive facts from 5s and doubles, and explain 6 × n.
Today's mathematical question
Compute 6 × 6. Explain a strategy using a known fact.
Learning target
Represent six equal groups, derive facts from 5s and doubles, and explain 6 × n.
Before starting: Grade 3A: equal groups and multiplication facts. 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
What is 5 × 4?
Reveal explanation
Answer: 20
Five equal groups of four have 4 + 4 + 4 + 4 + 4 = 20 objects. You can also picture five rows with four dots each.
- P2
What is 3 × 6?
Reveal explanation
Answer: 18
Three groups of six have 18 objects.
- P3
What is 20 ÷ 5?
Reveal explanation
Answer: 4
Because five groups of four make 20.
Learn and understand
Six equal groups can be counted one group at a time, but a good mathematician also notices helpful relationships. Six groups are five groups plus one more, so 6 × 7 can be understood as 5 × 7 + 7. You can also see six groups as three groups doubled. These methods work because the groups contain the same number of objects. Try six groups of four: five groups make 20, and one more group makes 24. To check, arrange 24 counters in six equal rows. How do you know the groups are equal?
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Build an array with six rows. Partition it after row five, count the first five rows, and add the last row. Explain why multiplying 6 by 1 more than a known fact gives the next result.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- factor
- one of the numbers multiplied
- product
- the total from multiplication
- array
- equal rows and columns
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
Compute 6 × 6. Explain a strategy using a known fact.
- Identify the whole, the units, and what the question asks.
- 6 groups of 6 make 6 × 6 = 36. Or find 5 × 6 and add 6.
- Check that the answer uses the right units and makes sense.
Answer: 36
Check your understanding 1
There are 6 equal trays with 10 counters on each tray. How many counters are there?
Reveal answer and explanation
60 — 6 groups of 10 make 6 × 10 = 60. Or find 5 × 10 and add 10.
Worked example 2
Explore, calculate, verify
There are 6 equal trays with 5 counters on each tray. How many counters are there?
- Identify the whole, the units, and what the question asks.
- 6 groups of 5 make 6 × 5 = 30. Or find 5 × 5 and add 5.
- Check that the answer uses the right units and makes sense.
Answer: 30
Check your understanding 2
Find 6 groups of 9. Can you use 5 groups plus one more?
Reveal answer and explanation
54 — 6 groups of 9 make 6 × 9 = 54. Or find 5 × 9 and add 9.
Worked example 3
Explore, calculate, verify
Find 6 groups of 10. Can you use 5 groups plus one more?
- Identify the whole, the units, and what the question asks.
- 6 groups of 10 make 6 × 10 = 60. Or find 5 × 10 and add 10.
- Check that the answer uses the right units and makes sense.
Answer: 60
Check your understanding 3
Compute 6 × 5. Explain a strategy using a known fact.
Reveal answer and explanation
30 — 6 groups of 5 make 6 × 5 = 30. Or find 5 × 5 and add 5.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
Compute 6 × 10. Explain a strategy using a known fact.
Reveal explanation
Answer: 60
6 groups of 10 make 6 × 10 = 60. Or find 5 × 10 and add 10.
6 rows of 10 dots = 60 dots. - G2
There are 6 equal trays with 6 counters on each tray. How many counters are there?
Reveal explanation
Answer: 36
6 groups of 6 make 6 × 6 = 36. Or find 5 × 6 and add 6.
6 rows of 6 dots = 36 dots. - G3
Find 6 groups of 3. Can you use 5 groups plus one more?
Reveal explanation
Answer: 18
6 groups of 3 make 6 × 3 = 18. Or find 5 × 3 and add 3.
6 rows of 3 dots = 18 dots. - G4
Compute 6 × 8. Explain a strategy using a known fact.
Reveal explanation
Answer: 48
6 groups of 8 make 6 × 8 = 48. Or find 5 × 8 and add 8.
6 rows of 8 dots = 48 dots. - G5
There are 6 equal trays with 9 counters on each tray. How many counters are there?
Reveal explanation
Answer: 54
6 groups of 9 make 6 × 9 = 54. Or find 5 × 9 and add 9.
6 rows of 9 dots = 54 dots.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
Compute 6 × 9. Explain a strategy using a known fact.
Reveal explanation
Answer: 54
6 groups of 9 make 6 × 9 = 54. Or find 5 × 9 and add 9.
6 rows of 9 dots = 54 dots. - I2
Find 6 groups of 6. Can you use 5 groups plus one more?
Reveal explanation
Answer: 36
6 groups of 6 make 6 × 6 = 36. Or find 5 × 6 and add 6.
6 rows of 6 dots = 36 dots. - I3
There are 6 equal trays with 8 counters on each tray. How many counters are there?
Reveal explanation
Answer: 48
6 groups of 8 make 6 × 8 = 48. Or find 5 × 8 and add 8.
6 rows of 8 dots = 48 dots. - I4
There are 6 equal trays with 4 counters on each tray. How many counters are there?
Reveal explanation
Answer: 24
6 groups of 4 make 6 × 4 = 24. Or find 5 × 4 and add 4.
6 rows of 4 dots = 24 dots. - I5
Find 6 groups of 8. Can you use 5 groups plus one more?
Reveal explanation
Answer: 48
6 groups of 8 make 6 × 8 = 48. Or find 5 × 8 and add 8.
6 rows of 8 dots = 48 dots. - I6
There are 6 equal trays with 3 counters on each tray. How many counters are there?
Reveal explanation
Answer: 18
6 groups of 3 make 6 × 3 = 18. Or find 5 × 3 and add 3.
6 rows of 3 dots = 18 dots. - I7
Find 6 groups of 4. Can you use 5 groups plus one more?
Reveal explanation
Answer: 24
6 groups of 4 make 6 × 4 = 24. Or find 5 × 4 and add 4.
6 rows of 4 dots = 24 dots. - I8
Find 6 groups of 5. Can you use 5 groups plus one more?
Reveal explanation
Answer: 30
6 groups of 5 make 6 × 5 = 30. Or find 5 × 5 and add 5.
6 rows of 5 dots = 30 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 6 × 7, and explain why both work.
Reveal explanation
Answer: 42
One decomposition is (5 × 7) + (1 × 7) = 42. Another is (3 × 7) + (3 × 7) = 42. The partitions use different group splits but preserve the same product.
- C2
An array has 6 rows of 4 dots. A student says turning it creates 4 more dots. Explain the error and find the total.
Reveal explanation
Answer: 24
Turning an array swaps rows and columns but adds no dots. Both 6 × 4 and 4 × 6 equal 24.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
Compute 6 × 3. Explain a strategy using a known fact.
Reveal explanation
Answer: 18
6 groups of 3 make 6 × 3 = 18. Or find 5 × 3 and add 3.
6 rows of 3 dots = 18 dots. - E2
Find 6 groups of 7. Can you use 5 groups plus one more?
Reveal explanation
Answer: 42
6 groups of 7 make 6 × 7 = 42. Or find 5 × 7 and add 7.
6 rows of 7 dots = 42 dots. - E3
There are 6 equal trays with 7 counters on each tray. How many counters are there?
Reveal explanation
Answer: 42
6 groups of 7 make 6 × 7 = 42. Or find 5 × 7 and add 7.
6 rows of 7 dots = 42 dots.