3B · Chapter 8 · Lesson 2
The Multiplication Table of 7
Build seven-times facts from known products and identify useful patterns.
Today's mathematical question
Find 7 groups of 5. Can you use 6 groups plus one more?
Learning target
Build seven-times facts from known products and identify useful patterns.
Before starting: Prior lesson: The Multiplication Table of 6. 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
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. - P2
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. - P3
Compute 6 × 7. Explain a strategy using a known fact.
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.
Learn and understand
A seven-times fact can be broken into smaller known facts. For example, seven copies of 8 equal five copies of 8 plus two copies of 8. You can also use 7 × 8 = 8 × 7 because turning an array does not change the number of dots. Explain the picture before memorizing the fact. For 7 × 6, split seven rows into four rows and three rows. Count 24 and 18, then combine them to get 42. A different partition should still produce 42.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Draw seven equal bars or seven array rows. Separate them into five rows and two rows; find both subtotal products and combine them.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- factor
- number multiplied
- commutative property
- changing factor order without changing product
- array
- rectangular equal groups
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
Find 7 groups of 5. Can you use 6 groups plus one more?
- Identify the whole, the units, and what the question asks.
- 7 groups of 5 make 7 × 5 = 35. Or find 6 × 5 and add 5.
- Check that the answer uses the right units and makes sense.
Answer: 35
Check your understanding 1
Compute 7 × 8. Explain a strategy using a known fact.
Reveal answer and explanation
56 — 7 groups of 8 make 7 × 8 = 56. Or find 6 × 8 and add 8.
Worked example 2
Explore, calculate, verify
Compute 7 × 10. Explain a strategy using a known fact.
- Identify the whole, the units, and what the question asks.
- 7 groups of 10 make 7 × 10 = 70. Or find 6 × 10 and add 10.
- Check that the answer uses the right units and makes sense.
Answer: 70
Check your understanding 2
There are 7 equal trays with 5 counters on each tray. How many counters are there?
Reveal answer and explanation
35 — 7 groups of 5 make 7 × 5 = 35. Or find 6 × 5 and add 5.
Worked example 3
Explore, calculate, verify
There are 7 equal trays with 3 counters on each tray. How many counters are there?
- Identify the whole, the units, and what the question asks.
- 7 groups of 3 make 7 × 3 = 21. Or find 6 × 3 and add 3.
- Check that the answer uses the right units and makes sense.
Answer: 21
Check your understanding 3
Find 7 groups of 9. Can you use 6 groups plus one more?
Reveal answer and explanation
63 — 7 groups of 9 make 7 × 9 = 63. Or find 6 × 9 and add 9.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
Find 7 groups of 7. Can you use 6 groups plus one more?
Reveal explanation
Answer: 49
7 groups of 7 make 7 × 7 = 49. Or find 6 × 7 and add 7.
7 rows of 7 dots = 49 dots. - G2
Compute 7 × 5. Explain a strategy using a known fact.
Reveal explanation
Answer: 35
7 groups of 5 make 7 × 5 = 35. Or find 6 × 5 and add 5.
7 rows of 5 dots = 35 dots. - G3
There are 7 equal trays with 8 counters on each tray. How many counters are there?
Reveal explanation
Answer: 56
7 groups of 8 make 7 × 8 = 56. Or find 6 × 8 and add 8.
7 rows of 8 dots = 56 dots. - G4
Find 7 groups of 6. Can you use 6 groups plus one more?
Reveal explanation
Answer: 42
7 groups of 6 make 7 × 6 = 42. Or find 6 × 6 and add 6.
7 rows of 6 dots = 42 dots. - G5
Compute 7 × 9. Explain a strategy using a known fact.
Reveal explanation
Answer: 63
7 groups of 9 make 7 × 9 = 63. Or find 6 × 9 and add 9.
7 rows of 9 dots = 63 dots.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
Compute 7 × 3. Explain a strategy using a known fact.
Reveal explanation
Answer: 21
7 groups of 3 make 7 × 3 = 21. Or find 6 × 3 and add 3.
7 rows of 3 dots = 21 dots. - I2
There are 7 equal trays with 10 counters on each tray. How many counters are there?
Reveal explanation
Answer: 70
7 groups of 10 make 7 × 10 = 70. Or find 6 × 10 and add 10.
7 rows of 10 dots = 70 dots. - I3
Find 7 groups of 10. Can you use 6 groups plus one more?
Reveal explanation
Answer: 70
7 groups of 10 make 7 × 10 = 70. Or find 6 × 10 and add 10.
7 rows of 10 dots = 70 dots. - I4
There are 7 equal trays with 4 counters on each tray. How many counters are there?
Reveal explanation
Answer: 28
7 groups of 4 make 7 × 4 = 28. Or find 6 × 4 and add 4.
7 rows of 4 dots = 28 dots. - I5
Find 7 groups of 8. Can you use 6 groups plus one more?
Reveal explanation
Answer: 56
7 groups of 8 make 7 × 8 = 56. Or find 6 × 8 and add 8.
7 rows of 8 dots = 56 dots. - I6
Compute 7 × 7. Explain a strategy using a known fact.
Reveal explanation
Answer: 49
7 groups of 7 make 7 × 7 = 49. Or find 6 × 7 and add 7.
7 rows of 7 dots = 49 dots. - I7
There are 7 equal trays with 9 counters on each tray. How many counters are there?
Reveal explanation
Answer: 63
7 groups of 9 make 7 × 9 = 63. Or find 6 × 9 and add 9.
7 rows of 9 dots = 63 dots. - I8
There are 7 equal trays with 7 counters on each tray. How many counters are there?
Reveal explanation
Answer: 49
7 groups of 7 make 7 × 7 = 49. Or find 6 × 7 and add 7.
7 rows of 7 dots = 49 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 7 × 3, and explain why both work.
Reveal explanation
Answer: 21
One decomposition is (6 × 3) + (1 × 3) = 21. Another is (3 × 3) + (4 × 3) = 21. The partitions use different group splits but preserve the same product.
- C2
An array has 7 rows of 4 dots. A student says turning it creates 4 more dots. Explain the error and find the total.
Reveal explanation
Answer: 28
Turning an array swaps rows and columns but adds no dots. Both 7 × 4 and 4 × 7 equal 28.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
Compute 7 × 4. Explain a strategy using a known fact.
Reveal explanation
Answer: 28
7 groups of 4 make 7 × 4 = 28. Or find 6 × 4 and add 4.
7 rows of 4 dots = 28 dots. - E2
Compute 7 × 6. Explain a strategy using a known fact.
Reveal explanation
Answer: 42
7 groups of 6 make 7 × 6 = 42. Or find 6 × 6 and add 6.
7 rows of 6 dots = 42 dots. - E3
There are 7 equal trays with 6 counters on each tray. How many counters are there?
Reveal explanation
Answer: 42
7 groups of 6 make 7 × 6 = 42. Or find 6 × 6 and add 6.
7 rows of 6 dots = 42 dots.