Chapter 5 of 8

All 8 chapters
  1. 1Equal groups, readunderstood
  2. 2The 2, 5 and 10 times tables, readunderstood
  3. 3Sharing and grouping, readunderstood
  4. 4The 3, 4 and 8 times tables, readunderstood
  5. 5The 6, 7 and 9 times tables, readunderstood
  6. 6Times and divide facts together, readunderstood
  7. 7Remainders, readunderstood
  8. 8Times and divide with bigger numbers, readunderstood

M2.3.5 Chapter 5

The 6, 7 and 9 times tables

I can never remember 6 × 7 or 9 × 8. Is there a trick?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Say the 6, 7 and 9 times tables
  • Work out 9 × 7 as 10 × 7 − 7

A times table lists the answers for one number. You know the 2, 3, 4, 5 and 10 tables. Now we build the last three from them.

Start with the sixes. A six is two threes. So 6 × 4 is double 3 × 4. To double is to make twice as much.

3 × 4 = 12. Double 12 is 24. So 6 × 4 = 24.

Now the nines. Nine is one less than ten. So 9 × 7 is 10 rows of 7, less one row.

Draw it first

Find 9 × 7 from 10 × 7

  1. Ten rows of 7 dots. Step 1 labels it 10 × 7 = 70. Step 2 fills in the top row and labels it take away 7. Step 3 labels what is left 70 − 7 = 63 and 9 × 7 = 63.10 × 7 = 70

    1 Draw 10 rows of 7 dots. That is 10 × 7 = 70.

  2. Ten rows of 7 dots. Step 1 labels it 10 × 7 = 70. Step 2 fills in the top row and labels it take away 7. Step 3 labels what is left 70 − 7 = 63 and 9 × 7 = 63.10 × 7 = 70take away 7

    2 Fill in one whole row. This is the row to take away. It has 7 dots.

  3. Ten rows of 7 dots. Step 1 labels it 10 × 7 = 70. Step 2 fills in the top row and labels it take away 7. Step 3 labels what is left 70 − 7 = 63 and 9 × 7 = 63.10 × 7 = 70take away 770 − 7 = 639 × 7 = 63

    3 Count the empty rows. There are 9. So 9 × 7 = 70 − 7 = 63.

The rule for nines: work out 10 × the number. Then take away the number.

Worked example

Work out 9 × 6.

  1. 10 × 6 = 60.
  2. Take away one 6. 60 − 6 = 54.

Answer: 9 × 6 = 54

The sevens are a five and a two. For 7 × 8, do 5 × 8 and 2 × 8. Then add.

See it first with 7 rows of 4 dots. Fill in 5 rows. The other 2 rows are empty.

Seven rows of 4 dots. The top five rows are filled in and labelled 5 × 4 = 20. The bottom two rows are empty and labelled 2 × 4 = 8.5 × 4 = 202 × 4 = 8
A seven is a five and a two. 7 × 4 = 20 + 8 = 28.

Worked example

Work out 7 × 8.

  1. 5 × 8 = 40.
  2. 2 × 8 = 16.
  3. 40 + 16 = 56.

Answer: 7 × 8 = 56

Three rows of answers for 1 to 10 groups. Row 6s reads 6, 12, 18, 24, 30, 36, 42, 48, 54, 60. Row 7s reads 7, 14, 21, 28, 35, 42, 49, 56, 63, 70. Row 9s reads 9, 18, 27, 36, 45, 54, 63, 72, 81, 90.6s61218243036424854607s71421283542495663709s9182736455463728190
The three tables. Say each row out loud.

See it three ways

With things

Put 4 stones in each of 6 rows. Cover 3 rows with your hand. Count 12. Double it.

As a picture

Six rows of 4 stones. The top three rows are filled in and labelled 3 × 4 = 12. The bottom three rows are empty and labelled 3 × 4 = 12.3 × 4 = 123 × 4 = 12

In symbols

6 × 4 = 3 × 4 + 3 × 4 = 12 + 12 = 24.

Try it

Look for a pattern in the nines

You need: a pencil, a sheet of paper, or an old page.

  1. Write 9 × 2 = 18 and 9 × 3 = 27. Then 9 × 4 = 36 and 9 × 5 = 45.
  2. Beside each answer, add its two digits.
  3. Carry on to 9 × 10 = 90.

What you will see: The digits of every answer add to 9. The tens digit goes up by 1. The ones digit goes down by 1. You can use this to check a nine.

If you cannot try it, this is what happens.
Four lines. On the left, 9 × 2 = 18, 9 × 3 = 27, 9 × 4 = 36 and 9 × 5 = 45. On the right, the digits added: 1 + 8 = 9, 2 + 7 = 9, 3 + 6 = 9 and 4 + 5 = 9.9 × 2 = 181 + 8 = 99 × 3 = 272 + 7 = 99 × 4 = 363 + 6 = 99 × 5 = 454 + 5 = 9

A wrong idea many people have

9 × 7 is 10 × 7 take away 9. So it is 61.

Why it feels right: The nine is right there in 9 × 7. It seems the number to take away.

The test that breaks it: Make 10 rows of 7 dots. Take away one row. Count what is left. You get 63, not 61. One row is 7 dots, not 9.

What is true: Take away one row. One row is the other number. 9 × 7 = 70 − 7 = 63.

Key words

double
to make twice as much.
times table
the answers when you count in equal groups of one number.

Back to your guess

The answer is B: Yes. Each hard fact is built from a fact I know.

Sixes are double the threes. Nines are tens with one group taken away. Sevens are fives plus twos. You already know those tables.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. What is 6 × 8? Double 3 × 8 to find out.

    Tap your answer.

    1. Yes, that is right. 3 × 8 = 24. Double 24 is 48. So 6 × 8 = 48.

    2. Not this one. You may have 6 × 7 in mind. Double 3 × 8 = 24 is 48. Try another.

    3. Not this one. You added 6 + 8. Times means 6 equal groups of 8. Go to M2.3.1. Try another.

    See the answer

    48

    3 × 8 = 24. Double 24 is 48. So 6 × 8 = 48.

    • If you chose B: You may have 6 × 7 in mind. Double 3 × 8 = 24 is 48.
    • If you chose C: You added 6 + 8. Times means 6 equal groups of 8. Go to M2.3.1.

  2. Use 10 × 6 to work out 9 × 6.

    See the answer

    54

    10 × 6 = 60. Take away one 6. 60 − 6 = 54.

  3. Mei puts 8 stones in each of 7 bags. How many stones is that?

    See the answer

    56 stones

    7 bags of 8 is 7 × 8. That is 5 × 8 plus 2 × 8. 40 + 16 = 56.

  4. Kofi says 9 × 4 = 32. Is he right?

    Tap your answer.

    1. Not this one. That is the eights. 9 × 4 is one more group of 4 than that. Try another.

    2. Yes, that is right. 10 × 4 = 40. Take away one 4. 40 − 4 = 36.

    3. Not this one. You took away 9 from 40. Take away one group of 4, not 9. Try another.

    See the answer

    No. 9 × 4 = 36.

    10 × 4 = 40. Take away one 4. 40 − 4 = 36.

    • If you chose A: That is the eights. 9 × 4 is one more group of 4 than that.
    • If you chose C: You took away 9 from 40. Take away one group of 4, not 9.

  5. From an earlier chapter

    Use 4 × 6 = 24 to find 8 × 6.

    See the answer

    48

    Eight is double four. Double 24 is 48. So 8 × 6 = 48.

  6. Look at the dots. Take away the shaded row. How many dots are left?

    Ten rows of 5 dots with the top row shaded, labelled 10 rows of 5.10 rows of 5
    Tap your answer.

    1. Not this one. You took away 9. The shaded row has 5 dots, so take away 5. Try another.

    2. Not this one. You took away one dot. The shaded row has 5 dots, so take away 5. Try another.

    3. Yes, that is right. 10 rows of 5 is 50. Take away one row of 5. 50 − 5 = 45. That is 9 × 5.

    See the answer

    45

    10 rows of 5 is 50. Take away one row of 5. 50 − 5 = 45. That is 9 × 5.

    • If you chose A: You took away 9. The shaded row has 5 dots, so take away 5.
    • If you chose B: You took away one dot. The shaded row has 5 dots, so take away 5.

  7. What is 7 × 6? Use 5 × 6 and 2 × 6.

    Tap your answer.

    1. Not this one. You added 7 and 6. Times means 7 groups of 6. Go to M2.3.1. Try another.

    2. Yes, that is right. 5 × 6 = 30 and 2 × 6 = 12. 30 + 12 = 42.

    3. Not this one. That is only 5 × 6. Add 2 × 6 = 12 as well. Try another.

    See the answer

    42

    5 × 6 = 30 and 2 × 6 = 12. 30 + 12 = 42.

    • If you chose A: You added 7 and 6. Times means 7 groups of 6. Go to M2.3.1.
    • If you chose C: That is only 5 × 6. Add 2 × 6 = 12 as well.

  8. Hana knows 3 × 9 = 27. Which sum gives 6 × 9?

    Tap your answer.

    1. Not this one. You added the 6. Six is double three, so double 27. Try another.

    2. Not this one. That is 4 × 9, one more group of 9. Six groups is double three groups. Try another.

    3. Yes, that is right. Six is double three. Double 27 is 27 + 27 = 54. So 6 × 9 = 54.

    See the answer

    27 + 27 = 54

    Six is double three. Double 27 is 27 + 27 = 54. So 6 × 9 = 54.

    • If you chose A: You added the 6. Six is double three, so double 27.
    • If you chose B: That is 4 × 9, one more group of 9. Six groups is double three groups.

Keep it

Copy this into your exercise book.

Sixes are double threes: 6 × 4 = 12 + 12. Nines are tens less one group: 9 × 7 = 70 − 7. Sevens are fives plus twos: 7 × 8 = 40 + 16.

Draw: Ten rows of 7 dots. Fill in one row. Write 70 − 7 = 63.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (905 KB). It opens on any phone.