Chapter 4 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

M2.3.4 Chapter 4

The 3, 4 and 8 times tables

I know my 4 times table. How can that help me with the 8 times table?

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 3, 4 and 8 times tables
  • Get the 8 times table by doubling the 4 times table

You can count in 3s and in 4s. Do it as you did in 5s.

The 3 times table counts 3, 6, 9, 12 and on. The 4 times table counts 4, 8, 12, 16 and on.

A line from 0 to 18. Six hops of 3 land on 3, 6, 9, 12, 15 and 18. Each hop is labelled +3.+3+3+3+3+3+30369121518
Six hops of 3 land on 18. So 6 × 3 = 18.

The 4 times table is the 2 times table doubled. To double is to make twice as many. The 8 times table is the 4 times table doubled.

Two arrays of dots. The left array has 2 rows of 5 dots, labelled 2 × 5 = 10. The right array has 4 rows of 5 dots, labelled 4 × 5 = 20.2 × 5 = 104 × 5 = 20
Twice as many rows gives twice as many dots. 10 doubled is 20.

Draw it first

Double 4 × 3 to get 8 × 3

  1. A first array of 4 rows of 3 dots, labelled 4 × 3 = 12. A second array of 4 rows of 3 dots below it, labelled 12 again. Together they make 8 rows of 3, labelled 12 + 12 = 24 and 8 × 3 = 24.4 × 3 = 12

    1 Draw 4 rows of 3 dots. That is 4 × 3 = 12.

  2. A first array of 4 rows of 3 dots, labelled 4 × 3 = 12. A second array of 4 rows of 3 dots below it, labelled 12 again. Together they make 8 rows of 3, labelled 12 + 12 = 24 and 8 × 3 = 24.4 × 3 = 1212 again

    2 Draw 4 more rows of 3 dots below. That is 12 again.

  3. A first array of 4 rows of 3 dots, labelled 4 × 3 = 12. A second array of 4 rows of 3 dots below it, labelled 12 again. Together they make 8 rows of 3, labelled 12 + 12 = 24 and 8 × 3 = 24.12 + 12 = 248 × 3 = 24

    3 Now there are 8 rows of 3. Add: 12 + 12 = 24.

8 rows is double 4 rows. So 8 × 3 is double 4 × 3. The 8 times table is the 4 times table doubled.

Two rows of answers for 1 to 10 groups. Row 4s reads 4, 8, 12, 16, 20, 24, 28, 32, 36, 40. Row 8s reads 8, 16, 24, 32, 40, 48, 56, 64, 72, 80. Each answer in 8s is double the answer above it.4s4812162024283236408s8162432404856647280
Each answer in the 8s is double the answer above it.

Worked example

Find 8 × 7. Use the 4 times table.

  1. Find 4 × 7 first. Count in 4s seven times to get 28.
  2. 8 is double 4, so double the answer.
  3. Double 28 is 28 + 28, which is 56.

Answer: 8 × 7 = 56

Now look at the last digits of the 3s, 4s and 8s. They make patterns.

The last digit of each answer. Row 3s: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0. Row 4s: 4, 8, 2, 6, 0, then again 4, 8, 2, 6, 0. Row 8s: 8, 6, 4, 2, 0, then again 8, 6, 4, 2, 0.3s36925814704s48260482608s8642086420
The 3s use every digit. The 4s and 8s use only even digits.

The 4s go 4, 8, 2, 6, 0. The 8s go down in twos: 8, 6, 4, 2, 0. Both repeat.

See it three ways

With things

Put 18 stones in 6 rows. Put 3 stones in each row. Count in 3s.

As a picture

Eighteen stones in an array of 6 rows with 3 stones in each row, labelled 6 rows of 3.6 rows of 3

In symbols

6 × 3 = 18. Count: 3, 6, 9, 12, 15, 18.

Try it

Double an array of beans

You need: 32 beans, or 32 small stones, a flat table.

  1. Make an array of 4 rows with 4 beans in each row.
  2. Count the beans. That is 4 × 4.
  3. Make a second array exactly the same, under the first.
  4. Count all the beans. Is it double?

What you will see: The first array has 16 beans. Both arrays make 8 rows of 4, which is 32. So 8 × 4 = 32.

If you cannot try it, this is what happens.
Thirty-two beans in an array of 8 rows with 4 beans in each row, labelled 8 rows of 4.8 rows of 4

A wrong idea many people have

8 × 7 is 54.

Why it feels right: 54 sounds right. It is a real answer in the tables, because 6 × 9 = 54.

The test that breaks it: Double the 4 times table. 4 × 7 is 28. Now double 28.

What is true: 28 + 28 = 56. So 8 × 7 = 56. The number 54 belongs to 6 × 9.

Key words

double
to make twice as many. Double 4 is 8.

Back to your guess

The answer is B: Double each answer.

8 is double 4. So 8 groups are double 4 groups. 4 × 6 = 24, so 8 × 6 = 24 + 24 = 48.

Check yourself

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

  1. 4 × 6 = 24. Use it to find 8 × 6.

    Tap your answer.

    1. Yes, that is right. 8 × 6 is double 4 × 6. 24 + 24 = 48.

    2. Not this one. You added 4. Eight groups is double four groups, so double 24. Try another.

    3. Not this one. You took half. 8 is more than 4, so the answer is more than 24. Try another.

    See the answer

    48

    8 × 6 is double 4 × 6. 24 + 24 = 48.

    • If you chose B: You added 4. Eight groups is double four groups, so double 24.
    • If you chose C: You took half. 8 is more than 4, so the answer is more than 24.

  2. Count in 3s to find 3 × 9.

    See the answer

    27

    Count in 3s nine times. You say 3, 6, 9 and so on, up to 27.

  3. Write the 4 times table, from 1 × 4 to 10 × 4.

    See the answer

    4, 8, 12, 16, 20, 24, 28, 32, 36, 40

    Count in 4s ten times. Each answer is 4 more than the last.

  4. From an earlier chapter

    Amina shares 24 stones between 8 friends. How many stones does each friend get?

    Tap your answer.

    1. Yes, that is right. 8 × 3 = 24, so 24 ÷ 8 = 3.

    2. Not this one. You took 8 away. Sharing means dealing out equally. Think: 8 times what is 24? Go to M2.3.3. Try another.

    3. Not this one. The 8 is the number of friends. Each friend gets fewer than 8. Go to M2.3.3. Try another.

    See the answer

    3 stones

    8 × 3 = 24, so 24 ÷ 8 = 3.

    • If you chose B: You took 8 away. Sharing means dealing out equally. Think: 8 times what is 24? Go to M2.3.3.
    • If you chose C: The 8 is the number of friends. Each friend gets fewer than 8. Go to M2.3.3.

  5. What is 8 × 7?

    Tap your answer.

    1. Not this one. 54 is 6 × 9. Double 4 × 7 instead: 28 + 28. Try another.

    2. Yes, that is right. 4 × 7 = 28. Double it: 28 + 28 = 56.

    3. Not this one. 64 is 8 × 8. You need 8 sevens, not 8 eights. Try another.

    See the answer

    56

    4 × 7 = 28. Double it: 28 + 28 = 56.

    • If you chose A: 54 is 6 × 9. Double 4 × 7 instead: 28 + 28.
    • If you chose C: 64 is 8 × 8. You need 8 sevens, not 8 eights.

  6. Ravi counts in 3s: 3, 6, 9, 12. Which number comes next?

    Tap your answer.

    1. Not this one. You added 1. Counting in 3s adds 3 each time. Try another.

    2. Not this one. You added 4. That is counting in 4s. Counting in 3s adds 3 each time. Try another.

    3. Yes, that is right. Each number is 3 more than the last. 12 + 3 = 15. So 5 × 3 = 15.

    See the answer

    15

    Each number is 3 more than the last. 12 + 3 = 15. So 5 × 3 = 15.

    • If you chose A: You added 1. Counting in 3s adds 3 each time.
    • If you chose B: You added 4. That is counting in 4s. Counting in 3s adds 3 each time.

  7. Kofi has 6 stools. Each stool has 4 legs. How many legs are there?

    Tap your answer.

    1. Yes, that is right. Count in 4s six times: 4, 8, 12, 16, 20, 24. So 6 × 4 = 24.

    2. Not this one. You added 6 and 4. Times means 6 groups of 4. Go to M2.3.1. Try another.

    3. Not this one. That is 5 groups of 4. Count one more 4 to reach 6 groups. Try another.

    See the answer

    24

    Count in 4s six times: 4, 8, 12, 16, 20, 24. So 6 × 4 = 24.

    • If you chose B: You added 6 and 4. Times means 6 groups of 4. Go to M2.3.1.
    • If you chose C: That is 5 groups of 4. Count one more 4 to reach 6 groups.

  8. Think of 8, 16, 24, 32 and 40. Which list shows the last digit of each?

    Tap your answer.

    1. Not this one. Those are the first digits. The last digit is on the right: 16 ends in 6. Try another.

    2. Yes, that is right. The last digit of 8 is 8. Of 16 it is 6. Of 24 it is 4. Of 32 it is 2. Of 40 it is 0.

    3. Not this one. The last digit changes each time. 16 ends in 6, and 24 ends in 4. Try another.

    See the answer

    8, 6, 4, 2, 0

    The last digit of 8 is 8. Of 16 it is 6. Of 24 it is 4. Of 32 it is 2. Of 40 it is 0.

    • If you chose A: Those are the first digits. The last digit is on the right: 16 ends in 6.
    • If you chose C: The last digit changes each time. 16 ends in 6, and 24 ends in 4.

  9. Look at the two arrays. Together they show 8 × 5. What is 8 × 5?

    Two arrays of dots, each with 4 rows of 5 dots, labelled first array and second array.first arraysecond array
    Tap your answer.

    1. Not this one. That is one array. 8 × 5 is both arrays together. Try another.

    2. Not this one. You added 8 and 5. Times means 8 groups of 5. Go to M2.3.1. Try another.

    3. Yes, that is right. Each array is 4 × 5 = 20. Double it: 20 + 20 = 40. So 8 × 5 = 40.

    See the answer

    40

    Each array is 4 × 5 = 20. Double it: 20 + 20 = 40. So 8 × 5 = 40.

    • If you chose A: That is one array. 8 × 5 is both arrays together.
    • If you chose B: You added 8 and 5. Times means 8 groups of 5. Go to M2.3.1.

Keep it

Copy this into your exercise book.

Count in 3s and 4s. The 4 times table is double the 2 times table. The 8 times table is double the 4 times table. 8 × 7 = 28 + 28 = 56.

Draw: Draw 4 rows of 3 dots, then 4 more rows below. Write 4 × 3 = 12 and 8 × 3 = 24.

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.