Chapter 2 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

M2.3.2 Chapter 2

The 2, 5 and 10 times tables

The answers in the 5 times table end in 5 or 0. Why?

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 2, 5 and 10 times tables
  • Spot the pattern in the last digits of each table

A times table is a list of answers. Each answer is for one more group of the same size.

The 5 times table starts 1 × 5, 2 × 5, 3 × 5. You get each answer by counting in 5s.

Draw it first

Count in 5s along a line

  1. A line from 0 to 30. Hops of 5 land on 5, 10, 15, 20, 25 and 30. The labels read 1 × 5 = 5, then 3 × 5 = 15, then 6 × 5 = 30.501 × 5 = 5

    1 Start at 0. Hop 5. You land on 5. That is 1 × 5.

  2. A line from 0 to 30. Hops of 5 land on 5, 10, 15, 20, 25 and 30. The labels read 1 × 5 = 5, then 3 × 5 = 15, then 6 × 5 = 30.5101503 × 5 = 15

    2 Hop 5 again, twice more. You land on 15. That is 3 × 5.

  3. A line from 0 to 30. Hops of 5 land on 5, 10, 15, 20, 25 and 30. The labels read 1 × 5 = 5, then 3 × 5 = 15, then 6 × 5 = 30.5101520253006 × 5 = 30

    3 Keep going. Six hops of 5 land on 30. That is 6 × 5.

The 10 times table counts in 10s. Each answer is a number of tens. 4 × 10 is 4 tens, which is 40.

Four rods of ten, labelled 4 × 10 = 40.4 × 10 = 40
Each rod is one ten. 4 rods make 40.

The 2 times table counts in 2s. Each answer is a double. 4 × 2 is 4 + 4, which is 8.

Four pairs of stones, 2 in each pair, labelled 4 × 2 = 8.4 × 2 = 8
Each pair is a group of 2. Four pairs make 8.
Three columns of answers for 1 to 10 groups. The first column, headed × 2, reads 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. The second, headed × 5, reads 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. The third, headed × 10, reads 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.× 22468101214161820× 55101520253035404550× 10102030405060708090100
The three tables side by side. Look down each column.

Now look at only the last digit of each answer. A digit is one of the figures 0 to 9.

The last digit of each answer. In the row 2s: 2, 4, 6, 8, 0, then again 2, 4, 6, 8, 0. In the row 5s: 5, 0, 5, 0, and so on. In the row 10s: all 0.2s24680246805s505050505010s0000000000
The last digits repeat. They never stop repeating.

The 2s end in 2, 4, 6, 8 or 0. These are even numbers. An even number shares into 2 equal groups with none left.

The 5s end in 5, then 0, then 5, then 0. The 10s all end in 0.

Two sets of rods. The first set is 8 rods, labelled 8 × 10 = 80. The second set is 4 rods, half as many, labelled 8 × 5 = 40.8 × 10 = 808 × 5 = 40
Take half of the rods. 4 rods are 40, so 8 × 5 = 40.

Worked example

Find 8 × 5 without counting in 5s.

  1. The 5 times table is half of the 10 times table.
  2. Find 8 × 10. That is 8 tens, which is 80.
  3. Take half of 80. Half of 80 is 40.

Answer: 8 × 5 = 40

See it three ways

With things

Put 20 stones in 4 rows of 5. Count along the rows in 5s.

As a picture

Twenty stones in an array of 4 rows with 5 stones in each row.

In symbols

4 × 5 = 20. Count: 5, 10, 15, 20.

Try it

Count in 5s with stones

You need: 15 small stones, or beans, a flat table.

  1. Put 5 stones in a pile. Say "5".
  2. Make a second pile of 5. Say the total so far, "10".
  3. Make a third pile of 5. Say the total, "15".
  4. Look at the last digit of each number you said.

What you will see: You said 5, 10, 15. The last digits go 5, 0, 5. The next is 20. The last digit goes back to 0.

If you cannot try it, this is what happens.
Three piles of 5 stones. The piles are labelled 5, 10 and 15.51015

A wrong idea many people have

The answers in the 5 times table all end in 5.

Why it feels right: The first answers are 5, 15 and 25. Many of them do end in 5.

The test that breaks it: Count in 5s with stones: 5, 10, 15, 20. Look at the last digit of each number.

What is true: They end in 5, then 0, then 5, then 0. 4 × 5 = 20 ends in 0.

Key words

times table
a list of answers for more and more equal groups.
digit
one of the figures 0 to 9. In 35, the last digit is 5.
even
a number that shares into 2 equal groups with none left.

Back to your guess

The answer is B: Each step adds 5. Two steps add 10, so the last digit comes back.

Each step adds 5. Two steps add 10, which does not change the last digit. So the last digits go 5, 0, 5, 0.

Check yourself

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

  1. Which number is not in the 5 times table?

    Tap your answer.

    1. Not this one. Count 7 fives and you reach 35. Try another.

    2. Not this one. 40 ends in 0, as many 5 table answers do. Count 8 fives and you reach 40. Try another.

    3. Yes, that is right. Answers in the 5 times table end in 5 or 0. 52 ends in 2.

    See the answer

    52

    Answers in the 5 times table end in 5 or 0. 52 ends in 2.

    • If you chose A: Count 7 fives and you reach 35.
    • If you chose B: 40 ends in 0, as many 5 table answers do. Count 8 fives and you reach 40.

  2. Write the answers to 6 × 2, 6 × 5 and 6 × 10.

    See the answer

    12, 30 and 60

    6 × 2 is the double of 6, which is 12. Six fives are 30. Six tens are 60.

  3. From an earlier chapter

    Ravi has 4 bags with 5 stones in each bag. Which sum tells how many stones?

    Tap your answer.

    1. Not this one. That puts 4 and 5 together. Times means 4 groups of 5. Go to M2.3.1. Try another.

    2. Yes, that is right. 4 groups of 5 is 4 × 5. Count in 5s: 5, 10, 15, 20.

    See the answer

    4 × 5 = 20

    4 groups of 5 is 4 × 5. Count in 5s: 5, 10, 15, 20.

    • If you chose A: That puts 4 and 5 together. Times means 4 groups of 5. Go to M2.3.1.

  4. Tariq says 45 is in the 2 times table. It ends in 5. Is he right?

    Tap your answer.

    1. Not this one. Count in 2s: 44, 46. You jump over 45. Every answer in the 2 times table is even. Try another.

    2. Not this one. Even depends on the last digit only. 45 ends in 5, so it is odd. Try another.

    3. Yes, that is right. 45 ends in 5, so it is not even. It is in the 5 times table instead: 9 × 5 = 45.

    See the answer

    No. Those answers end in 0, 2, 4, 6 or 8.

    45 ends in 5, so it is not even. It is in the 5 times table instead: 9 × 5 = 45.

    • If you chose A: Count in 2s: 44, 46. You jump over 45. Every answer in the 2 times table is even.
    • If you chose B: Even depends on the last digit only. 45 ends in 5, so it is odd.

  5. Joseph has 9 pairs of sandals. How many sandals is that? Use the 2 times table.

    See the answer

    18 sandals

    A pair is 2. 9 pairs is 9 × 2, which is 9 + 9 = 18.

  6. What is 7 × 5?

    Tap your answer.

    1. Not this one. You added 7 + 5. Times means 7 groups of 5. Go to M2.3.1. Try another.

    2. Not this one. That is 6 fives. Count one more 5 to reach 7 fives. Try another.

    3. Yes, that is right. Count 7 fives: 5, 10, 15, 20, 25, 30, 35. 7 × 5 = 35.

    See the answer

    35

    Count 7 fives: 5, 10, 15, 20, 25, 30, 35. 7 × 5 = 35.

    • If you chose A: You added 7 + 5. Times means 7 groups of 5. Go to M2.3.1.
    • If you chose B: That is 6 fives. Count one more 5 to reach 7 fives.

  7. Look at the rods. Each rod is 10. What is the total?

    Some rods of ten, labelled rods of ten.rods of ten
    Tap your answer.

    1. Yes, that is right. 6 rods of 10 is 6 × 10. Count in 10s: 10, 20, 30, 40, 50, 60.

    2. Not this one. You added 6 and 10. Each rod is worth 10, so count in 10s. Go to M2.3.1. Try another.

    3. Not this one. That is how many rods there are. Each rod is worth 10, so 6 rods are 6 tens. Try another.

    See the answer

    60

    6 rods of 10 is 6 × 10. Count in 10s: 10, 20, 30, 40, 50, 60.

    • If you chose B: You added 6 and 10. Each rod is worth 10, so count in 10s. Go to M2.3.1.
    • If you chose C: That is how many rods there are. Each rod is worth 10, so 6 rods are 6 tens.

  8. Think of 5, 10, 15 and 20. Which list shows the last digit of each?

    Tap your answer.

    1. Not this one. That is the wrong idea that every answer ends in 5. 2 × 5 = 10 ends in 0. Try another.

    2. Yes, that is right. The last digit of 5 is 5. Of 10 it is 0. Of 15 it is 5. Of 20 it is 0.

    3. Not this one. Those are the first digits. The last digit is on the right: 15 ends in 5. Try another.

    See the answer

    5, 0, 5, 0

    The last digit of 5 is 5. Of 10 it is 0. Of 15 it is 5. Of 20 it is 0.

    • If you chose A: That is the wrong idea that every answer ends in 5. 2 × 5 = 10 ends in 0.
    • If you chose C: Those are the first digits. The last digit is on the right: 15 ends in 5.

  9. Which sentence is true for every answer in the 2 times table?

    Tap your answer.

    1. Not this one. 5 × 2 = 10 ends in 0. The last digits go 2, 4, 6, 8, 0 and repeat. Try another.

    2. Not this one. That is the 5 times table. The 2 times table ends in 2, 4, 6, 8 or 0. Try another.

    3. Yes, that is right. Each answer is a double. A double shares into 2 equal groups with none left. That is what even means.

    See the answer

    It is always even.

    Each answer is a double. A double shares into 2 equal groups with none left. That is what even means.

    • If you chose A: 5 × 2 = 10 ends in 0. The last digits go 2, 4, 6, 8, 0 and repeat.
    • If you chose B: That is the 5 times table. The 2 times table ends in 2, 4, 6, 8 or 0.

Keep it

Copy this into your exercise book.

The 2 times table gives even numbers. The 5 times table ends in 5, 0, 5, 0. The 10 times table always ends in 0. Count in 2s, 5s or 10s to find an answer.

Draw: Write 5, 10, 15, 20, 25, 30 along a line. Circle the last digit of each number.

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.