Lesson 3 of 10 · Grades 3 to 4

Times tables strategies

You do not have to memorise every times table fact by itself. Many facts grow out of facts you already know. Double a small fact and you have a larger one. Use 10 times a number and step back one group, and the nines become easy.

Start from what you know

The times tables are not 144 separate facts to swallow one by one. They are connected. Facts you already know can grow into facts you do not know yet, using three simple moves: double, add a group, or take a group away.

The 2s, 5s and 10s make a good home base. You can skip count in 2s without thinking, the 5s end in 0 or 5, and multiplying by 10 adds a zero. Every other table can be reached from those anchor facts.

Double to reach the 4s and 8s

Doubling is the most powerful move. If you know 2 × 8 = 16, then 4 × 8 = 32, because four groups of 8 is just two groups of 8 doubled. Double it once more and you have 8 × 8 = 64. The 4 times table is the 2 times table doubled, and the 8 times table is the 4 times table doubled.

Group 1 Group 2 Group 3 Group 4
Four groups of 8 is two groups of 8 doubled. 2 × 8 = 16, so 4 × 8 = 32.

Add or take away one group

Each fact in a table is one group more than the fact before it. If you know 5 × 7 = 35, then 6 × 7 is one more group of 7: 35 + 7 = 42. Going the other way works too. If you know 10 × 6 = 60, then 9 × 6 is one group of 6 less: 60 - 6 = 54. The nines are a favourite use of this move, because the 10s are so easy.

You can also jump two steps at a time. From 4 × 6 = 24, adding two groups of 6 gives 6 × 6 = 36. Choose the neighbour that gets you to the answer with the fewest steps.

0 6 12 18 24 30 36 42 48 54 9 jumps of 6
Nine jumps of 6 lands on 54. Start at ten jumps (60) and step back one jump of 6 to get the same answer.

Halve to reach the 5s

The 5 times table sits halfway between easy neighbours. Half of 10 × 8 is 5 × 8, so 5 × 8 = 40. Halving works because 5 is half of 10. If the number you are multiplying by 5 is even, you can also halve that number first: 5 × 8 is the same as 10 × 4, and halving first often makes the numbers friendlier.

Useful tip

Learn the squares as anchor facts: 1 × 1, 2 × 2, 3 × 3 and so on. They are the middle of each table, and you can reach a neighbour from a square by adding or taking away one group. For example, 7 × 7 = 49, so 8 × 7 = 49 + 7 = 56.

Worked example

Use the fact 10 × 8 = 80 to work out 9 × 8, and use doubling to work out 4 × 8.

Step 1: 9 × 8 is one group of 8 fewer than 10 × 8. Start from 10 × 8 = 80.

Step 2: take one group of 8 away: 80 - 8 = 72. So 9 × 8 = 72.

Step 3: for 4 × 8, start with 2 × 8 = 16.

Step 4: double the fact: 4 × 8 is twice 2 × 8, and double 16 is 32.

Answer: 9 × 8 = 72 and 4 × 8 = 32.

Remember

  • Double a known fact to reach the 4s and the 8s.
  • Add one group to move up a table.
  • Take one group away to move down a table.
  • Halve a 10 times fact to reach the 5s.

Try it

Answer the five questions below. Work them out first, then open each answer to check.

  1. Double 8, then double the answer again. What number do you reach?

    Show answer

    32. Double 8 is 16, and double 16 is 32, so 4 × 8 = 32.

  2. You know that 5 × 7 = 35. Use it to find 6 × 7.

    Show answer

    42. Add one more group of 7: 35 + 7 = 42.

  3. Find 9 × 6 by starting with 10 × 6 and taking one group of 6 away.

    Show answer

    54. 10 × 6 = 60, and 60 - 6 = 54.

  4. What is 4 × 9?

    Show answer

    36.

  5. Find 8 × 7 by doubling 4 × 7.

    Show answer

    56. 4 × 7 = 28, and double 28 is 56.

Puzzle · Number line jumps

Puzzle time

A grasshopper makes equal jumps of 7 along the number line. Ten jumps land on 70. Where do nine jumps land?

Pick your answer

Show a hint

Nine jumps is one jump of 7 less than ten jumps. Start at 70 and step back 7.

Show the answer

Answer: 63. Ten jumps of 7 land on 70, so nine jumps land on 70 - 7 = 63. The answer 56 is eight jumps, and 72 is not a multiple of 7.