doing math

courses › Mental Arithmetic

Times tables

level 3 course

Every fact from 1 × 1 to 12 × 12, recalled rather than counted.

Best in your head · no pen, no calculator why?

Learn first (about 3 minutes)

Opens at level 3.

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Builds on: Small facts

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

The times tables hold 78 different facts, from 1 × 1 to 12 × 12, because 7 × 8 and 8 × 7 are the same fact. The goal is to recall each one on its own, not to recite a table from the start.

A fact you can't recall yet can be built from one you can. Three anchors do the building: doubling, × 10, and half of × 10. Build the fact, say it, and it comes faster each time. Two kinds need no work at all: anything × 0 is 0, and anything × 1 stays the same.

Techniques

Double your way up

Multiplying by 2, 4 or 8.

  1. × 2 is one doubling.
  2. × 4 is two doublings, and × 8 is three.
  3. Keep count: each doubling multiplies by 2, so three doublings multiply by 8.
worked example

Example: 8 × 9

  1. 9 doubled is 18.
  2. 18 doubled is 36.
  3. 36 doubled is 72.

Answer: 72

Start from × 10

Multiplying by 5, 9, 10, 11 or 12.

  1. × 10 puts a 0 on the end: 7 × 10 = 70.
  2. × 5 is half of × 10.
  3. × 9 is × 10 minus one copy of the number. × 11 is × 10 plus one copy.
  4. × 12 is × 10 plus × 2.
worked example

Example: 9 × 6

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

Answer: 54

Build from facts you know

Multiplying by 3, 6 or 7.

  1. × 3 is double plus one more copy.
  2. × 6 is × 3, doubled.
  3. × 7 is × 5 plus × 2.
worked example

Example: 7 × 8

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

Answer: 56

Tips by skill

  • Tip× 2, 4, 5, 8, 10: Double once for × 2, twice for × 4, three times for × 8. For × 5, halve × 10. Anything × 0 is 0.
  • Tip× 3, 6, 9: × 9 is × 10 minus one copy. × 3 is double plus one copy, and × 6 is × 3 doubled.
  • Tip× 7, 11, 12 and squares: × 7 is × 5 plus × 2. × 11 and × 12 are × 10 plus one or two copies. Squares follow the same rules.
  • TipMixed facts: Start from the factor with the simplest rule, like × 10, × 2, × 5 or × 9, and build from there.

Watch out for

  • Losing count of doublings. Two doublings is × 4 and three is × 8, so 8 × 6 is 48, not 24.
  • Taking away 1 instead of a whole copy for × 9. 9 × 7 is 70 minus 7, which is 63, not 69.
  • Dropping the ten in × 12. 12 × 7 is 70 plus 14, not 70 plus 4.
  • Mixing up the neighbours 7 × 8 and 6 × 9. Learn them as a pair: 7 × 8 = 56, and 6 × 9 = 54.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

  1. 1 day
  2. 3 days
  3. 7 days
  4. 14 days
  5. 30 days
  6. 60 days
  7. mastered · every 90 days

your rounds

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