Times tables
Every fact from 1 × 1 to 12 × 12, recalled rather than counted.
Best in your head · no pen, no calculator why?
Opens at level 3. You're level 1. You can read and practice here now.
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
- × 2 is one doubling.
- × 4 is two doublings, and × 8 is three.
- Keep count: each doubling multiplies by 2, so three doublings multiply by 8.
worked example
8 × 9
- 9 doubled is 18.
- 18 doubled is 36.
- 36 doubled is 72.
Answer: 72
Start from × 10
- × 10 puts a 0 on the end: 7 × 10 = 70.
- × 5 is half of × 10.
- × 9 is × 10 minus one copy of the number. × 11 is × 10 plus one copy.
- × 12 is × 10 plus × 2.
worked example
9 × 6
- 6 × 10 = 60.
- Take away one copy of 6: 60 − 6 = 54.
Answer: 54
Build from facts you know
- × 3 is double plus one more copy.
- × 6 is × 3, doubled.
- × 7 is × 5 plus × 2.
worked example
7 × 8
- 5 × 8 = 40.
- 2 × 8 = 16.
- 40 + 16 = 56.
Answer: 56
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.
practice
× 2, 4, 5, 8, 10
worked example
11 × 4
Answer: 44
- × 4 is two doublings: 11 → 22 → 44.
× 3, 6, 9
worked example
9 × 1
Answer: 9
- × 9 is × 10 minus one copy: 10 − 1 = 9.
× 7, 11, 12 and squares
worked example
11 × 1
Answer: 11
- × 11 is × 10 plus one copy: 10 + 1 = 11.
Mixed facts
worked example
12 × 2
Answer: 24
- × 2 is doubling: 12 + 12 = 24.