Times tables: 21 facts to learn, not 100

To find 7 × 8, many pupils recite the 7 times table from the start: 7, 14, 21, 28… They get there in the end, but slowly, and one counting slip along the way gives 49 or 63. Reciting a table is not knowing it: a fact is known when the answer comes on its own, without counting.

Fewer facts than it looks

A 1 to 10 multiplication chart has 100 squares. But 6 × 4 and 4 × 6 give the same answer, so there are only 55 different products. The 1, 2, 5 and 10 times tables come almost for free. That leaves 21 products to really memorise, including 6 square numbers such as 7 × 7. Tell your pupils: the mountain becomes a hill.

Understand before you memorise

A product is a set of equal rows. 6 × 4 is 6 rows of 4 counters. Turn the grid a quarter turn and you see 4 rows of 6: the answer stays the same, and pupils see why they only need to learn half the chart.

Have pupils build rectangles with counters or on squared paper, then count row by row: 6, 12, 18, 24. This skip counting later becomes their safety net.

Rebuilding a forgotten fact

Before working on speed, give pupils strategies to rebuild one fact from another:

• × 4: double, then double again. 4 × 7 is double 14, so 28.
• × 8: one more double. 8 × 7 is double 28, so 56.
• × 5: half of × 10. 5 × 8 is half of 80, so 40.
• × 9: × 10 take away one row. 9 × 7 is 70 − 7, so 63.
• × 3 and × 6: one more row. 6 × 7 is 5 × 7 + 7, so 42.

A strategy is not the goal: it helps out while memory is being built.

Making facts automatic

Memorisation improves with short, frequent sessions: ten minutes a day works better than an hour a week. Mix the questions instead of following the order of the table, bring a missed fact back soon, and ask the question the other way round too: 7 × ? = 56. The missing number prepares the ground for division.

Finally, set a speed goal. In Times Table Mosaic, a square only becomes a mosaic tile after two correct answers in under six seconds, and a missed fact comes back a few questions later.

Times Table MosaicTimes tables practice: every mastered fact becomes a mosaic tile.See the game

Four common mistakes

• Adding: 7 × 8 = 15. Go back to rows: 7 rows of 8 is not 7 counters and 8 counters.
• Giving a neighbouring fact: 7 × 8 = 48 or 63, which are 6 × 8 and 7 × 9. These mix-ups show the table is only roughly known; bring those facts back more often.
• Swapping the digits: 56 becomes 65. In some languages, such as Arabic or German, the units are said first, which makes this swap more likely for bilingual pupils.
• Losing track while reciting: one skip too many or too few. Doubling or using × 10 avoids counting everything again.

A five-week sequence

1. The 2, 5 and 10 times tables, with rectangles of counters.
2. The 4 and 8 times tables, through doubling.
3. The 3 and 6 times tables, by adding one row.
4. The 9 times table, then 7 × 7: that is all that is left of the 7 times table.
5. Everything mixed, with missing numbers and reading the multiplication chart.

Well-known tables also show in written calculation: many mistakes in long multiplication are really times table mistakes.

The Magic ColumnWritten addition, subtraction and multiplication, digit by digit, carrying included.See the game