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Shortcuts, not memory

What Patterns Hide in the Times Tables?

Times tables are full of patterns, and spotting them beats memorising every fact.

Rows and columns ofdotsEach square is one factPatterns run down thecolumnsLearn the pattern, notthe list
Not a list to memorise. A grid full of patterns.
  1. Step 1 of 5

    Every fact is really a rectangle of dots.

    Four rowsSix in each rowTwenty-four intotal

    Four times six is not a phrase to recite, it is four rows of six counters. Seeing the rectangle makes the answer something you can check.

  2. Step 2 of 5

    Half the grid is a mirror of the other half.

    4 × 6 Four rows of six6 × 4 The same rectangle,turned

    Four rows of six holds the same as six rows of four, so learning one fact quietly gives you the other one for free.

  3. Step 3 of 5

    The nine times table folds in on itself.

    9 × 2 = 181 + 8 = 99 × 3 = 272 + 7 = 99 × 4 = 363 + 6 = 9

    Every answer's digits add to nine, and as the tens climb the units fall. Eighteen, twenty-seven, thirty-six — a pattern, not a list.

  4. Step 4 of 5

    The easy tables carry the hard ones.

    1 Double for 2sand 4s210Shift a digitfor 10s3+Combine thosefor the rest

    Doubling handles the twos and fours, and tens are simply a shifted digit. Seven eights is just five eights plus two eights.

  5. Step 5 of 5

    Only a handful of facts are genuinely hard.

    All facts to 12looks enormousAfter removing mirrorsabout halfGenuinely hard onesa manageablehandful

    Strip out the mirrors, the tens, the twos and the fives and barely a dozen awkward facts remain. That is a much smaller job.

    Of the 144 facts up to 12 × 12, mirrors and easy tables account for most, leaving roughly fifteen that need real practice.

The short version

Times tables are a grid of patterns rather than a list of facts, and using the mirrors and shortcuts leaves only a dozen hard cases.

Try it yourself

Write out the nine times table and add each answer's digits. Every single one comes to nine, all the way up.

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