Times tables

Why times tables don't stick, and what works instead

Times tables fade when they are practiced by chanting in order, or in one long sitting. They stay when your child pulls each fact out of memory, a few facts at a time, on several short days, with facts they already know mixed in.

9 minute read · Updated

You may recognize this. On Sunday evening your child says the 7 times table from top to bottom without a stumble, and you both go to bed pleased. On Friday someone asks "7 × 8?" and there is a long silence, then a guess, then tears or a shrug.

Nothing is wrong with your child's memory. The trouble is in how the table was practiced.

Why does my child know a table tonight and lose it by Friday?

A table learned in one sitting, in order, is held up by rhythm and by the line that came just before. Asked 7 × 8 on its own a few days later, your child has nothing to lean on. The fact was said many times, but it was never pulled out of memory cold.

Saying a table in order is like singing a song: each line cues the next. A quick check: ask five facts from the table out of order. If the answers come slowly, or your child whispers the chant to get there, the table is known as a song and not yet as facts.

One small classroom study looked at exactly this. Researchers had 48 second-grade pupils practice multiplication facts either by recalling answers from flashcards or by chanting them aloud. Recalling led to a stronger gain in how fluently the children could produce the facts, both five minutes later and one week later. It is one small study, so treat it as a pointer.

The second reason is the single long sitting. One review that pooled 317 experiments found that spreading practice over time beats packing it into one session. Those experiments used word and fact recall tasks, not times tables, so take the direction and not a number: several short days are a safer bet than one long one.

Do children still need to know the tables by heart?

Yes. Schools in both the US and England expect the multiplication facts to be known from memory, and the reason is practical. A child who has to work out 7 × 8 in the middle of a long multiplication or a division has less attention left for the method itself.

Ofsted, England's school inspectorate, puts it this way: "Pupils who are not able to quickly and easily recall maths facts struggle with calculations due to their working memory being overloaded." A US federal practice guide adds: "Automatic retrieval gives students more mental energy to understand relatively complex mathematical tasks and execute multistep mathematical procedures."

Here is what the two sets of standards ask for by the end of each school year.

WhereWhenWhat is expected
EnglandYear 2Recall and use the facts for the 2, 5 and 10 tables.
EnglandYear 3Recall and use the facts for the 3, 4 and 8 tables.
EnglandYear 4Recall the facts for the tables up to 12 × 12.
United States (Common Core)Grade 3Know from memory all products of two one-digit numbers, and multiply and divide within 100 fluently.

Knowing by heart does not mean knowing without understanding. Guidance for teachers from England's Education Endowment Foundation notes that understanding lets pupils "reconstruct steps in a procedure that they may have forgotten". We think the same holds for a single fact: a child who knows that 7 × 8 is 7 × 7 and one more 7 has a way back when it slips.

In what order do schools teach the tables?

England's national curriculum sets the order by year: the 2, 5 and 10 tables in Year 2, the 3, 4 and 8 tables in Year 3, and the rest up to 12 × 12 by the end of Year 4. The easy patterns come first, then the tables that double from each other.

The order is kinder than it looks. The 4 times table is the 2 doubled, and the 8 is the 4 doubled. And every fact works both ways round: 6 × 8 is the same as 8 × 6, which your child met in the 8 times table.

Follow that through and the hard tables shrink. A child who knows the 2, 3, 4, 5, 8 and 10 tables, and who knows a fact can be turned around, has only six new facts left to learn up to 10 × 10:

Even 7 × 8 is not on the list: it belongs to the 8 times table from the year before. The 11 and 12 tables add nine more new facts. "Six left" is a very different job from "three whole tables".

The stubborn tables are the same for everyone. The government agency that writes England's Year 4 multiplication tables check puts extra questions on the 6, 7, 8, 9 and 12 tables "because these have been determined to be the most difficult multiplication tables". More in our parent's guide to the Year 4 check.

What works instead of chanting?

Four changes do most of the work: ask for facts out of order so your child has to recall them, teach only a few new facts at a time, mix them with facts already known, and spread the practice over several short days.

1

Ask, do not recite

Write each fact on a card with the answer on the back, or ask aloud in a jumbled order. Your child answers before seeing the answer. Digging the fact out is the practice.

2

Three or four new facts at a time

Take the three or four your child does not know and leave the rest of the table for later in the week.

3

Mix in facts they already know

Shuffle the new cards in with six or so old ones. A US federal practice guide written for children who struggle with math recommends "a mix of previously and newly learned material" in practice.

4

Short and often

Stop while it is still going well, and come back tomorrow.

5

Turn it around

Ask 7 × 8, then 8 × 7, then "56 divided by 7?". Both sets of standards expect the division facts alongside the multiplication ones.

When a fact is missed, give it straight away: "7 × 8 is 56. Say the whole thing back to me." Then put that card three places down the pile so it returns in a minute. The same federal guide advises that when children do not correct themselves in fact practice, the adult should "immediately ask them to fix their incorrect answer".

Should I time my child?

Not while a table is new. Add a clock only for facts your child can already answer correctly, keep it to a minute or two, and have them race their own last score. The evidence on timing is argued over, and the guidance that supports it attaches clear conditions.

The argument, told fairly: the US math teachers' council NCTM urges teachers to avoid timed tests, as the Hechinger Report notes, while a US federal practice guide recommends brief timed activities and Ofsted says pupils benefit from timed practice of facts that should be easily recalled. The federal guide's conditions are worth copying at home. Timed activities are brief, usually 1 to 5 minutes, they cover "previously learned content", and the aim "isn't to simply generate answers quickly, but instead to generate accurate answers in a short amount of time".

If your child freezes when a timer appears, put it away. Accuracy without a clock is the first goal.

A two-week plan for ten minutes a day

This plan takes one table and gives it two weeks of short, spaced, mixed recall. No research sets a number of minutes for practice at home, so the ten minutes and the day-by-day layout are our suggestion. Shorten it for a younger child.

DayWhat to do
1Sort the table. Ask all twelve facts out of order and make three piles: instant, slow, not yet. Show how one missing fact can be built, such as 7 × 6 from 7 × 5 plus one more 7.
2 to 4Shuffle three or four "not yet" cards with six instant ones. Go through the pile twice. Missed cards go back three places down.
5A cold check: the week's new facts, jumbled, no hints. Whatever is missed stays in next week's pile.
6 and 7Rest. The gap is part of the plan.
8 to 10Add the remaining "not yet" facts, mixed with last week's and a few from an older table. Turn facts around and ask the division.
11No practice.
12Cold check of the whole table, jumbled, with no clock. Note which facts are still slow.
13Only if day 12 went well: one minute on the facts they know. The number right is the score to beat next time.
14The slow facts from day 12 once more. Then leave the table alone for a week and check it again.

The check a week later matters most: it tells you whether the table has really stayed.

Where Plusy fits

We built Plusy's times tables road around the same ideas. After a short stop at the 1 times table, the road follows the order schools teach them, 2, 10, 5, 3, 4, 8, then 6, 7, 9, 11 and 12, and a level introduces only four facts. Each is first picked from four answers and then typed from memory.

After each answer to a basic fact, the whole fact is said aloud. A missed question comes back once later in the same round, with a trick to remember it by: see what Plusy does after a wrong answer. Rounds are not timed. The one timed game, the speed run, opens on a road only after your child has passed a test there, and it asks only facts from the worlds already passed.

Every road, world and game is free. A round uses one heart, and hearts come back on their own. Start free, or carry on with paper cards: the plan above works either way.

Questions

Why does my child forget times tables so quickly?

Usually because the table was practiced in order and in one sitting. Chanting ties each fact to the one before it, so a fact asked alone has no cue. Recalling facts out of order, on several short days, is what makes them last.

What is the best order to learn the times tables?

England's national curriculum teaches the 2, 5 and 10 tables in Year 2, the 3, 4 and 8 tables in Year 3 and the rest up to 12 × 12 by the end of Year 4. That order works at home too, because the 4 and 8 tables double from the 2.

How many minutes a day should we practice times tables?

No research gives a number of minutes for practice at home. Our suggestion is about ten minutes, on most days, stopping while it is still going well. Several short sessions do more than one long one.

Which times tables are the hardest?

The agency that writes England's Year 4 multiplication tables check names the 6, 7, 8, 9 and 12 tables as the most difficult and puts more questions on them. Once the easier tables are known, though, only six facts up to 10 × 10 are truly new.

By what age should a child know their times tables?

In England the national curriculum expects the tables up to 12 × 12 to be memorized by the end of Year 4. In the US, the Common Core standards expect all products of two one-digit numbers to be known from memory by the end of Grade 3. Both describe the end of the school year.

Are timed times tables tests bad for children?

It is argued over. NCTM urges teachers to avoid timed tests, while a US federal practice guide and Ofsted support timed practice of facts already learned. A sensible rule at home is accuracy first, a clock only later, and only against the child's own last score.

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