How to Learn Times Tables: Say Them, Write Them, Use Them

In England, the national curriculum asks children in Year 2 to recall the 2, 5 and 10 times tables, in Year 3 the 3, 4 and 8 tables, and by the end of Year 4 to have “memorised their multiplication tables up to and including the 12 multiplication table” (Department for Education, mathematics programmes of study). In Japan, the tables stop at 9 × 9 and are taught in the second year of primary school. The official course of study asks that children know the tables and can do single-digit multiplication “reliably” (MEXT, Course of Study for Elementary Schools, 2017, in Japanese).

Different countries, different upper limits, but the same goal: a child who sees 7 × 8 should not calculate it. They should simply remember 56. Everything that comes later, long multiplication, division, fractions, leans on that.

I think the tables are best learned in three stages, in this order: say them, write them, use them. This post goes through each stage and the places where children usually get stuck. It is written for parents whose children are just starting.

There are fewer facts than it looks

A 12 × 12 grid holds 144 facts. That sounds like a lot, but the real number is much smaller.

First, 3 × 7 and 7 × 3 are the same fact. Multiplication does not care about order, so the 144 shrink to 78. Then several tables follow simple patterns. The 1 times table gives back the number you started with. The 2s go up by two. The 5s end in 5 and 0 in turn. The 10s add a zero. In the 9s, up to 9 × 10, the two digits of each answer add up to 9 (18, 27, 36 and so on).

Inside the 10 × 10 core, once a child has the 1s, 2s, 5s, 9s and 10s, what remains are the combinations of 3, 4, 6, 7 and 8 with each other. Counting each pair once, that is only fifteen facts: 3×3, 3×4, 3×6, 3×7, 3×8, 4×4, 4×6, 4×7, 4×8, 6×6, 6×7, 6×8, 7×7, 7×8 and 8×8. In my view, most of the real struggle happens inside this list. It helps parents to know this before they start.

Stage 1: say them

Most countries learn the tables by saying them aloud, and some have turned this into a chant. Japan’s version is called kuku (nine-nine). Each fact is a short, rhythmic phrase: ni-nin-ga-shi (2 × 2 = 4), sa-zan-ga-ku (3 × 3 = 9), shichi-shichi-shijūku (7 × 7 = 49), ku-ku-hachijūichi (9 × 9 = 81). A small rule is built in: when the answer has one digit, the syllable ga is added. Chinese children learn a similar chant, chéngfǎ kǒujué, with lines like 三七二十一 (three sevens, twenty-one).

The chant is a clever device. Once the rhythm is in the body, the answer comes out without thought. The child is not calculating, only remembering, and that is exactly the state we want.

Start one table at a time, from the top. Then say it backwards. When a child can do both, they are ready for the next stage.

Saying has one weakness. A child who has only chanted in order will often answer “what is 7 × 6?” by running through the table from 7 × 1. The facts are stored as a sequence, so they cannot yet be pulled out from the middle. This is not failure. It is simply an unfinished stage.

Stage 2: write them

Writing gives two things that saying does not.

The first is precision. When facts live only as sound, similar ones blur. 7 × 8 = 56 and 6 × 9 = 54 sit close together. On paper, the child has to commit to one number, and the shaky facts show up.

The second is shape. Draw an empty grid and let the child fill in the answers. When it is full, they can see that the numbers mirror each other across the diagonal, which is the swap rule made visible. They can see the 5 and 0 column, and in the 9s column the tens digit going up as the ones digit goes down.

For daily practice, writing only the answer is enough. Copying the whole sum takes time and wears children out.

Stage 3: use them

The last stage is to cut the facts loose from their order.

First, mix the questions. A child who can recite the 7s will stumble on 7 × 4, then 7 × 9, then 7 × 2. When those answers come quickly, the table has become knowledge you can reach into, not a song you must sing from the start. Shuffled cards or a parent asking at random both work.

Then use the facts in situations that mean something. “There are 4 bags with 6 sweets in each. How many sweets?” The child has to decide which number is the size of a group and which is the number of groups. This is where the chant meets the idea of equal groups.

Use them backwards too. What goes in the box in □ × 6 = 42? That is division. A child who can retrieve facts out of order finds division much easier.

Where children get stuck

The 6s, 7s and 8s. Of the fifteen facts above, 6×7, 6×8, 7×7, 7×8 and 8×8 tend to hang on longest, because they have no friendly pattern. The best help is the swap rule. If a child learns the tables in order up to 6 before starting the 7s, then 7 × 1 to 7 × 6 are facts they already know the other way round. Only 7 × 7, 7 × 8 and 7 × 9 are new (more if your curriculum goes to 12). Showing a child how short that list is makes a real difference.

Chants fine, answers wrong. The facts are still stored as a sequence. More writing and more shuffled practice help.

Unsure what multiplication means. If a child can recite the tables but freezes on word problems, go back before the tables. Lay out counters in 4 rows of 3 and count them. The rows and columns are the same shape as the grid.

Timing too early. Speed matters, but it is the last step. Push for speed while facts are shaky and you get guessing. Right first, fast later.

Where MathCal fits

MathCal is a math drill app I make, where children write their answers on the screen by hand. I think it suits the writing and using stages.

In the Basic Calculation Drill, turn on No Addition, No Subtraction and No Division, and only multiplication questions remain. The two numbers are picked at random from 1 to 9, so the questions come shuffled, not table by table. Note that the drill covers the 9 × 9 range only, so the 11s and 12s are not included. Children write each answer with a finger. You can set the Number of Questions to one of ten options between 10 and 300, and results are recorded in seconds per question, with a Score Trend chart to follow the change over time. I would look at the speed only after the answers are reliably right.

To go back to the meaning of multiplication, there is a Multiplication Beads lesson. For what comes after the tables, there is the Column Arithmetic Drill (Multiplication).

Today’s Drill, Today’s Challenge and Today’s Lesson on the home screen are free every day. Choosing any drill or lesson from the full lists requires a one-time purchase.

For how MathCal compares with paper workbooks and other apps, see MathCal vs Other Ways to Practice Mental Math. For daily routines, see Ideas for Getting More out of MathCal.

A child who can chant the tables has done half the work. Writing them and using them is the other half, and it is worth the patience.