Learning the Times Tables — Beyond Rote Chanting, and the Rows That Trip Children Up
In Japan, the times tables are the big event of second-grade math — the term where you sit next to your child every evening listening to them chant.
I assumed at first that this was simply a matter of persistence: you memorise them or you don't. When I looked into it, the national curriculum commentary asks for both — chanting to remember, and building the tables up from their meaning. With only one of the two, children stall at the 6, 7 and 8 rows.
Chanting is right. It's just one wheel
Japan's Ministry of Education, in its commentary on the national curriculum guidelines for elementary mathematics (2017), says that multiplication has the feature that "by memorising the traditional chant of the multiplication tables, handed down in our country from long ago, the result can be obtained easily" (Grade 2, Numbers and Calculation). Chanting is explicitly endorsed.
The same commentary also asks children to construct the tables. While building the 3 row, for instance, a child notices that "when the multiplier goes up by one, the answer goes up by three", and then checks whether that holds for other rows, filling in the table themselves.
Remembering, and constructing. With both in place, a child who forgets a fact can get back to it on their own.
Where it goes wrong
Cause 1: the chant isn't connected to meaning
A child can say the chant for 3 × 4 and still have no link to "3, four times over". When the chant doesn't come, the hand stops. With the meaning in place, they can recover: "I forgot 3 × 4, but 3 × 3 is 9, so add 3."
Cause 2: the later rows are hard to say
In Japanese, the 7 row in particular is full of facts whose chants sound alike and are awkward to say. The facts children get wrong are concentrated in around ten of the 81 — so targeting just those is far more efficient than starting over.
How to progress at home
Step 1: 2 → 5 → 3 → 4, together with the meaning
The 2 and 5 rows have a good rhythm and connect to everyday experience (two at a time, five-cent coins), so start there, then move to 3 and 4. When starting a row, count it out once — "3 × 4 is three, four times: 3, 6, 9, 12" — before chanting. diglabo's worksheets are ordered the same way: Times Tables: 5, 2, 3, and 4 then Times Tables: 6 to 9 and 1.
Step 2: once the chant works in order, break the order
Reciting a row in order is really remembering a song: each sound pulls up the next. Tests ask one random fact at a time. Only when your child can answer shuffled cards one by one do they have times tables they can actually use.
Step 3: make a personal list of the ones they get wrong
Write down the facts missed on the shuffled cards and the list usually comes to fewer than ten. Don't make them relearn everything. Three minutes a day on that list alone is lighter and gets there faster.
Step 4: finish by using them backwards
"Which facts make 24?" (3 × 8, 4 × 6, 6 × 4, 8 × 3.) Working backwards is direct preparation for Division in grade 3. Looking at the table while doing it is fine.
How to practise
- Times Tables: 5, 2, 3, and 4, one sheet a day. Different number variations of the same content let you repeat the same range on a bad day
- Times Tables: 6 to 9 and 1, one row at a time. Plan on a week for the 7 row
- Finish with Multiplication Word Problems. Once "which situations use multiplication" has landed, grade 3 is well prepared
Frequently asked questions
Q. Is it enough to learn them from a song or an app?
A. As a way in, they're excellent. But a song is memory in order, so the bridge to random recall still has to be built separately. After the song, add card practice one fact at a time.
Q. How fast should they be?
A. Around two seconds per fact. Division and column arithmetic in grade 3 assume the tables come without thinking. That said, timing every session pressures some children — once a week is plenty.
Times tables are one of the topics where time spent comes back most directly. Even if a row is stuck now, a few minutes a day on that row alone will get there. There's no need to start over.
This article is written by a parent who builds diglabo. I am not a teacher or an education specialist. The general guidance here is based on how the topic is taught in Japanese primary schools, checked against Japan's national curriculum guidelines.
diglabo's worksheets follow the Japanese curriculum. What that means if you are outside Japan