P3's 6-9 Times Tables and the Split-It-Up Trick

Every hero has an origin. This one begins on the top bunk of a bedroom, with a bath towel for a cape and a desk fan for the wind. The Mastermind needs a superpower, and he has chosen one: "Five questions. Every day." The Partner, standing in the doorway with a juice box that now wears a paper SIDEKICK badge, is not convinced. "...Five?"

That is The Origin Story, the third episode of our comedy series, The Mastermind. Watch it first (it is under a minute), then read on. The hero's secret is a Primary 3 times table.

The Origin Story: five a day. Nobody has to know.

After a training montage of times-table cards, the hero's own comic book, Captain Five, Issue #1, opens on a splash page: 7 capes, 8 stars on each. How many stars? Captain Five does not count 56 stars one by one. He splits the problem in two: 5 eights are 40, 2 eights are 16, and 40 + 16 = 56. The Partner is unmoved: "So your superpower is the multiplication table." The answer comes in a whisper: "Shh. Secret identity."

The good news is that this superpower can be taught.

Why the 6, 7, 8 and 9 times tables feel harder

In Primary 2, children learn the multiplication tables of 2, 3, 4, 5 and 10. In Primary 3, the tables of 6, 7, 8 and 9 arrive, and with them the facts many children find hardest to remember, such as 7 × 8 and 6 × 9.

A few things make these tables feel harder:

The patterns are harder to see. The 2s are all even, the 5s end in 5 or 0, and the 10s end in 0. The 7s have no pattern a child can spot at a glance.
The answers are bigger. Products now go up to 90, so a wrong guess is harder to notice.
Counting up from the start is slow. Chanting "8, 16, 24 ..." to reach 7 eights takes seven steps, and every step is a chance to slip.

Here is the reassuring part: your child already knows most of these facts. Every multiplication fact can be turned around: 6 × 4 and 4 × 6 have the same answer, 24, and your child already knows it from the table of 4. Times 1 gives the number itself, and times 10 is familiar from P2. Take those away and only ten facts in the tables of 6, 7, 8 and 9 are new: 6 × 6, 6 × 7, 6 × 8, 6 × 9, 7 × 7, 7 × 8, 7 × 9, 8 × 8, 8 × 9 and 9 × 9, along with their turn-arounds. The split-it-up trick is how your child reaches those ten from facts they already know.

The split-it-up trick

The trick is simple: when a fact is new, split it into facts your child already knows, then put the answers back together.

Worked example: 7 capes, 8 stars on each

Step 1: Say what the multiplication means. 7 capes with 8 stars on each is 7 groups of 8, or 7 eights. We write it as 7 × 8.

Step 2: Split the groups into friendly ones. 7 eights is 5 eights and 2 eights. Count the groups to check the split: 5 + 2 = 7.

Step 3: Work out each part with a known fact.

Part	What to think	Answer
5 eights	`5 × 8 = 40` (half of 10 eights, which is 80)	40
2 eights	`2 × 8 = 16` (double 8)	16

Step 4: Put the parts back together. 40 + 16 = 56. There are 56 stars.

Step 5: Check with a different split. 7 eights is also 4 eights and 3 eights: 4 × 8 = 32, 3 × 8 = 24, and 32 + 24 = 56. Same answer.

Picture it first

If the numbers alone feel slippery, draw the stars. Make 7 rows with 8 dots in each row, then draw a line under the fifth row. Above the line are 5 rows of 8, which is 40. Below it are 2 rows of 8, which is 16. No dots were lost or added; the line only splits the picture into two pieces your child can count quickly. Objects first, then a drawing, then the number sentence: this is the concrete, pictorial, abstract order of Singapore math teaching.

A split for each table

Splitting off 5 groups works well because the 5s are easy: 5 groups is always half of 10 groups. What is left is a small piece of 1, 2 or 3 groups.

Table	Split	Example
6	5 groups and 1 more group	`6 × 7`: `5 × 7 = 35`, `1 × 7 = 7`, `35 + 7 = 42`
7	5 groups and 2 more groups	`7 × 8`: `5 × 8 = 40`, `2 × 8 = 16`, `40 + 16 = 56`
8	5 groups and 3 more groups	`8 × 4`: `5 × 4 = 20`, `3 × 4 = 12`, `20 + 12 = 32`

The 9s use the same idea from the other side: go one group too far, to the easy 10 groups, then take one group back. The fourth montage card in the episode, 6 × 9, works with the 6s split: 5 nines and 1 nine, 45 + 9 = 54. Some children prefer other splits, such as doubling 4 groups for the 8s. Any split is fine, as long as your child has a method to fall back on when a fact will not come to mind.

Common slips

Losing a part. Your child works out 5 eights is 40 and stops there. Ask, "How many groups have you used? How many do you need?"
Adding the numbers in the split instead of the answers. 5 eights and 2 eights is 40 and 16, not 5 and 2. Saying the words "5 eights" aloud keeps the meaning attached.
Rushing for speed. Fast recall comes later and comes from practice. In P3, an accurate method your child understands is worth more than a quick guess.

Five ways to practise at home

You do not need worksheets for this. Paper, a pencil and five minutes are enough.

Star rows. Draw rows of stars or dots, such as 6 rows of 7. Ask your child to draw one line that splits the rows into two groups they know, then add the two answers.
Split it two ways. Pick one fact, say 7 × 7, and ask for two different splits: 5 sevens and 2 sevens (35 + 14 = 49), or 4 sevens and 3 sevens (28 + 21 = 49). Getting the same answer twice is very convincing.
Training cards. Like Captain Five's montage, write five facts on cards, such as 6 × 7, 9 × 3, 8 × 4, 6 × 9 and 7 × 8. Your child shouts a comic sound ("POW!") for each one they solve, then tells you how they split it.
Turn-around hunt. Show a fact such as 6 × 4 and ask, "Which table do you already know this from?" Spotting that 6 × 4 and 4 × 6 give the same answer, 24, which your child knows from the table of 4, takes the fear out of a new-looking fact.
Groups around the house. Ask real questions with equal groups. How many days are there in 6 weeks? That is 6 sevens: 5 sevens and 1 seven, 35 + 7 = 42 days.

Keep each session short and stop while your child still wants to play. When your child is stuck, ask "Which part do you already know?" before showing a split, and praise the method rather than the speed.

If you would like more Primary 3 examples, our guide to Primary 3 sample questions explained shows another question worked as rows and groups.

Five calm questions a day

In the episode, Captain Five's superpower is five questions every day, and his training counter goes Day 1, Day 7, Day 30. It only ever goes up. Times tables work the same way: a few facts, met often and worked out with a method your child trusts, slowly become facts your child simply knows.

That is the idea we built Singapore Math Drills around:

Daily Five drills: five hand-picked drill cards are waiting each day, so your child never has to decide what to practise.
Streaks and mastery stars: steady progress markers that reward turning up and getting things right, never speed.
Calm by design: no guilt-tripping over a missed streak and no dark patterns. Your child's progress is only ever measured against their own.

Captain Five keeps his superpower behind a secret identity. Your child's can stay just as quiet: five a day. Nobody has to know.

Try it free

Try a free interactive Primary 3 worksheet and see how calm practice feels, with no signup or credit card required.

Try the free Primary 3 sample worksheet