P3 Times Tables 6 to 9 and Division with Remainder

A winding trail of stepping stones crosses a stream. Four sign posts pop up beside it, "6", "7", "8" and "9", and a little boot-print steps onto the first stone. "Four new tables on the trail. 6, 7, 8 and 9."

That is Times-Table Trail, a 30-second Primary 3 episode of our Topic Explainers series. It is made for your child to watch, with short lines on screen and no voice-over. Watch it together first, then read on for the method behind each stretch of the trail.

Times-Table Trail: hop along, one table at a time.

The trail has four stretches, one for each new table. On every stretch, four stones light up one at a time: 6, 12, 18, 24 for the 6s, then 7, 14, 21, 28, then 8, 16, 24, 32, then 9, 18, 27, 36. Then the trail ends at a boat. There are 29 stones to carry across, and the boat takes 6 at a time. How many full trips, and how many are left?

Both ideas come from Primary 3 Multiplication and Division in the Singapore syllabus: the tables of 6, 7, 8 and 9, which are new at P3, and division with remainder.

The method

Each stone is one more group

A times table is a count in equal jumps. On the 7 trail, every stone is 7 more than the one before it: 7, 14, 21, 28. The fourth stone is 28 because four sevens make 28.

The video writes that fourth stone as 7 × 4 = 28, a way of reading it as 7, four times. In our app we read 4 × 7 as 4 groups of 7. Either order gives 28, so 4 sevens and 7 fours are both 28. That is worth saying aloud to your child once, because it halves the number of facts to learn: if they know 4 × 7, they also know 7 × 4.

So when a fact will not come, your child can count along the trail: start at the first stone and add the same number each time, keeping track of how many stones they have stepped on.

The 9s have a pattern

The 9 trail comes with a note in the video: "Tens go up, ones go down." Look at 9, 18, 27, 36. The tens digits go 0, 1, 2, 3, and the ones digits go 9, 8, 7, 6. Each time we add 9, we are really adding 10 and taking 1 away, so the tens digit goes up by one and the ones digit goes down by one.

Division with remainder: share in full groups, then look at what is left

Dividing 29 stones into boat trips of 6 asks: how many full groups of 6 fit into 29? We count along the 6 trail until the next stone would go past 29. 6, 12, 18, 24 fit. The next stone, 30, is too far. So 4 full trips fit, carrying 24 stones, and 29 − 24 = 5 stones are left over.

We write it as 29 ÷ 6 = 4 r 5, where "r" stands for remainder.

Worked examples

Every number below is from the video, except where Example 2 carries the 9 trail on past 36, and the try-at-home questions at the end.

Example 1: Count along the 8 trail

What is the fourth stone on the 8 trail?

Step 1: Start at the first stone. The first stone is 8.

Step 2: Add 8 at each stone. 8 + 8 = 16, 16 + 8 = 24, 24 + 8 = 32.

Step 3: Count the stones. 8, 16, 24, 32 is four stones, so four eights make 32. The video shows it as 8 × 4 = 32.

Notice that 24 is on two trails. It is the fourth stone on the 6 trail and the third stone on the 8 trail, because four sixes and three eights both make 24. Spotting a number that lives on two trails is a good way to link the tables together.

Example 2: Use the 9s pattern

Carry on the 9 trail. What are the next three stones after 36?

Step 1: Tens go up. The tens digit of 36 is 3, so the next tens digits are 4, 5 and 6.

Step 2: Ones go down. The ones digit of 36 is 6, so the next ones digits are 5, 4 and 3.

Step 3: Put them together. The next three stones are 45, 54 and 63.

Check: add 9 each time. 36 + 9 = 45, 45 + 9 = 54, 54 + 9 = 63. The pattern and the adding agree.

There is a second check hiding in the 9 table: from 9 × 1 up to 9 × 10, the two digits always add up to 9. For 63, 6 + 3 = 9. For 54, 5 + 4 = 9. If the digits do not add up to 9, something has slipped.

Example 3: The boat crossing

29 stones. A boat carries 6 at a time. How many full trips? How many are left?

Step 1: Name the question. Putting stones into equal boatloads is division: 29 ÷ 6.

Step 2: Count along the 6 trail. 6, 12, 18, 24. The next stone is 30, which is more than 29, so we stop at 24. That is 4 full trips.

Step 3: Find what is left. 29 − 24 = 5. There are 5 stones left over.

Answer: 29 ÷ 6 = 4 r 5. The boat makes 4 full trips, and 5 stones are left.

Check: 4 × 6 = 24 and 24 + 5 = 29. The remainder, 5, is less than 6, so there are not enough stones left for another full boatload. The video's working line, 6 × 4 = 24, 29 − 24 = 5, says the same thing.

Try these at home

If every stone must reach the far bank, how many trips does the boat need?

The 4 full trips carry 24 stones, and 5 stones are still on the near bank. One more trip carries those 5, so the boat needs 5 trips. The answer to 29 ÷ 6 is still 4 r 5. The question decides what we do with the remainder.

There are 30 stones, and a bigger boat carries 8 at a time. How many full trips, and how many are left?

Count along the 8 trail: 8, 16, 24. The next stone, 32, is too far. So there are 3 full trips carrying 24 stones, and 30 − 24 = 6 are left: 30 ÷ 8 = 3 r 6. The remainder 6 is less than 8, so the answer checks out.

Common mistakes

Losing count of the stones. When counting along, children often know they have reached 28 but not how many sevens that was. Ask your child to hold up a finger for each stone.
Stopping one stone too early or too late. For 29 ÷ 6, some children stop at 18 (3 trips, 11 left), or go on to 30. Ask, "Is there enough left for one more full boat? Did we go past 29?"
A remainder that is too big. Writing 29 ÷ 6 = 3 r 11. If the remainder is 6 or more, another full group still fits.
Forgetting the remainder. Writing just "4". The 5 left over is part of the answer, and the question asked for it.
Mixing up the 9s pattern. Writing 9, 18, 27, 38 by adding 1 to both digits. The tens go up, but the ones go down.
Thinking 7 × 4 and 4 × 7 are different answers. They are different groupings, but they always give the same number.

Parent tips

Make a trail on the floor. Lay out sheets of paper as stepping stones and write a table on them, one stone at a time. Your child hops along and says each number as they land. Then turn the papers over and hop again from memory.
Start from a stone they know. If 7 × 6 is hard, start at the fifth stone, 35, which comes from the friendlier 5s, and hop one more: 42.
Play boat trips. Use dried beans, buttons or Lego bricks. Pick a number up to about 50 and a boat size from 6 to 9, then fill the boats together and count what is left on the bank.
Ask what happens to the leftovers. Change the story: stones on a boat, children in cars, cupcakes in boxes. Sometimes the remainder needs one more trip, and sometimes it is simply left over. Talking about it builds real understanding of remainders.
One table at a time. Spend a few days on one stretch before moving on, and come back to the earlier tables often. Little and often works better than one long session.

If your child finds the 7s and 8s slippery, our post on the split-it-up trick for the 6 to 9 times tables shows how to build any new fact from two easier ones. For more Primary 3 question types, see Primary 3 sample questions explained.

How Singapore Math Drills supports the habit

After the boat crossing, the video shows a worked-solution page with rows that open one at a time. "Every question has a worked solution. Open a hint when you want a step."

Progressive hints and worked solutions: every question can be opened up step by step, so your child can take one hint and then carry on alone, and every question has a full worked solution to read afterwards.
Calm by design: no guilt-tripping over a missed day and no dark patterns, and your child's progress is only ever measured against their own.

Times tables settle in through short, steady practice, not long drills. Hop along, one table at a time.

Try a sample

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

Try a free Singapore math sample