Times tables 3 and 4 · Martinとコード

Threes and fours through two

You already know two. And both three and four can be built on two.

Four is two times two. 4 × 6? Work out 2 × 6 = 12 and double: 24. That is called “double twice”: you double the number and then double the result once more.

Three is two and one extra pile. 3 × 6? Work out 2 × 6 = 12 and add one more six: 18.

You only need these bridges at the start. The goal is still the same: after a few days of practice you say 3 × 6 = 18 straight away, with no thinking. Bridges are scaffolding — once the building stands, the scaffolding goes.

Today you will go through both rows forwards and backwards. And watch: the three row has a nice rhythm: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. Try saying it out loud like a rhyme.

Tereza helps in the school canteen getting snacks ready. Four rolls belong on each tray and there are three trays. The cook asks how many rolls to bring. Tereza remembers two: two trays of four is 8. And the third tray another 4, so 12. “Twelve!” she says before the cook reaches the roll basket. From then on she always counts trays the same way: first two, then add the third. After a week she does not count — she just knows that 3 × 4 is 12.

💡

Say the three row out loud in threes like a rhyme: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. The rhythm remembers itself — like a verse of a song.

Two bridges: double twice and add a pile

Bridge for four: double twice.

Example 4 × 7:

Double seven: 7 + 7 = 14.
Double the result: 14 + 14 = 28.

Done: 4 × 7 = 28. It works because 4 piles are 2 and 2 — twice two piles.

Bridge for three: two plus one pile.

Example 3 × 8:

Work out 2 × 8 = 16.
Add one more eight: 16 + 8 = 24.

Done: 3 × 8 = 24. Three piles = two piles + one.

And swapping still holds: 8 × 3 you flip to 3 × 8. Whenever you see a three or a four, the bridges work.

How do you know you no longer need the bridge? When you say the result in two seconds. Until then, counting through two is an honest path — much better than guessing. A guessed result can stick in your head even when it is wrong. A counted one is always right.

Four: double twice

Example: 4 × 6.

Step 1: I double six: 6 + 6 = 12.

Step 2: I double twelve: 12 + 12 = 24.

Result: 4 × 6 = 24.

Check through piles: 6 + 6 + 6 + 6. The first two sixes = 12, the second two = 12, together 24. It fits. Double twice is just a faster write-up of the same thing.

Three: two and one extra pile

Example: 3 × 6.

Step 1: two piles: 2 × 6 = 12.

Step 2: the third pile: 12 + 6 = 18.

One more: 3 × 9.

Step 1: 2 × 9 = 18.

Step 2: 18 + 9 = 27.

Notice that adding nine is easy when you go through ten: 18 + 9 is 18 + 10 − 1 = 27.

Swap and use the bridge

Example: 7 × 4. Seven piles of four — that would be long adding.

Step 1: I swap: 4 × 7. Four piles of seven.

Step 2: double twice: 7 + 7 = 14, then 14 + 14 = 28.

So 7 × 4 = 28. Swapping + a bridge = almost every question in the three and four rows you can solve through two, which you already know.

⚠️

On the “double twice” bridge, do not forget the second doubling. A common mistake: 4 × 6, a child works out 6 + 6 = 12 and writes 12. But that is only 2 × 6. Four wants you to double once more: 24.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. スタート with ten. When it goes well, add more.

Threes and fours. If you do not know, go through two: double, or double twice.

Practise the questions

On paper

Write the whole methods, not just the results. The method is what you are practising.

Write the whole 3 row (3, 6, 9, … up to 30) and the whole 4 row (4, 8, 12, … up to 40). Say them out loud as you write.
Work out through the “double twice” bridge and write both steps: 4 × 5, 4 × 8, 4 × 9.
Work out through the “two + a pile” bridge and write both steps: 3 × 5, 3 × 7, 3 × 9.
Quiz the other way: which number belongs in the box? 3 × ☐ = 21, 4 × ☐ = 32, ☐ × 3 = 15.

Now you 💪

You can work out 4 × 7 with the “double twice” bridge and explain why it works.
You can work out 3 × 8 as 2 × 8 + 8.
You can say the three row in threes from 3 to 30 without getting stuck.

✅

Done when: You can do the 3 and 4 rows through the bridges from two, and you already say the most common facts from memory.

What to take from this lesson

Four = double twice: 4 × 7 → 14 → 28.
Three = two + one pile: 3 × 8 = 16 + 8 = 24.
Swapping numbers lets you use the bridge both ways: 7 × 4 = 4 × 7.
Bridges are scaffolding. Once you know the results by heart, you will stop needing them.
Counting it out is always better than guessing — a guessed mistake sticks too.