Times tables 2, 5 and 10 · Code with Martin

Three rows for free

The times tables look like a mountain of numbers. But three rows you get almost for free: two, five and ten.

The 2 row is doubling. 2 × 7 means 7 + 7. You already know how to double.

The 10 row is the easiest of all. 10 × 7 = 70. You just add a zero on the end. 10 × 3 = 30, 10 × 9 = 90.

The 5 row is half of the 10 row. 5 × 7? First 10 × 7 = 70, then half: 35. Also, every result in the five row ends in 5 or 0. That is how you know you did not mix it up.

Today you will go through these three rows so many times that they pour out of your head. That is the goal: not to calculate, but to know. Times tables are like riding a bike — at first you think about every push, then it just goes.

Adam plays a card game with his dad. Who says the result first, takes the card. Dad wins, because he does not calculate the times tables — he knows them. Adam counts 5 × 6 on his fingers and before he finishes, the card is gone. Then dad tells him the trick: “Do not take fives in fives. Take ten and split it. 10 × 6 is 60, half is 30.” Adam tries it on 5 × 8: ten times eight is 80, half 40. For the first time he is faster than dad.

💡

Results in the 5 row always end in 0 or 5. Results in the 10 row always end in 0. If you get 5 × 6 = 32, you know at once it is wrong — it does not end in 0 or 5.

A trick for each row

The 10 row: add a zero. 10 × 4: write four and a zero after it — 40. Why does it work? Ten piles of four is 40, so 4 tens. We will say more about numbers and tens in the lesson on numbers to 1 000.

The 2 row: double. 2 × 8 = 8 + 8 = 16. 2 × 9 = 9 + 9 = 18. The two row is even numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

The 5 row: half of ten. 5 × 8: work out 10 × 8 = 80 and take half: 40. Or go in fives: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 — like counting five-crown coins.

And do not forget swapping from the last lesson: 7 × 5 you can flip to 5 × 7. Whenever there is a two, a five or a ten in your question — in either place — today’s tricks work.

Finally two specials: times 1 leaves the number as it is (1 × 6 = 6). Times 0 always gives zero (0 × 6 = 0) — zero piles is just nothing.

Five through ten

Example: 5 × 8.

Step 1: I work out 10 × 8. I add a zero after eight: 80.

Step 2: I take half of 80. Half of 8 tens is 4 tens: 40.

Check: does the result end in 0 or 5? Yes, 40 ends in zero. It fits.

Once more: 5 × 6. Ten times six is 60, half is 30.

Two is doubling

Example: 2 × 9.

Two piles of nine = 9 + 9.

I count: 9 + 9 = 18.

And the other way: 7 × 2. I swap to 2 × 7, so 7 + 7 = 14.

Notice: every result in the two row is even — it can be split into two equal halves. 18 is even, 14 is even. If a two times gave you an odd number, there is a mistake somewhere.

Ten and a zero on the end

Example: 10 × 7.

I write seven and add a zero: 70.

Why? Ten piles of seven. Ten ones is a ten, so ten sevens is seven tens. And seven tens is written 70.

And 10 × 10: I write 10 and add a zero: 100. A hundred — that is ten tens. The biggest number in the small times tables.

⚠️

Do not mix up times 0 and times 1. 6 × 1 = 6 (one pile of six is six). But 6 × 0 = 0 (six empty piles is still nothing). Zero swallows everything.

Practice: now you do it 🎲

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

Practise the 2, 5 and 10 rows. For fives, go through ten and half.

Practise the questions

On paper

Write the whole rows. A hand remembers better than eyes.

Write the whole 2 row under each other: from 2 × 1 = 2 to 2 × 10 = 20. Then the 5 row and the 10 row.
Circle in your rows every result that ends in zero. Which rows have them?
Work out from memory and write: 5 × 4, 2 × 8, 10 × 6, 5 × 9, 2 × 6, 10 × 3.
Five-crown coins: how many crowns is 7 five-crown coins? And how many is 9 five-crown coins? Write it as multiplying.

Now you 💪

You say 10 × 8, 2 × 7 and 5 × 6 from memory with no counting on fingers.
You can explain the trick “five is half of ten” on the example 5 × 8.
You know which digits the five-row results end in, and you can use that as a check.

✅

Done when: The 2, 5 and 10 rows pour out of your head and you know the trick for counting fives through tens.

What to take from this lesson

The 10 row: add a zero on the end. 10 × 7 = 70.
The 2 row: doubling. 2 × 9 = 9 + 9 = 18. Results are always even.
The 5 row: half of the ten row. 5 × 8 = half of 80 = 40. Endings: 0 or 5.
Times 1 leaves the number as it is, times 0 always gives zero.
The goal with times tables is not to calculate, but to know. Practise until it goes by itself.