Times tables 6 and 7 · Kode bersama Martin

Six and seven: the hardest hill

The 6 and 7 rows are the hardest part of the times tables. It is not your fault — they are hard for everyone. They do not have such a nice rhythm as five, and they are not doubles like four.

But we have weapons for them.

Six is five and one extra pile. 6 × 7? Work out 5 × 7 = 35 and add seven: 42. You already know five through half of ten, so six is just one extra step.

Seven is the trickiest — but you already know almost all of it! 7 × 2 you know from two. 7 × 5 from five. 7 × 3 and 7 × 4 from the last lesson. What is left to learn is really just 7 × 6, 7 × 7, 7 × 8 and 7 × 9. Four facts. That is doable.

Today we climb that hill. At the top the view is nice: whoever knows six and seven knows almost the whole times tables.

Jonáš is stacking football cards into packs of seven. He has six packs and a friend asks how many cards that is altogether. Jonáš tries adding in sevens and at the fourth seven he gets lost. Then he remembers the five trick: five packs of seven is 35. And the sixth pack adds another 7. “35 and 7… 42!” The friend does not believe it, so they count again card by card. It comes to 42. From then on Jonáš calls six “five with a bonus”.

💡

For 7 × 8 there is a famous helper: 5, 6, 7, 8. Read it as 56 = 7 × 8. Four numbers in a row — half is the result, half is the question.

Six through five, seven in pieces

Bridge for six: five + one pile.

Example 6 × 8:

Five piles: 5 × 8 = 40 (half of 10 × 8 = 80).
The sixth pile: 40 + 8 = 48.

Done: 6 × 8 = 48.

Seven: first swap, then finish the rest.

When you see 7 × 4, swap to 4 × 7 and use the four bridge (double twice: 14, 28). When you see 7 × 5, swap to 5 × 7 (half of 70 = 35).

Four hard facts are left, which you just learn by heart:

7 × 6 = 42 (or through the six bridge: 5 × 6 = 30, plus two sixes… wait, it is easier to swap to 6 × 7 = 35 + 7).
7 × 7 = 49.
7 × 8 = 56 (helper 5, 6, 7, 8).
7 × 9 = 63 (we will keep that for the next lesson with nine too).

Write those four facts on a card and carry it in your pocket today. Four numbers you will learn faster than you think.

Six through five

Example: 6 × 7.

Step 1: five piles of seven: 5 × 7. Through ten: 10 × 7 = 70, half is 35.

Step 2: the sixth pile: 35 + 7 = 42.

So 6 × 7 = 42.

Check: 42 is even — and that fits, because six piles of anything can be split into two equal halves (3 + 3 piles).

Seven by swapping

Example: 7 × 3.

Step 1: I swap: 3 × 7. Three piles of seven.

Step 2: the three bridge: 2 × 7 = 14, plus seven: 14 + 7 = 21.

One more: 7 × 4.

Step 1: I swap: 4 × 7.

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

You almost never count seven “in sevens” — always swap it onto a row you already know.

Four hard facts

Learn these four like a phone number:

7 × 6 = 42
7 × 7 = 49
7 × 8 = 56 (helper: 5, 6, 7, 8)
7 × 9 = 63

Test right now: cover the lines with your hand and answer. How much is 7 × 8? Uncover and check. How much is 7 × 7? Again. Two minutes of covering like that is worth half an hour of reading.

⚠️

The most common mix-up in the whole times tables: 7 × 8 = 56, not 54. And 6 × 9 = 54, not 56. If you are not sure, remember the helper 5, 6, 7, 8 — that belongs to seven times eight.

Practice: now you do it 🎲

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

Sixes and sevens. Take six through five, swap seven.

Practise the questions

On paper

Make yourself cards — the best helper for hard facts.

Cut out four cards. On one side write the question (7 × 6, 7 × 7, 7 × 8, 7 × 9), on the other the result. Test yourself three times.
Work out through the “five + a pile” bridge and write both steps: 6 × 4, 6 × 7, 6 × 9.
Work out by swapping: 7 × 2, 7 × 5, 7 × 10. For each one write which row you swapped to.
Fill the boxes: 6 × ☐ = 36, 7 × ☐ = 56, ☐ × 6 = 42.

Now you 💪

You say 7 × 8 from memory and do not mix it up with 6 × 9.
You can work out 6 × 8 through five (40 + 8) and explain the method.
Of the four hard facts (42, 49, 56, 63) you hit at least three without thinking.

✅

Done when: You count six through five, you swap seven onto known rows, and you have the four hard facts on cards.

What to take from this lesson

Six = five + one pile: 6 × 8 = 40 + 8 = 48.
Swap seven onto a row you already know: 7 × 4 = 4 × 7.
Four facts by heart: 7 × 6 = 42, 7 × 7 = 49, 7 × 8 = 56, 7 × 9 = 63.
Helper 5, 6, 7, 8: fifty-six is seven times eight.
Cards with the question on the front and the answer on the back are the fastest practice.