Four equal heaps

Liri had discovered four little star clusters. In each cluster, exactly two stars were shining.

Liri: “I’ll count: 2 + 2 + 2 + 2 = 8. But that took for ever.”
Erklärus: “Because you added the same thing four times. There’s a shortcut for that: 4 times 2 stars, in short 4 × 2 = 8.”
Liri: “Four times two… that’s much quicker to write down!”

🥚 From plus to times – repeated addition

Four space capsules land, and in each of them sit 2 little robots.

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2 + 2 + 2 + 2 = 8   is the same as   4 × 2 = 8

3 × 5 =

⚫ The dot array – key facts

You can also lay out a multiplication as rows of dots: 3 rows of 5 dots each.

3 × 5 = 15

The easiest ones are the key facts: those with 1, 2, 5 and 10. You can work out all the others from them!

Erklärus: “You don’t know 6 × 7 by heart yet? No problem: 6 × 7 is the same as 5 × 7 + 1 × 7. So 35 + 7 = 42.”
Now you: work out 6 × 8. First 5 × 8 = , then + 1 × 8. Answer:

🔢 The times tables – the foundation of all multiplication

Before you multiply big numbers, you need to know the small times tables. Click on a cell – and see how the product comes about:

← Click on a number in the times table!
Erklärus: “The times tables aren’t magic – they are structure. If you know them, you can split any multiplication into small steps.”
🌌 Multiplying in the universe

A constellation made of 3 rows of 4 stars each has 3 × 4 = 12 stars altogether.
A lunar lander carries 2 astronauts. 5 landers together carry 2 × 5 = 10 astronauts.
Key facts with 10 are especially easy: 7 × 10 = 70 – just add a zero!

❌ Common mistake

Multiplication is often mixed up with addition: 4 × 2 is NOT 4 + 2 = 6, but “4 times the 2”, so 2+2+2+2 = 8.

Tip: say the problem out loud as “… times” – that helps you feel the difference.

✖️ Exercise 1 – Repeated addition
3 rockets launch with 4 engines each. How many engines is that altogether? (3 × 4)
⚫ Exercise 2 – Key fact
A star field has 5 rows of 9 stars each. How many stars altogether? (5 × 9)
🚀 Exercise 3 – Working it out
Work out 7 × 6: first 5 × 6 = 30, then add 2 × 6 = 12. How much is 7 × 6 altogether?

The shortcut

Liri no longer had to count long chains of additions. One glance at the rows was enough.

Liri: “Multiplication is like a shortcut through space.”
Erklärus: “Exactly. And the key facts with 1, 2, 5 and 10 are your signposts along the way.”

A shortcut through space – exactly what Liri liked best to draw on her star map.

“Multiplication: repeated addition, written in short with ·. Remember the key facts (1, 2, 5, 10) and work out everything else from them – e.g. 6×7 = 5×7 + 1×7.”
What you learned today
4 × 2 = 2+2+2+2 = 8
Key facts: 1, 2, 5, 10  ·  Work out everything else
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Chapter 9 mastered!

Liri now understands what multiplication really means – and how to work it out cleverly.

Erklärus’s notebook – page 9:
“Multiplication: repeated addition, e.g. 4×2 = 2+2+2+2 = 8. Key facts with 1, 2, 5, 10 are easy. Work out harder ones from them: 6×7 = 5×7 + 1×7 = 35+7 = 42.”
← Back to overview 9 – Multiplication, Part 1