Times is adding piles · Code with Martin

Three piles of four

You can add. So you can almost multiply already.

When you have three piles of stickers and each pile has four, you can count 4 + 4 + 4. That makes 12. You can write it shorter: 3 × 4 = 12. You say it “three times four” and it means exactly this: add four, three times.

The sign × is called times. The number before it says how many piles you have. The number after it says how many are in one pile.

So multiplying is a shortcut for adding the same number again and again. Nothing more. If you are not sure, you can always go back to adding and count it the old way.

In this level you will learn the whole times tables, division, written methods and units. Today we start with the most important bit: what times actually means.

Ema is putting stickers into an album. Four fit on each page. She has filled three pages and wants to know how many stickers she has. She starts counting one by one: one, two, three… at ten she mixes it up and has to start again. Her brother looks and says: “Three pages of four. Three times four. Twelve.” It took him two seconds. Ema wants that trick too. Good news: it is not a trick, it is multiplying. And you can learn it.

💡

The word of is a times signal. “Three pages of four stickers” = 3 × 4. When you see “of” in a word problem, you will almost surely multiply.

How to turn adding into multiplying

The method has three steps.

Step 1: find the same numbers. Multiplying only works when you keep adding the same number. 4 + 4 + 4 yes. 4 + 5 + 3 no — that you have to add normally.

Step 2: count how many times the number is there. In 4 + 4 + 4, four is there three times.

Step 3: write it with times. How many times × which number: 3 × 4.

It works the other way too. When you see 5 × 2, read it as “five piles of two” and write it out: 2 + 2 + 2 + 2 + 2 = 10.

And now one important thing: the order of the numbers does not matter. 3 × 4 is 12 and 4 × 3 is 12 too. Three piles of four have the same stickers as four piles of three. You can pick whichever is easier to count. That is called swapping the factors — you can swap the numbers in a times and the result stays the same.

From adding to multiplying

Write-up: 4 + 4 + 4.

Step 1: are the numbers the same? Yes, all fours.

Step 2: how many times? Three times.

Step 3: I write 3 × 4.

I get the result by adding: 4 + 4 = 8, 8 + 4 = 12. So 3 × 4 = 12. Both write-ups say the same thing. The one with times is just shorter.

From multiplying to adding

Write-up: 5 × 2. I read: five piles of two.

I write it out as adding: 2 + 2 + 2 + 2 + 2.

I add step by step: 2 + 2 = 4, 4 + 2 = 6, 6 + 2 = 8, 8 + 2 = 10.

So 5 × 2 = 10. Once you know the times tables by heart, you will not write them out. But whenever you are not sure, this is the emergency brake.

Swapping the numbers

I need to work out 6 × 3 — six piles of three: 3 + 3 + 3 + 3 + 3 + 3. That is long.

I swap the numbers: 3 × 6 — three piles of six: 6 + 6 + 6.

I count: 6 + 6 = 12, 12 + 6 = 18.

So 6 × 3 = 18 and 3 × 6 = 18. Less adding, same result. Always pick the shorter path.

⚠️

Times is not plus. 3 × 4 is not 3 + 4. Seven and twelve are completely different numbers. If you are not sure what the sign means, write the question out as piles. Piles do not lie.

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.

Small multiplying. If you get stuck, write the question out as adding on paper.

Practise the questions

On paper

Take paper and a pencil. Draw the piles if you like — circles are enough.

Draw 4 piles of 3 circles. Under them write the plus version (3 + 3 + 3 + 3), the times version (4 × 3) and the result.
Rewrite as multiplying and work out: 5 + 5 + 5, 2 + 2 + 2 + 2, 10 + 10.
Write out as adding and work out: 3 × 4, 6 × 2, 2 × 9.
Write 7 × 2 and 2 × 7. Work out both and check that you get the same.

Now you 💪

You can read 3 × 4 out loud and say what it means (three piles of four).
You rewrote 5 + 5 + 5 as 3 × 5 and got 15.
You know that 6 × 3 and 3 × 6 give the same result, and you can say why.

✅

Done when: You can turn adding the same numbers into multiplying and back, and you know that the order of the numbers in a times does not matter.

What to take from this lesson

Multiplying is a shortcut for adding the same numbers: 4 + 4 + 4 = 3 × 4.
The first number says how many piles, the second how many are in one pile.
You can swap the numbers in a times: 3 × 4 = 4 × 3. Pick the shorter path.
The word “of” in a word problem is a times signal.
If you are not sure, write the times back out as adding.