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Concept 1 of 8

Length Ladder: mm, cm, m, km

1

Today's big idea

Each rung of the length ladder is one swap, so you multiply down and divide up.

Knowing which rung you are on decides whether the swap is 10, 100 or 1000.

2

How it works

👀 What's going on?

Your pencil is about 15 cm long. Your classroom is about 3 m tall. The next town might be 50 km away. Three sizes of thing, three different units.

💡 Here's the trick

The Length Ladder1 km= 1,000 m1 m= 100 cm1 cm= 10 mm1 mmtiny!×÷Multiply going DOWN. Divide going UP.

Look at the ladder above. Four length units sit on it, with mm at the bottom and km at the top. Each rung carries its own swap: 1 km = 1000 m, 1 m = 100 cm, and 1 cm = 10 mm. The arrow beside the ladder says the rest in two words. Multiply going down, divide going up.

🪄 How to do it

  1. 1.Find your two units on the ladder above.
  2. 2.Decide which way you are moving, down or up.
  3. 3.Multiply going down, divide going up, using the swap on that rung.

✍️ Try it

  1. 1.A ribbon is 8 cm long. How many mm is that?
  2. 2.A wall is 3 m 40 cm long. How many cm is that altogether?

The ribbon drops one rung, from cm to mm, so 8 × 10 = 80 mm. The wall drops one rung too, from m to cm, so 3 m becomes 300 cm. Then 300 + 40 = 340 cm.

⚠️ Watch out

You might be thinking every swap on the ladder is × 10. It is not. A metre holds 100 cm, so 3 m is 300 cm, never 30 cm. Read the rung before you multiply.

🌟 Why this matters

You climb this ladder buying ribbon, checking your height, and reading a road sign. Nobody sells 2000 mm of tape; they sell 2 m. Swapping units quickly is the only way to compare two lengths that arrived in different units.
Exam tip: Rewrite both lengths in the smaller unit first, then compare or add.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“Convert 4 m to centimetres.”

  1. 1

    Recall the conversion

    1 m = 100 cm. 📏

  2. 2

    Going UNITS DOWN → multiply

    m is bigger than cm, so multiply by 100.

  3. 3

    Do the math

    4 × 100 = 400

  4. 4

    Answer ✓

    4 m = 400 cm

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

Move down for smaller units (×) and up for bigger ones (÷). Land on cm.

CONVERT · ROUND 1 OF 3

3 m = ? cm

km
m3
cmland here
mm
5

Quick check

✅ VERIFICATION

Which is longer, 250 cm or 2 m 40 cm?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Liquid Pouring

1 L = 1000 mL. Multiply to go small, divide to go big.

Concept 2 of 8 →