L3 · Zero the placeholder; building numbers from parts

Learning goal

“I can build numbers from parts, and I know zero holds a place when a part is missing.”

Placeholder — a digit that holds a place so the other digits stay in the right places.

Zero — the digit 0. As a placeholder, it says "none of this place, but the place is still there."

Part — one piece of a pulled-apart number, like the 400 in 400 + 30 + 7.

Build — to put parts together in their places to make one number.

Worked example

Build 405 from blocks. Step 1 (count each kind): 405 needs 4 flats, 0 rods, and 5 cubes. Step 2 (the empty place): there are no rods, but the tens place is still there. The digit 0 holds it. Step 3 (why it matters): if the 0 is dropped, the number reads 45 - a different number. 405 is four hundred five; 45 is forty-five. Say it plainly: zero is a working digit. It holds an empty place so every other digit keeps its value.

Check yourself — explain it

405 and 45 are different numbers because...

Paired problem — example still visible

How many ten rods are used to build 603? -> 0 (603 has 0 tens; the 0 holds the tens place)

Faded completion — last step is yours

"To build 708: 7 flats, ___ rods, 8 cubes" -> 0

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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