L2 · Regrouping by place value: modelling addition and subtraction

Learning goal

“I can show regrouping with base-ten blocks: trading 10 ones for 1 ten, and 10 tens for 1 hundred. A trade never changes the value. It only moves it.”

Regroup — to trade 10 of one place for 1 of the place beside it, so the blocks are easier to work with.

Trade — the swap itself: 10 ones become 1 ten rod; 1 hundred flat becomes 10 ten rods. The value stays the same.

Base-ten blocks — hundreds flats, tens rods and ones cubes. Each block is worth 10 of the block one size smaller.

Place value — the value of a digit's place: in 458, the 5 sits in the tens place and is worth 50.

Worked example

278 + 156, with blocks. Ones: 8 cubes + 6 cubes = 14 cubes. Trade 10 cubes for 1 ten rod. Ones left: 4. Tens: 7 rods + 5 rods + the traded rod = 13 rods. Trade 10 rods for 1 hundred flat. Tens left: 3. Hundreds: 2 flats + 1 flat + the traded flat = 4 flats. Read the blocks: 434. Say it plainly: we never had more or fewer blocks' worth of value. We only repacked it.

Check yourself — explain it

Trading 10 ones for 1 ten does not change the total because...

Paired problem — example still visible

389 + 247 with blocks: ones 9 + 7 = 16 -> trade, 6 left; tens 8 + 4 + 1 = 13 -> trade, 3 left; hundreds 3 + 2 + 1 -> 636

Faded completion — last step is yours

"467 + 285: ones 7 + 5 = 12 -> trade, 2 left; tens 6 + 8 + 1 = 15 -> trade, 5 left; hundreds 4 + 2 + 1 = ___" -> 7 (sum 752)

Ready to practise?

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

Start practice →Take the unit quiz