Mathematics K–6 · Years 3–4

Trading with base-ten materials: regrouping to add and subtract

Number and algebra

Practical, model not builtLow risk

This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.

The idea

When a column holds ten or more pieces, ten are traded for one piece of the next place, and when a column holds too few to take away, one piece of the next place is traded for ten, so the value never changes while the pieces do.

What you need

base-ten materials per pair: 20 ones (1 cm cubes), 20 tens (longs) and 10 hundreds (flats)
a place-value mat with hundreds, tens and ones columns
a recording sheet with space for the written method beside a sketch of the mat

How to do it

Make 47 and 38 on the mat. Push the ones together and count them. Trade ten ones for one ten and move it to the tens column.
Push the tens together and read the total. Record the trade in the written method as a 1 carried into the tens column.
Make 256 + 178. Trade in the ones column, then in the tens column, and record both trades.
Make 403 and take away 167. There are too few ones and no tens, so trade one hundred for ten tens first, then one ten for ten ones. Record each trade.
Make 300 and take away 1, counting the trades needed.
Check every subtraction by adding the answer to the number taken away.

What you should see

47 + 38: the ones make 15, one trade gives 1 ten and 5 ones, and the total is 85. 256 + 178: the ones make 14 (one trade), the tens make 13 with the traded ten (a second trade) and the total is 434. 403 - 167 needs two trades and gives 236, and 236 + 167 returns 403. 300 - 1 also needs two trades and gives 299. The number of pieces on the mat changes with every trade while the value stays the same, which is why each carried or renamed digit in the written method is correct.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

In 52 - 27 you take the smaller digit from the larger in each column, which gives 35.
Trading a ten for ten ones changes the number.

Safety card

Low riskLearners carry it out

Hazards

small cubes on the floor

Controls

work on mats and count pieces back into their tubs

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA2-AR-01 MAO-WM-01
Australian Curriculum v9AC9M3N03AC9M4N06

Sources

The pages the author read to write this activity.

All Concept Studio activities