The idea, step by step
Trade equal amounts
A trade changes the grouping, not the total. One ten can be exchanged for 10 ones. One hundred can be exchanged for 10 tens. Count the value before and after a trade to check it stayed the same.
More than one name
126 can be 1 hundred, 2 tens and 6 ones. It can also be 12 tens and 6 ones. Trading one of its tens gives 1 hundred, 1 ten and 16 ones. These are different names for the same number.
| Hundreds | Tens | Ones |
|---|---|---|
| 1 | 2 | 6 |
| 0 | 12 | 6 |
| 1 | 1 | 16 |
A common trap
Thinking that 13 ones are not allowed.
Instead: The usual written numeral uses one digit per place, but a collection may be grouped as 13 ones. Regroup them when writing the standard numeral.
See the thinking
Trade a hundred
Rename 240 using only tens.
- 2 hundreds are 20 tens.
- Add the 4 tens already there: 20 tens + 4 tens = 24 tens.
Trade for more ones
Rename 153 using 4 tens.
- 153 starts as 1 hundred, 5 tens and 3 ones.
- Trade one ten for 10 ones: 5 tens become 4 tens and 3 ones become 13 ones.
Check your understanding
Are 17 tens and 4 ones equal to 174?
Show answer
Yes
17 tens are 170; 170 + 4 = 174.
Your turn
6 questions · Work at your own pace.
Read the questions online
- Rename 60 as ones.
- Rename 300 using only tens.
- What number is 18 tens and 2 ones?
- Complete: 147 = 1 hundred + 3 tens + ___ ones.
- Are 2 hundreds and 15 tens equal to 350? Explain.
- Give two different groupings of 208.
Read the worked solutions
- Rename 60 as ones.
6 tens are equal to 60 ones.
60 ones. - Rename 300 using only tens.
Each hundred is 10 tens: 3 groups of 10 tens = 30 tens.
30 tens. - What number is 18 tens and 2 ones?
180 + 2 = 182.
182 - Complete: 147 = 1 hundred + 3 tens + ___ ones.
100 + 30 = 130; 17 more makes 147.
17 - Are 2 hundreds and 15 tens equal to 350? Explain.
2 hundreds are 200 and 15 tens are 150; together they make 350.
Yes. - Give two different groupings of 208.
200 = 20 tens, so both groupings have value 208.
For example, 2 hundreds and 8 ones; or 20 tens and 8 ones.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Reading/ordering numbers; hundreds/tens/ones; zero; regrouping and renaming.
Official curriculum source ↗