Mathematics K–6 · Years 3–4
Place-value slide: multiplying and dividing by 10, 100 and 1000
Number and algebra
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The idea
Multiplying by 10 moves every digit one place to the left and dividing by 10 moves every digit one place to the right, because each place is worth ten times the place on its right.
What you need
- a place-value chart on card with columns ten thousands, thousands, hundreds, tens and ones
- two sets of digit cards 0 to 9 and four extra zero cards
- base-ten materials: 10 ones, 10 tens and 10 hundreds
- a metre ruler marked in centimetres and millimetres
How to do it
- Put 36 on the chart with digit cards and make it with base-ten materials: 3 tens and 6 ones.
- Replace every piece with the piece ten times bigger (each one becomes a ten, each ten a hundred). Count the new value and slide the digit cards to match, putting a zero card in the empty ones place.
- Multiply 36 by 100 and by 1000 by sliding the digits two and three places left.
- Put 4500 on the chart. Divide by 10 and then by 100 by sliding the digits right, removing zero cards that fall off the ones place.
- On the metre ruler, change 3 m to centimetres and 250 cm to millimetres, and say which way and how far the digits slide.
- Work out 7 × 1000, 40 × 30 and 2400 ÷ 60 by splitting off the tens, and check each on the chart.
What you should see
3 tens and 6 ones become 3 hundreds and 6 tens, which is 360, and the digits slide one place left with a zero in the ones place. 36 × 100 = 3600 and 36 × 1000 = 36 000. 4500 ÷ 10 = 450 and 4500 ÷ 100 = 45. 3 m is 300 cm and 250 cm is 2500 mm. 7 × 1000 = 7000, 40 × 30 = 4 × 3 × 100 = 1200 and 2400 ÷ 60 = 240 ÷ 6 = 40. In every case the digits keep their order and only their places change.
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.
- Multiplying by 10 means writing a zero on the end, a rule that breaks for decimals such as 0.5 × 10.
- Dividing by 100 takes 100 away.
Safety card
Hazards
- small pieces on the floor
Controls
- work on a mat
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.
Sources
The pages the author read to write this activity.