Mathematics K–6 · Years 5–6
One sheet of paper: dividing measurements by 10, 100 and 500
Number and algebra
The idea
A quantity too small to measure directly is found by measuring many copies and dividing, and dividing by 10 or 100 moves every digit one or two places to the right, while dividing by 500 is that two-place shift followed by a division by 5.
What you need
- 1 unopened ream of A4 copy paper whose label states 500 sheets, 80 g/m² and 210 mm × 297 mm
- a kitchen scale reading to 1 g
- a ruler marked in millimetres and two set squares to square up the stack
- a calculator for checking
How to do it
- Read the ream label: the number of sheets, the sheet size and the paper mass per square metre (g/m²).
- Weigh 1 sheet and record the reading. Weigh 10 sheets and divide by 10. Weigh 100 sheets and divide by 100. Compare the three results.
- Unwrap the ream, square it up between the set squares, press it flat and measure its thickness in millimetres. Divide by 500 to find the thickness of one sheet, then write the result as millimetres and as hundredths of a millimetre.
- Calculate the mass of one sheet from the label: area in square metres times 80 g/m². Compare with the weighings.
- Explain why the weighing of 100 sheets gives a better value for one sheet than weighing a single sheet.
What you should see
An A4 sheet has an area of 0.210 m × 0.297 m = 0.06237 m², so at the label's 80 g/m² it has a mass of 4.99 g; by the label, 10 sheets weigh about 50 g and 100 sheets about 499 g, giving 4.99 g per sheet (499 ÷ 100 moves each digit two places right). The label's 80 g/m² is a nominal figure and a kitchen scale that shows whole grams is not necessarily accurate to the gram, so the weighings land near these values rather than exactly on them. One sheet alone reads 5 g, and rounding alone could hide anything from 4.5 g to 5.5 g; weighing 100 sheets and dividing by 100 shrinks that rounding to 0.005 g per sheet, and any error in the scale itself is divided by 100 in the same way, so the 100-sheet weighing gives a far better value for one sheet than a single weighing. By the label, the ream of 500 sheets has a mass of about 2.49 kg without its wrapper (500 times 4.99 g). Its measured thickness divided by 500 gives one sheet; a ream measuring 50 mm, for example, gives 50 mm ÷ 500 = 0.1 mm.
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.
- Dividing by 100 makes a number 100 smaller.
- A scale reading of 5 g for one sheet is exact.
Safety card
Hazards
- a ream of about 2.5 kg can fall on feet
- paper edges can cut skin
Controls
- keep the ream on the table
- handle sheets by their faces, not their edges
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.
- curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/outcomes
- vocabulary.curriculum.edu.au/MRAC/2024/04/LA/MAT/cd12c643-f0e2-4df8-933c-ae83931d34d9
- www.mathematicshub.edu.au/planning-tool/6/measurement/metric-units-and-using-instruments
- amsi.org.au/teacher_modules/Using_place_value4-7.html