Measuring with paperclips: uniform units end to end · Concept Studio

The idea

A length is measured by laying identical units end to end with no gaps or overlaps, and a smaller unit gives a bigger count for the same length.

What you need

40 small paperclips of one size (measure one with a ruler first; a common size is 32 mm)
20 large paperclips of one size (a common size is 50 mm)
10 interlocking centimetre cubes joined into a rod
a 30 cm ruler (for the adult to check unit sizes only)
a picture book about 30 cm tall, a pencil and a shoe

How to do it

Estimate how many small paperclips fit along the long side of the book. Write the estimate down.
Lay small paperclips end to end along the edge, touching but not overlapping. Count them and record the count, including any part clip at the end.
Measure the same edge with large paperclips. Record the count. Compare the two counts and explain why they differ.
Measure the pencil and the shoe with small paperclips. Order the three objects from shortest to longest by their counts.
Measure the book edge with a hand span (partner and child each do it). Compare the two counts and discuss why they disagree.

What you should see

A 300 mm book edge takes about 9 small paperclips of 32 mm (300 divided by 32 is 9.4, so 9 clips and a part clip) and 6 large paperclips of 50 mm. The count is smaller when the unit is longer. Two children measuring with their own hand spans get different counts for the same edge, and the counts agree only when both use the same paperclips. Leaving gaps makes the count smaller and overlapping clips makes it larger, which the pair can show by re-laying the clips.

What changes

What you change: the unit used (small paperclip, large paperclip, hand span)
What you measure: the number of units along the edge
What you keep the same: the same book edge
units laid touching with no overlap
starting at the very end of the edge

Common misconceptions

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

A bigger count always means a longer object, whatever unit was used.
Leaving gaps between the units does not change the measurement.

Safety card

Low riskLearners carry it out

Hazards

paperclips can scratch

Controls

use plastic-coated clips for young children

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 AuthorityMA1-GM-02 MAO-WM-01
Australian Curriculum v9AC9M1M02AC9M2M01

Sources

The pages the author read to write this activity.