Longer or shorter: comparing lengths end to end · Concept Studio

The idea

Two lengths can only be compared when one end of each is lined up on the same baseline, so that the other ends show which is longer.

Safety card

Low riskAn adult supervises

Hazards

straw ends near eyes
small items on the floor

Controls

cut straws with blunt ends
work at a table with an adult present

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.

What you need

10 drinking straws cut to lengths between 5 cm and 25 cm (no two the same)
6 pencils of different lengths
1 piece of string, 1 m long
a flat table edge or a strip of masking tape on the floor as a baseline

How to do it

Pick two straws. Stand them side by side with both bottoms touching the baseline. Say which is longer and which is shorter, and point to the end that sticks out.
Repeat with the same two straws, but lift the shorter straw off the baseline by more than the difference in their lengths. Notice the shorter straw now looks longer, then put both back on the baseline and check.
Take five straws and order them from shortest to longest along the baseline. Swap with a partner and check each other's order. Put the straws back, choose a different five from the ten, and repeat three times.
Hold the 1 m string beside pencils, books and other objects. Sort the objects into three piles: longer than the string, shorter than the string, about the same.
Use the words longer, shorter, taller, the same length while sorting, and record the three piles as a drawing.

What you should see

With the bottoms on the baseline, the longer straw sticks out above the shorter one; a 20 cm straw beside a 15 cm straw shows 5 cm of overhang. When the shorter straw is lifted by more than the difference in length, its top sits higher than the longer straw, so looking at the tops alone gives the wrong answer until both bottoms are back on the baseline. Because no two straws are the same length, five straws standing on the baseline have exactly one order from shortest to longest, which is how partners check each other. Laying the string along each object decides which pile it goes in.

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.

The straw whose top is higher is longer, even when the bottoms are not level.
A string that is curled up has become shorter than when it was straight.

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 AuthorityMAE-GM-02 MAO-WM-01
Australian Curriculum v9AC9MFM01

Sources

The pages the author read to write this activity.