Mathematics K–6 · Years 5–6

Ruler drop: measuring reaction time and comparing two hands

Statistics and probability

Practical, model not builtLow risk

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The idea

Reaction time can be measured by how far a falling ruler drops before it is caught, and a class investigation compares two groups of such measurements with displays on a shared scale.

What you need

a 30 cm ruler per pair
a conversion table from catch distance (cm) to reaction time (s), computed from t = √(2d / g) with g = 9.80665 m/s²
a recording sheet for 5 catches with each hand
1 cm grid paper

How to do it

Pose the question: is reaction time shorter with the writing hand than with the other hand.
The catcher rests a forearm on the edge of a desk with thumb and finger 2 cm apart level with the 0 cm mark. The dropper lets go without warning; the catcher pinches the ruler and reads the mark at the top of the thumb.
Take 5 catches with each hand, alternating hands, and record the distances in centimetres.
Convert each distance to a reaction time with the table.
Pool the class's catches, keeping the two hands apart. Draw a column graph for each hand in intervals of 0.02 s, the writing hand above and the other hand below on the same time scale, with one square standing for two catches.
Mark the range and the most frequent interval for each hand, answer the question from the graphs and list what could have made the test unfair.

What you should see

The conversion table gives 0.101 s for a 5 cm catch, 0.143 s for 10 cm, 0.175 s for 15 cm, 0.202 s for 20 cm, 0.226 s for 25 cm and 0.247 s for 30 cm, so a missed catch means a reaction time above 0.247 s, and four times the distance is only twice the time. Each learner's five catches vary, so a single catch says little about a person. The two column graphs on one scale show whether the writing-hand catches cluster to the left (shorter times) of the other-hand catches, how the ranges and the most frequent intervals of the two hands compare, and how much the groups overlap; where they overlap, the class can state a difference in the most common times but not a rule for every person.

What changes

What you change: the hand used (writing hand or other hand)
What you measure: reaction time found from the catch distance (s)
What you keep the same: the same ruler
a 2 cm gap between thumb and finger at the start
forearm resting on the desk
drops made without warning
the same dropper for each catcher
5 catches with each hand

Common misconceptions

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

A catch at 20 cm took twice as long as a catch at 10 cm.
One fast catch shows who has the shortest reaction time.

Safety card

Low riskLearners carry it out

Hazards

a falling ruler can knock fingers or a desk edge

Controls

use a plastic ruler
drop from hand height only, never from above a head

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 AuthorityMA3-DATA-01 MA3-DATA-02 MAO-WM-01
Australian Curriculum v9AC9M5ST03AC9M6ST03

Sources

The pages the author read to write this activity.

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