Mathematics K–6 · Years 5–6

Hand spans: a dot plot, the mode and the range

Statistics and probability

Practical, model not builtLow risk

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The idea

Measurements collected from a group vary, and a dot plot shows the shape of that variation together with the most common value and the spread from smallest to largest.

What you need

a 30 cm ruler per pair
a class recording sheet and sticky dots
a long strip of paper marked from 12 cm to 24 cm in half-centimetres for the class dot plot
a spreadsheet (optional)

How to do it

Agree on a method: right hand spread as wide as possible on the desk, measured from thumb tip to little-finger tip to the nearest half centimetre. Each child is measured twice and records the second reading.
Each child places a sticky dot above their value on the class strip.
Read the mode (the value with the most dots) and the range (largest minus smallest). Describe the shape: where the dots pile up, whether there are gaps or dots far from the rest.
Compare the class dot plot with one from another class or year group, using the same method, and say how the mode and range differ.
Pose a follow-up question the data could answer (do longer hand spans go with taller children) and plan what would need to be collected.

What you should see

The class dots pile up in a band a few centimetres wide with one mode, or two adjacent values tied for it, and a few dots trailing either side; the exact values belong to the class that measured them. A child measured twice may get two slightly different readings, which is why the method is agreed first and the second reading is used. A dot plot from another group measured the same way is compared by where its pile sits and how wide its range is. For the data set 16, 17, 17, 18, 18, 18, 19, 20 the mode is 18 and the range is 4.

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 mode is the tallest dot stack no matter what value it sits on, so it is a count, not a measurement.
The range is the largest value.

Safety card

Low riskLearners carry it out

Hazards

none beyond ordinary classroom materials

Controls

record first names or initials only

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 v9AC9M5ST01AC9M6ST01AC9M6ST03

Sources

The pages the author read to write this activity.

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