Mathematics K–6 · Years 3–4

One data set, three displays: handfuls of cubes

Statistics and probability

Practical, model not builtLow risk

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The idea

The same data can be shown as a list, a dot plot or a column graph, and a display that keeps every value on a shared scale shows the shape and spread of the data and makes two groups easier to compare.

What you need

a tub of at least 300 interlocking 2 cm cubes
a class recording list with two columns: writing hand, other hand
a paper number line from 0 to 40 and 1 cm grid paper
a spreadsheet program

How to do it

Pose the question: do we grab more cubes with the writing hand or with the other hand.
Each learner grabs one handful from the tub with the writing hand, counts the cubes and returns them, then does the same with the other hand. Record both counts in the class list.
Draw a dot plot of the writing-hand counts on the number line, one dot per learner, and a second dot plot of the other-hand counts on the same scale directly underneath.
Draw a column graph of the writing-hand counts grouped in intervals of 5 (10 to 14, 15 to 19 and so on).
Enter the list in a spreadsheet and make a column graph showing each learner's two counts side by side.
Compare the displays: which shows the most common count, which shows the spread from smallest to largest, and which answers the question most clearly.

What you should see

The unsorted class list holds every value but shows no pattern until it is sorted. The two dot plots on one scale show the most common count, the smallest and largest counts, and whether the writing-hand dots sit to the right of the other-hand dots, which answers the question directly. The grouped column graph shows where the counts bunch but hides individual values, so counts of 10 and 14 look the same. The side-by-side spreadsheet graph shows each learner's pair, but the class comparison has to be read across every pair of columns rather than from one picture. Each dot plot has exactly one dot per learner, a check that no value was lost.

What changes

What you change: the hand used to grab (writing hand or other hand)
What you measure: the number of cubes in one handful
What you keep the same: the same tub and size of cube
one grab per hand
cubes returned before the next grab
counts recorded straight away

Common misconceptions

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

Two groups can be compared fairly on graphs drawn with different scales.
A column graph with taller columns always means more data was collected.

Safety card

Low riskLearners carry it out

Hazards

cubes dropped on the floor

Controls

grab and count over the tub

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 AuthorityMA2-DATA-01 MA2-DATA-02 MAO-WM-01
Australian Curriculum v9AC9M4ST02AC9M4ST03

Sources

The pages the author read to write this activity.

All Concept Studio activities