Mathematics K–6 · Years 3–4
Fair or unfair: spinners with unequal sectors
Statistics and probability
This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.
The idea
On a spinner the chance of a colour depends on how much of the circle it covers, so a colour with a bigger sector comes up more often over many spins.
What you need
- card circles 12 cm across, a paperclip and a pencil to hold it at the centre as a pointer
- a protractor and coloured pencils
- a tally sheet
How to do it
- Make spinner A with two equal sectors (red and blue). Make spinner B with red covering half the circle, blue a quarter and green a quarter, using the protractor to mark 180, 90 and 90 degrees.
- Predict for each spinner how many times each colour will come up in 40 spins.
- Spin each spinner 40 times and tally. Compare with the predictions.
- Pool the class results for spinner B and compare the three colour totals as fractions of the total spins.
- Design a spinner where blue is three times as likely as red, mark the angles, and test it with 40 spins.
What you should see
Spinner A gives about 20 red and 20 blue in 40 spins with counts between 14 and 26 happening in about 96 percent of runs of 40. Spinner B gives about 20 red, 10 blue and 10 green; pooled over a class of 12 pairs (480 spins) the fractions come out near one half, one quarter and one quarter. A spinner with blue three times as likely as red needs blue on 270 degrees and red on 90, and 40 spins give about 30 blue and 10 red.
What changes
- What you change
- the angle of each sector
- What you measure
- the number of spins landing on each colour
- What you keep the same
- 40 spins per spinner
- the pointer spun with the same flick
- the spinner flat on the desk
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Each colour on a spinner has the same chance because there is one of each.
- The colour that came up last is less likely next time.
Safety card
Hazards
- pencil points
- paperclip ends
Controls
- hold the pencil upright on the desk; plastic-coated paperclips
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-CHAN-01MAO-WM-01
- Australian Curriculum v9AC9M4P01AC9M4P02
Sources
The pages the author read to write this activity.