Mathematics K–6 · Years 3–4

Toss and roll: recording repeated chance experiments

Statistics and probability

Practical, model not builtLow risk

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

Repeating a chance experiment many times gives results that vary from trial to trial, yet the counts for equally likely outcomes come out close to each other over many trials.

What you need

a coin and a six-sided die per pair
a tally sheet with rows heads and tails, and a second sheet with rows 1 to 6
a class chart to pool results

How to do it

Predict how many heads you will get in 20 tosses. Toss the coin 20 times, tallying heads and tails.
Write your head count on the class chart. Look at the smallest and largest counts across pairs, then add up the whole class.
Predict how many sixes in 30 rolls. Roll the die 30 times, tallying each face.
Pool the die results for the class and compare the six counts. Say whether any face came up far more than the others and whether the die seems fair.
Repeat the 20 tosses and compare your two head counts.

What you should see

With a fair coin, 20 tosses give between 6 and 14 heads in about 96 percent of pairs, and a pair's two head counts match about one time in eight (probability 0.125). A class of 12 pairs pools 240 tosses, and the head total lands between 105 and 135 in about 95 percent of classes. In 30 rolls each face is expected 5 times, and a count from 2 to 8 happens in about 92 percent of runs; pooled over 12 pairs (360 rolls) each face is expected 60 times with a standard deviation of 7, so the six counts spread over a band of roughly 20 for a fair die (the average gap between the largest and smallest count is 19.6 in 100 000 simulated classes).

What changes

What you change: the number of trials
What you measure: the count of each outcome
What you keep the same: the same coin or die
a fair toss or roll onto a flat surface
every trial recorded

Common misconceptions

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

A fair coin tossed 20 times must give exactly 10 heads.
After several tails in a row, heads is due.

Safety card

Low riskLearners carry it out

Hazards

coins and dice are a choking hazard for very young children

Controls

collect coins and dice at the end

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-01 MAO-WM-01
Australian Curriculum v9AC9M3P02AC9M4P02

Sources

The pages the author read to write this activity.

All Concept Studio activities