Mathematics K–6 · Years 5–6

Coin toss: more trials, less variation

Statistics and probability

Practical, model not builtLow risk

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The idea

The fraction of heads in a run of tosses wanders far from one half for a few tosses and settles closer to one half as the number of tosses grows.

What you need

a coin per child
a recording strip of 50 boxes per child
a class chart with columns 10 tosses, 50 tosses, class total
a spreadsheet with a random-number function (for example RANDBETWEEN(0,1) filled down 1000 rows) for 1000 tosses

How to do it

Toss the coin 10 times and record H or T in the boxes. Write the fraction of heads as a decimal.
Continue to 50 tosses and write the fraction of heads again.
Pool every child's 50 tosses on the class chart (for example 24 children, 1200 tosses) and write the class fraction.
Compare the spread of the 10-toss fractions across the class with the spread of the 50-toss fractions.
Run 1000 tosses in the spreadsheet ten times and record the ten fractions. Compare their spread with the class spreads.

What you should see

After 10 tosses the fractions across a class of 24 range widely, commonly from 0.2 to 0.8, and after 50 tosses most sit between 0.36 and 0.64. The class total of 1200 tosses gives a fraction within about 0.03 of 0.5. Each run of 1000 tosses falls between 0.47 and 0.53 about 95 percent of the time, so most of the ten runs land in that band and one may fall outside it (all ten land inside only about 58 percent of the time). The spread shrinks by about half each time the number of tosses grows by four times, because the standard deviation of the fraction is 0.5 divided by the square root of the number of tosses.

What changes

What you change: the number of tosses in a run
What you measure: the fraction of heads in the run
What you keep the same: the same coin
the same tossing method
every toss recorded

Common misconceptions

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

A long run of tosses must come out exactly half heads.
After many tails, the coin owes some heads to even things up.

Safety card

Low riskLearners carry it out

Hazards

coins on the floor

Controls

toss over the desk

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-CHAN-01 MAO-WM-01
Australian Curriculum v9AC9M6P02AC9M6P01AC9M5P02

Sources

The pages the author read to write this activity.

All Concept Studio activities