Science 7–10 · Year 10

Coin-toss crosses: why a 3 to 1 ratio only appears in large numbers

Science understanding: Biological sciences

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The idea

Each parent passes one of two alleles at random, so a monohybrid cross between heterozygotes gives a 3 to 1 phenotype ratio on average but not in every small family.

What you need

Two coins per pair, one labelled for each parent, heads marked A (dominant allele) and tails marked a (recessive)
A tally sheet with columns AA, Aa, aa
Calculator

How to do it

Toss both coins together; the pair of faces is one offspring's genotype. Record it.
Repeat for 20 offspring and count the dominant phenotype (AA or Aa) against the recessive (aa).
Write the ratio for your 20 and compare it with the Punnett square prediction of 3 to 1 (1 AA : 2 Aa : 1 aa).
Pool the class results (for example 15 pairs, 300 offspring) and compare the pooled ratio with 3 to 1.
Repeat the 20-toss run for a test cross (one parent always gives a) and compare with the predicted 1 to 1.

What you should see

Individual runs of 20 scatter widely: the range from the 2.5th to the 97.5th percentile is 11 to 18 dominant offspring (it holds 96.2 % of runs), and exactly 15 of 20 occurs in only about one run in five (probability 0.202). The pooled class total sits close to 75 % dominant; with 100 offspring the same percentile range is 66 to 83 dominant (96.2 % of runs; standard deviation 4.33). The learner knows it worked when their own run falls inside the expected range and the pooled ratio is nearer 3 to 1 than most single runs.

What changes

What you change: Number of offspring counted (20, 100, 300)
What you measure: Fraction showing the dominant phenotype and its spread between runs
What you keep the same: Fair coins
Both coins tossed together
Same genotype rule

Common misconceptions

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

A 3 to 1 ratio means every four children include exactly one with the recessive trait.
The dominant allele is more common in the population because it is dominant.
Recessive traits skip a generation on purpose.

Safety card

Low riskLearners carry it out

Hazards

No hazard is listed.

Controls

No control is listed.

Note

No hazards.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Science 7–10 Syllabus (2023)SC5-GEV-02 SC5-WS-05 SC5-WS-06
Australian Curriculum v9AC9S10U01AC9S10I04AC9S10I05

Sources

The pages the author read to write this activity.

All Concept Studio activities