IB Biology: Genetics — Tutor Lesson Plan (monohybrid cross, genotype ratios, chi-squared)

2026-10-28

An IB genetics question does not ask you to memorise 3 to 1, it asks you to show that 3 to 1 survives the data. This lesson ties the Punnett square to the chi-squared test.

Objectives — the student can derive gametes and offspring ratios from parental genotypes, read 3 to 1 and 1 to 1 out of a Punnett square, and judge a ratio with chi-squared.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Alleles	Cross Aa with Aa: how many genotypes appear?	Three: AA, Aa, aa
Simplifying ratios	Which simple ratio is closest to 78 to 22?	About 3 to 1
Squares and division	What is (78 – 75) squared divided by 75?	0.12

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-10 min	Vocabulary first	Genotype, phenotype, allele	Separate the three terms
10-24 min	Punnett square	Four cells for Aa times Aa	Write 1 to 2 to 1
24-36 min	Phenotype ratio	Three dominant, one recessive	Reach 3 to 1
36-48 min	Chi-squared	Sum of observed minus expected squared over expected	Get 0.48
48-56 min	Writing the conclusion	df, critical value, accept or reject	Write one full sentence
56-60 min	Exit check	Three questions marked	Finish alone

03 Teaching script (read it out)

Scene 1: Genotype and phenotype: separate before counting

Aa crossed with Aa gives gametes A and a on both sides, so the four cells are AA, Aa, Aa and aa: genotype ratio 1 to 2 to 1.
With complete dominance A over a the phenotype ratio is 3 to 1, and IB asks why it is 3 and not 4, since Aa and aA are the same genotype.

Student explains how 1 to 2 to 1 and 3 to 1 can both be true.

Scene 2: From expectation to chi-squared

Out of 100 offspring the 3 to 1 expectation is 75 dominant and 25 recessive, while the counts observed are 78 and 22.
Chi-squared is 3 squared over 75 plus 3 squared over 25, that is 0.12 plus 0.36, so 0.48.

Student checks that each bracket is divided by the expected value, never the observed one.

Scene 3: Judging: the critical value is a ceiling, not a target

With df = 1 the critical value at p equal to 0.05 is 3.84, and 0.48 is below it, so the 3 to 1 hypothesis is not rejected.
Write it as: chi-squared 0.48 is below the critical value 3.84 for df 1, so the observed ratio does not differ significantly from 3 to 1.

Note: never write that the result proves 3 to 1, only that the data do not contradict it.

04 Question types and worked steps

Type	Example	Steps	Answer
Genotype ratio	Aa times Aa	Four-cell Punnett square	1 AA to 2 Aa to 1 aa
Phenotype ratio	Complete dominance	Merge AA with Aa	3 dominant to 1 recessive
Test cross	Aa times aa	Gametes A and a against a	1 to 1
Chi-squared	observed 78 to 22	Sum of squared deviations over expected	0.48, not significant

Sanity check (teach this): A genotype ratio must add up to the number of cells, so 1 plus 2 plus 1 is 4; expected counts must also total the observed counts, as 75 plus 25 equals 78 plus 22.

05 Independent practice (3 questions)

Question	Answer	What to watch
Genotype ratio for Aa times Aa	1 to 2 to 1	Aa and aA are one genotype
Phenotype ratio for Aa times aa	1 to 1	Write every gamete
Chi-squared for 78 and 22	0.48	Divide by 75 and 25

06 Common mistakes and what to say

Mistake	Student writes	Say this
Counting Aa and aA separately	ratio written 1 to 1 to 1 to 1	The four cells are positions, not four genotypes.
Dividing by observed values	chi-squared written 0.46	The denominator is always the expected count.
Mixing genotype and phenotype	calling 3 to 1 a genotype ratio	3 to 1 is what you can see; 1 to 2 to 1 is the genotype ratio.
Overstating the conclusion	writing that it proves 3 to 1	A test can only fail to find a significant difference.

07 Homework (paper, section and question numbers)

IB biology chapter index — Check the three questions in the index

08 Exit check (last 5 minutes)

Question	Answer	Decision
Phenotype ratio for Aa times Aa	3 to 1	All three right: move to linkage
Expected counts out of 100	75 and 25	One wrong: re-teach ratio scaling
Chi-squared and the conclusion	0.48, not significant	Two wrong: repeat scene 3

09 Tutor FAQ

Does IB supply a chi-squared table?

Yes, the data booklet carries critical values, but choosing df and the significance level is the student job.

Is a statistical test compulsory?

Paper 2 data questions usually ask for significance, and saying close to 3 to 1 loses marks.

How does this link to ecology?

The same ratios and tests reappear in population genetics, so this chapter underpins the later ones.

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