Free IB Maths AI SL lesson: Chi-squared test for independence
A ready-to-teach IB Maths AI SL lesson on Chi-squared test for independence (Unit 4 · Statistics & Probability): editable slides and teacher notes, free; a printable worksheet in 2 levels with answers for school plans. About 55 minutes.
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What's inside
- Slides (PowerPoint, editable) · freeabout 12 slides: do now, objectives, key ideas, a worked example step by step, “your turn”, practice QR code, exit ticket
- Teacher notes (PDF) · freelesson plan with timings, common mistakes, homework links
- Worksheet (PDF) · school plans4 questions, 13 marks: Fluency, Exam-style. Included with school plans and the teacher trial.
- Answers (PDF) · school plansthe answer to every worksheet question, from its mark scheme. Included with school plans and the teacher trial.
Learning objectives
- The χ² test for independence
Key ideas on the slides
- H₀: the two variables are independent; H₁: they are not independent.
- Expected frequency = (row total × column total)/(grand total).
- Degrees of freedom = (rows − 1)(columns − 1).
- Every expected frequency should be greater than 5 (in exams they always are). If one is 5 or less, as can happen in an IA, the test is less reliable: combine categories first.
By the end of the lesson, students should be able to answer a question like: Perform a chi-squared independence test on a 2x3 table at 5% significance.
Key vocabulary
- contingency table: A table of observed frequencies for two categorical variables.
- expected frequency: The frequency expected if H₀ is true.
- degrees of freedom: The number of values free to vary (ν).
Common mistakes this lesson tackles
- χ² and t-tests: hypotheses, the comparison and the conclusion in context. Use a fixed layout: H₀ and H₁ in symbols with the population parameter (μ₁ = μ₂; μ₁ > μ₂) or in words naming both variables for χ²; the p-value; "p < 0.05, so reject H₀" (or not); then one sentence in context.
- Hypotheses that do not name the variables.
- Wrong degrees of freedom (using rows × columns).
- Saying "accept H₁" or "H₀ is true".
The worked example
150 diners rate meals. 69 are Children; 67 ordered Shrimp. Under H₀, find the expected frequency of Children who ordered Shrimp.
- Formula: E = (Row × Column)/(Grand Total).
- Identify: Row =69, Column =67, Grand =150.
- Substitute: E = (69 × 67)/150.
- Numerator: 69 × 67 = 4623.
- Evaluate: 4623/150 = 30.8.
Tip: Never round expected frequencies during working — keep exact decimals so the final χ² statistic stays accurate.
Calculator tips
- Enter the observed matrix and use χ²-Test; the GDC stores the expected values in a second matrix.
Lesson plan
| 0–5 min | Do now: students write down what they remember about Spearman's rank correlation and Least-squares regression line |
| 5–8 min | Share the learning objective and success criteria |
| 8–20 min | Teach: the worked example, step by step; students copy the method |
| 20–25 min | Your turn: 1 mini-whiteboard question; check every board before moving on |
| 25–42 min | Practise: the worksheet (4 questions in 2 levels, with school plans and the teacher trial) or the topic's practice questions online; move up a level after two right in a row |
| 42–47 min | Plenary: 1-question exit ticket; collect it to plan the next lesson |
For students: practise this topic
The worksheet's QR code opens the IB Maths AI SL Unit 4: Statistical Testing practice questions.
What schools get
- Set this lesson as homework, marked by AI against the mark scheme, with every result in your markbook (with a School plan).
- This lesson's worksheet in three levels, with its answers, ready to print.
- Support, Core and Stretch versions and A/B copies of the worksheet from the full question bank, in the worksheet builder.
- Create lesson: this lesson rebuilt for your class's next scheme-of-work lesson, from the full bank.
School licences from €490 a year. Try everything free for 30 days as a teacher: no card.
Questions teachers ask
Is this lesson free?
The slides and the teacher notes are free to download with a free IB Math Revision teacher account (sign in with Google, Microsoft or email); no card. The printable worksheet in three levels and its answers are included with school plans and the free 30-day teacher trial.
Can I edit the slides?
Yes. The slides are an ordinary PowerPoint file: change, add or delete anything. They also open in Google Slides and Keynote. The logo and web address sit on the slide master, so your edits do not move them.
What do students use for homework?
The practice slide's QR code and web address take students to the IB Maths AI SL Unit 4: Statistical Testing practice questions on ibmathrevision.com, where the free questions are open and the full bank comes with a plan.