Free IB Maths AA SL lesson: Rationalising the denominator
A ready-to-teach IB Maths AA SL lesson on Rationalising the denominator (Unit 0 · Prior knowledge): editable slides and teacher notes, free; a printable worksheet in 3 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 plans6 questions, 13 marks: Fluency, Reasoning, 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
- Surds
Key ideas on the slides
- √ab = √a√b and √(a/b) = (√a)/(√b); but √(a+b) ≠ √a+√b.
- Simplify by taking out the largest square factor: √72 = √(36 × 2) = 6√2.
- Collect like surds only: 3√2 + 5√2 = 8√2, so simplify each surd first (√8 + √18 = 2√2 + 3√2).
- Rationalise a/(√b) by multiplying top and bottom by √b; rationalise a/(b+√c) with the conjugate b−√c, since (b+√c)(b−√c) = b² − c.
By the end of the lesson, students should be able to answer a question like: Rationalise the denominator of 6/√3.
Key vocabulary
- surd: A root that cannot be simplified to a whole number or fraction, such as √2.
- rationalise the denominator: Rewrite a fraction so that its denominator has no surd.
- conjugate: The same two terms with the sign between them changed: 3 − √2 for 3 + √2.
Common mistakes this lesson tackles
- Adding surds under one root: √2 + √3 ≠ √5.
- Multiplying only the denominator by the conjugate.
- Squaring (2+√3) as 4 + 3, missing the middle term.
Calculator tips
- A calculator can check a surd answer as a decimal, but questions saying "show your working" or "exact" need the algebra.
Lesson plan
| 0–5 min | Do now: students write down what they remember about Basic probability and Averages & basic data handling |
| 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 (6 questions in 3 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 Prior Knowledge 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 Prior Knowledge practice questions on ibmathrevision.com, where the free questions are open and the full bank comes with a plan.