Free IB Maths AI SL lesson: Solving 2×2 systems on the GDC
A ready-to-teach IB Maths AI SL lesson on Solving 2×2 systems on the GDC (Unit 1 · Number & Algebra): 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, 24 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
- Two Variables — Elimination, Substitution & GDC
- Modelling Real-World Problems
Key ideas on the slides
- A system of linear equations can have one solution, no solution (inconsistent) or infinitely many solutions (dependent).
- Solve 2×2 systems by elimination or substitution; 3×3 systems by elimination (to row-echelon form) or with the GDC.
- For a 3×3 system with a parameter, reduce to find when the last equation becomes 0 = 0 (infinitely many) or 0 = k ≠ 0 (none).
- For infinitely many solutions, give the general solution in terms of a parameter: x = 1 + 2λ, y = λ, z = 3 − λ.
By the end of the lesson, students should be able to answer a question like: Solve 2x + y = 7 and 3x - y = 8.
Key vocabulary
- consistent: Having at least one solution.
- inconsistent: Having no solution.
- parameter: A letter (such as λ) used to describe infinitely many solutions.
Common mistakes this lesson tackles
- Stopping at 0 = 0 without describing the infinitely many solutions.
- Arithmetic slips when eliminating; check in all three equations.
- Entering the equations into the GDC with a term in the wrong column.
The worked example
Two straight lines have equations y = 2x − 3 and y = −0.5x + 7. Find the exact coordinates of the point where these two lines intersect.
- Recognise that at intersection y-values agree.
- Equate: 2x − 3 = −0.5x + 7.
- Collect the x-terms: 2.5x − 3 = 7.
- Collect the constants: 2.5x = 10.
- Solve: x = 4.
- Substitute back: y = 2(4) − 3 = 5. Intersection = (4, 5).
Tip: Verify intersection coordinates fast on the GDC: graph both lines, then use the ISCT tool.
Calculator tips
- Use the simultaneous-equation solver (or rref of the augmented matrix) and write down the system you entered.
Lesson plan
| 0–5 min | Do now: students write down what they remember about Amortisation & annuities on the GDC and Simple & compound interest |
| 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 IB Maths AI SL Unit 1: Systems of Equations 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 1: Systems of Equations practice questions on ibmathrevision.com, where the free questions are open and the full bank comes with a plan.