Free IB Maths AI SL lesson: Upper & lower bounds of measurements
A ready-to-teach IB Maths AI SL lesson on Upper & lower bounds of measurements (Unit 1 · Number & Algebra): 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 plans3 questions, 15 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
- Upper and lower bounds
Key ideas on the slides
- A value rounded to the nearest unit u lies within half a unit either side: 8.4 to 1 d.p. has bounds 8.35 and 8.45, written 8.35 ≤ x < 8.45.
- For a sum or product use upper with upper for the maximum and lower with lower for the minimum.
- For a difference or quotient, the maximum uses upper − lower and upper ÷ lower; the minimum uses lower − upper and lower ÷ upper.
- To give an answer to a suitable accuracy, round both bounds and use the value they agree to.
By the end of the lesson, students should be able to answer a question like: Find the upper bound of 15 cm, rounded to the nearest cm.
Key vocabulary
- upper bound: The largest value the measurement could have been before it was rounded.
- lower bound: The smallest value the measurement could have been.
- error interval: The inequality LB ≤ x < UB giving all the possible values.
- percentage error: The error as a percentage of the exact value.
Common mistakes this lesson tackles
- Writing the upper bound as 8.449 or 8.4499…: the upper bound is 8.45.
- Using upper ÷ upper to find the largest possible quotient.
- Dividing by the approximate value in a percentage error.
The worked example
A rectangular garden has a length of 14 m and a width of 8 m, both measured correct to the nearest metre. Calculate the minimum possible area of the garden.
- Determine the maximum error: half of 1 m is 0.5 m.
- Find the lower bound of the length: Lₘᵢₙ = 14 − 0.5 = 13.5 m.
- Find the lower bound of the width: Wₘᵢₙ = 8 − 0.5 = 7.5 m.
- Multiply the lower bounds: Aₘᵢₙ = 13.5 × 7.5.
- Evaluate: Aₘᵢₙ = 101.25 m².
Tip: To minimise a product (area, volume), multiply the LOWER bounds of every dimension. Never compute the area first and then subtract 0.5.
Calculator tips
- Keep the bound values exact on the calculator; do not round them before the final step.
Lesson plan
| 0–5 min | Do now: students write down what they remember about Approximation & rounding and Operations with standard form |
| 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 (3 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 1: Approximations and Error 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: Approximations and Error practice questions on ibmathrevision.com, where the free questions are open and the full bank comes with a plan.