PLAI™ in practice
Turn your teaching brief into a lesson you can shape.
Watch a Year 11 geometry lesson develop, then see how one follow-up adds a new challenge.
A brief that starts with your class
For this Year 11 lesson, the teacher brings a timetable, a curriculum map and a Cambridge syllabus to a 50-minute arcs-and-sectors review.
- Timetable
- Year 11 curriculum map
- Cambridge syllabus
Using the attached Year 11 map, timetable and Cambridge syllabus, could you plan my 50-minute review lesson on arcs and sectors for 9 December? Keep the main work Core-friendly and add a little optional Extended challenge.
A plan you can build on
A teaching sequence, pupil tasks and worked answers take shape in Printing Studio. You have a complete plan to review and refine.
Push the thinking further
The first plan gives you a starting point. A follow-up lets you ask for the challenge you want to add.
A targeted request in Ask for changes:
Could you add a short stretch task where pupils compare the arc length and area of 90° and 120° sectors, explain which formula they chose, and check the units?
What that adds
A new Quick stretch: Compare two sectors task, with worked answers, sits between Core practice and the optional Extended challenge.
See the thinking behind the answer
The same radius, two different angles. This task asks pupils to compare results, explain their formula choices and check the units.
Quick stretch: Compare two sectors
Longer arc by π cmGreater area by 3π cm²
Two sectors have the same radius, 6 cm. One has angle 90°; the other has angle 120°. Find the arc length and area of each in terms of π. Which sector has the longer arc, and which has the greater area? For each type of result, write the formula you chose and explain why. Check that your units are correct.
Worked answers for your review
| Sector | Arc length | Sector area |
|---|---|---|
| 90°, radius 6 cm | 3π cm | 9π cm² |
| 120°, radius 6 cm | 4π cm | 12π cm² |
Arc length uses the same fraction of the circumference. Sector area uses that fraction of the circle's area.
The 120° sector has a longer arc by π cm and a greater area by 3π cm².
Independent check
A sector has radius 15 cm and angle 72°. Find its arc length and area in terms of π. Write one sentence explaining why one answer is in cm and the other is in cm².
See the whole lesson
Explore the complete plan, including the teacher key. Keep the answers separate from the pupil pages when you prepare your lesson.
Make it your lesson
PLAI gives you a lesson plan to work with. You decide what works for your pupils.
- Mathematics
- Challenge
- Timing
Questions about PLAI in practice
Can I ask PLAI to change a lesson plan?
Yes. In this lesson, a follow-up request adds a comparison between 90° and 120° sectors to the existing plan, with worked teacher answers. You can explore the task and its answer key above.
What can I include in my brief?
Your class, curriculum and chosen source files, along with the topic, lesson length and level of challenge. This Year 11 brief uses a timetable, curriculum map and Cambridge mathematics syllabus.
Can I use this lesson with my class?
Use it as a starting point. Check the mathematics, challenge and timing against your class and curriculum, and keep teacher answers separate from pupil materials.
Can I read the whole lesson plan?
Yes. The complete revised plan is embedded on this page, with a PDF to download. You can also read and download the Proof organiser worksheet here.
Where can I find more teaching ideas?
The public Library has more teaching resources to explore. Choose a resource that fits your teaching goal, then review it for your class.
Your next lesson could start here
Find a fresh idea in the Library and choose what works for your pupils.