What this problem-based lesson covers and why it sits here in Shape, Space and Measure.

• Single focus: Cosine Ratio only — no other trigonometry idea is introduced.
• Sits after the previous subtopic in Shape, Space and Measure and feeds the unit assessment.
• Runs in 60 minutes with the timeline below.

Written as student-facing, assessable statements.

• Recognise and define cosine ratio accurately.
• Explain the underlying rule of cosine ratio in your own words.
• Apply cosine ratio to routine and unfamiliar math problems.
• Justify a chosen method and spot errors in another student's work.

Displayed all lesson; used for the exit ticket sort.

• I can state what cosine ratio means without notes.
• I can complete a worked example with correct setting out.
• I can solve an unfamiliar question and explain my reasoning.

Check in the warm-up; reteach in five minutes if it is missing.

• Vocabulary from earlier in Trigonometry.
• The immediately preceding subtopic in Shape, Space and Measure.
• Number, notation and recording conventions for Preschool.

Pre-teach, display on the working wall, use in every answer.

• Cosine Ratio
• Trigonometry
• Shape, Space and Measure
• Method
• Justify
• Evidence

Printed and physical items to gather before the bell.

• Cosine Ratio worksheet — one per student
• Mini-whiteboards and pens
• Exit ticket slips
• Working-wall vocabulary cards

Optional where a low-tech alternative is listed.

• Projector or interactive display
• Slide outline (PowerPoint export)
• Optional: student devices for the interactive worksheet
• Low-tech alternative: printed model examples

Tick before the lesson starts.

• Print the student worksheet and the exit ticket
• Load the slide outline and the hook
• Prepare the three differentiation packs
• Set out practical or manipulative equipment
• Have the answer key to hand for live marking

Retrieval, not new learning.

• Four quick recall items from the previous subtopic.
• Students answer on whiteboards; you scan for the reteach decision.

Creates the need for the new idea.

• A short scenario where cosine ratio is the only thing that resolves the problem.
• Two predictions taken by cold call before any teaching.

Objectives, criteria and the shape of the lesson.

• Share the objectives and success criteria on the board.
• Students copy the criteria into their books for self-marking later.

I do — narrated worked examples.

• Model one full example, thinking aloud at each decision point.
• Model a second example with a deliberate error for students to catch.

We do — the pivot point of the lesson.

• Work the first two items together with whole-class checking.
• Release gradually; circulate and live-mark rather than sit down.

Structured talk with defined roles.

• Pairs: one solves, one questions the method, then swap.
• Each pair produces one agreed justification to share.

Concrete or pictorial representation of the same idea.

• Manipulatives, card sorts or a short practical linked only to this subtopic.
• Bridge explicitly back to the abstract notation before moving on.

You do — silent, unsupported, diagnostic.

• Students complete the Cosine Ratio worksheet section without help.
• No teacher talk; note who needs the support pack tomorrow.

Three parallel tracks on the same objective.

• Support: extra worked example, reduced numbers, sentence stems.
• Core: the standard sequence with success criteria displayed.
• Stretch: justification-only questions and an open-ended extension.
• SEND/EAL: vocabulary cards, dual coding and extra processing time.

Formative checks tied to each phase.

• Whiteboard show-me after direct instruction.
• Live marking during guided practice.
• Book scan during independent practice.
• Exit ticket sorted into secure / developing / reteach.

Plan the response before the lesson, not during it.

• Confusing cosine ratio with a neighbouring idea in trigonometry.
• Applying the method correctly but recording it incorrectly.
• Getting the right answer with an unreliable method.
• Stopping at a partially completed answer.

Practical points from the classroom.

• Keep the warm-up to five minutes — it is a diagnosis, not a lesson.
• Circulate during guided practice; sitting down here costs the lesson.
• Use the answer key as a self-marking station rather than collecting books.

Whole-class talk, hands down.

• Why does the rule for cosine ratio work?
• When would this method be the wrong choice?
• What is the same and what is different about these two answers?

Analyse, evaluate, create.

• Prove that the method always works, or find a counterexample.
• Evaluate two students' methods and justify which is more efficient.
• Design a question on cosine ratio and write its mark scheme.

Metacognition, thirty seconds each.

• Which success criterion are you least confident about?
• What will you practise before the next lesson?

Return to the criteria you opened with.

• Restate each success criterion and take a confidence signal.
• Preview how the next subtopic builds on this one.

One question, one minute, three piles.

• A single cosine ratio item that discriminates secure from developing.
• Sort as students leave; the sort sets tomorrow's starter.

Sized for independent completion.

• Homework worksheet on cosine ratio with a parent note.
• Spaced retrieval of the previous subtopic in the same unit.

For students already secure.

• Challenge worksheet on cosine ratio — justification only.
• Open investigation with multiple valid solutions.

Where this subtopic appears elsewhere.

• Where cosine ratio is used in other math units.
• Links to another subject on the timetable this term.

Context that survives outside the classroom.

• A workplace or everyday situation that depends on cosine ratio.
• A short news or data example to project.

Everything in the cluster, one click away.

• Worksheets, quizzes and flashcards for this subtopic
• Study notes, revision notes and slide outline
• Past paper questions and the question bank
• AI Tutor session prompt and one-to-one tutoring