A complete, ready-to-teach 60-minute lesson on function machines.

Students use one-step function machines to find outputs and operations, use two-step function machines, doing the operations in order, and use inverse operations to work backwards from an output to an input. The big idea: work backwards with the inverse.

WHAT’S INCLUDED (all fully editable)

PowerPoint: 43 slides (6 hidden for extra practice and solutions)
Student workbook: every task in lesson order, with answer boxes and slide numbers
Teacher guide: a one-page summary, guidance for every slide, misconceptions and all answers, plus an “If you’re short of time” route and notes for supporting adults
Independent practice worksheet: Sets A–D, from fully scaffolded to reasoning, ending with problem-solver questions
One-page worksheet: a condensed version of Sets A–D, with a solutions page

LESSON STRUCTURE

Do Now: 4 interleaved retrieval questions, with answers on click and a 4-minute timer
Learning objectives, key words and a “Maths in careers” slide (software developer, data scientist, currency exchange clerk, chef)
4 prior-knowledge hinge questions, with hidden back-up slides for when many students get them wrong
3 skills, each taught as I do → We do → You do, with 3 hinge questions per skill
Visual models: function machine diagrams, input–output tables, and machines run forwards and backwards
A hands-on activity (a match-up card sort) that you can use instead of the Think, pair, share
Quick practice that tells each student which set to start on, 20-minute independent practice (Sets A–D), GCSE exam-style extension questions, an exit ticket and a greater-depth challenge
Built-in countdown timers. Every answer is checked.

Misconceptions tackled: reversing the steps but not the operations when working backwards (undoes × 2 then + 6 with + 6 then × 2); using the inverse operations but in the original order; doing the two operations in the wrong order, or in their head without the middle number.

This is Lesson 2 of 8 in the Year 7 Unit 2 bundle (Algebraic notation & sequences).

Fits KS3 and the GCSE (9–1) Mathematics specifications from AQA, Pearson Edexcel, OCR and WJEC Eduqas, which all follow the DfE GCSE subject content. Not endorsed by AQA, Pearson, OCR or WJEC Eduqas. AQA, Edexcel, OCR and Eduqas are trademarks of their respective owners.