10 Common Maths Misconceptions – Diagnostic Grids for GCSE Topics
One-page guides that turn common errors into teaching moments. This free Topic Diagnostic Grids PDF covers 10 GCSE topics: expanding brackets, solving equations, fractions, percentages, ratio, Pythagoras, angles, area and perimeter, averages and probability. For each topic: the misconception, what students write, what they should write, a quick fix activity and teacher notes. Use in your planner, on the staffroom wall, with trainees or in department meetings.
What's inside
- 10 one-page diagnostic grids – one per topic
- Tables: the misconception | what students write | what they should write | quick fix activity
- Teacher notes: why it happens, pre-teaching strategies, follow-up questions
- Bonus: 15-minute department meeting agenda
- Bonus: quick quizzes for expanding brackets and fractions (plus ideas for the rest)
- Feedback form and link to more free resources
Topics you'll cover
- Expanding brackets (including the "Freshman's Dream")
- Solving equations (balance model, order of operations)
- Fractions (all operations, cancelling, common denominators)
- Percentages (multipliers, reverse percentages)
- Ratio (parts and whole, sharing)
- Pythagoras' theorem (hypotenuse vs shorter side)
- Angles (parallel lines, corresponding, alternate, co-interior)
- Area and perimeter (formulae, units, compound shapes)
- Averages (mean, median, mode, frequency tables)
- Probability (and vs or, sample space)
Who it's for
- Heads of department planning CPD or deep dives
- Trainee teachers and ECTs
- Teachers who want a quick reference when planning
- Departments addressing misconceptions systematically
Why these activities work
- One page per topic – print and keep in your planner or on the wall
- Quick fix activities you can use the next lesson
- Teacher notes explain why the misconception happens and how to pre-teach
- Department meeting agenda and quizzes included
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