12 hours

Year 9 Extension

Spring Term

Unit 15

Solving problems and investigations

NNS 2–35

Autumn Term

Spring Term

Summer Term

Support (from Y9 teaching programme) • Solve increasingly demanding problems and evaluate solutions; explore connections in mathematics across a range of contexts: number, algebra, shape, space and measures, handling data. • Represent problems and synthesise information in algebraic, geometric or graphical form; move from one form to another to gain a different perspective on the problem. • Solve substantial problems by breaking them into simpler tasks, using a range of efficient techniques, methods and resources, including ICT ; use trial and improvement where a more efficient method is not obvious. • Present a concise, reasoned argument, using symbols, diagrams, graphs and related explanatory text ; give solutions to problems to an appropriate degree of accuracy. • Suggest extensions to problems, conjecture and generalise; identify exceptional cases or counter-examples, explaining why
Core (from Y9 objectives for able pupils) • Generate fuller solutions to mathematical problems • Recognise limitations on the accuracy of data and measurements ; give reasons for choice of presentation, explaining selected features and showing insight into the problem's structure • Justify generalisations, arguments or solutions; pose extra constraints and investigate whether particular cases can be generalised further • Examine critically the results of a statistical enquiry, and justify choice of statistical representation in written presentations

Starters	Main	ICT	Scaffolding	Key Questions	Notes
	ATM 40 Problems ~ p7 Shortest path on a cube ~ p9 Turning rectangles into squares ~ p10 Path in a triangle ~ p12 Cyclic hexagon ~ p17 Lampshade ATM ~ PROOF in elementary geometry BOLT MAA ~ 125 The effect of inflation CORNWALL / Framework UAM ~ Handling data 2 MAP ~ Equable shapes ~ Areas of overlap ~ Exploring Pythagoras ~ Exploring trigonometry ~ Driving in France ~ Creative dice ~ Digame PoD ~ 1/7 Keep moving! SHELL (Red and Blue books) ~ Problems	SMILE Spreadsheets make sense ~ A Rich Aunt ~ Averaging out ~ Marbles ~ Strings ~ Converging sequences ~ Geometry sequences MAP ~ Is it worth buying a car for commuting?	MAP ~ Generic assessment criteria	What do you need to know before you begin? What are ‘the rules'? Can algebra be used to represent this problem? What is the first thing you need to do? Why? Justify? What difference does it make if you round part way through a complex calculation? Is this always / sometimes / never true?	Developing reasoning - all activities MAP Extended task: World Statistics Database Outline Task-sheet Mark-scheme