Engaging problem solving tasks (tested on KS3 pupils with Autism, Aspergers' and behavioural difficulties including PDA) also suitable for KS2 & KS4.
National Curriculum LO: to develop pupils' mathematical knowledge, through solving problems and evaluating the outcomes, including multi-step problems and by selecting appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.
The tasks are deliberately 'low floor, high ceiling', challenging but accessible. With limited instruction, students are encouraged to use their own ideas, not just following a method from a book, and develop their own way of solving the problems. The floor of the task can be lowered further by asking students to think visually about each problem.
Smartie Challenge 1: How many packs of SMARTIES fit end to end along the length of a football pitch?
Smartie Challenge 2: How many packs of SMARTIES will cover a football pitch and how many SMARTIES will there be in total?
Smartie Challenge 3: How much will it cost to cover a football pitch with packets of Smarties?
Smartie Challenge 4: Sorting Premier League Football teams by the size of their football pitches and how this affects the number of Smarties per pitch.
Smartie Challenge 5: Calculate how many SMARTIES can fit into the Centre Circle?
Smartie Challenge 6: Upper and Lower Bounds and how they affect the number of Smartie's on a pitch.
I have also included the FA Pitch Sizes pdf. You can extend the task to look at different sized pitches for different age groups. ie how many more Smarties will the U11-U12's get than the U9-U10's etc. There is even information about the recommended orientation of a football pitch, which could introduce ideas about angles and vectors.
Please let me know if you spot any errors. I hope that you like the tasks.