Pupils use their knowledge of area of circles and rectangles to solve a problem.
- National Curriculum levels 6 to 8
- About 1 hour
- Calculator, paper (may request squared, graph or plain), pair of compasses, a ruler
Key Processes involved
- Break the problem down into smaller steps.
- Use logical reasoning, and make calculations.
- Interpreting and evaluating
- Consider appropriateness and accuracy.
- Communicating and reflecting
- Communicate their findings effectively.
You might set the scene by showing the slides on a whiteboard. If asked, clarify that the thickness of the pastry when re-rolled should be the same as originally; don’t volunteer this information since it can form part of the assessment.
- This task looks at a practical issue – the making of pies. You are asked to calculate the maximum number of pies Anna can make from a rectangle of pastry; note she has to cut whole circles for the pies.
- You are given the dimensions of the pastry and are told Anna can roll the pastry, then re-roll the left over once only.
The task assesses geometric understanding, with a focus on circles.
During the task, the following probing questions may be helpful:
- Can Anna use all of the pastry in the first rolling? Why not?
- She wants to make as many pies as possible. What should she think about when rolling out the leftovers?
- When Anna uses the leftover pastry, what size rectangle should she make? Why?
- How certain are you that the number you have found is the maximum possible?
The following values may be helpful; they are given to two decimal places to help check pupils’ rounding skills.
Total area per pie = (25π = 78.54 cm2) + (9π = 28.27 cm2) = (34π = 106.81 cm2)
Assuming 12 pies cut from fist rectangle, remaining area = 518.23 cm2
Theoretical maximum number of pies: 16 (1800 ÷ 34π = 16.85)
Actual maximum number of pies: 15