# Fruit Pies

# Fruit Pies

Pupils use their knowledge of area of circles and rectangles to solve a problem.

# Links

# Practical details

- Suitability
- National Curriculum levels 6 to 8
- Time
- About 1 hour
- Resources
- Calculator, paper (may request squared, graph or plain), pair of compasses, a ruler

# Key Processes involved

- Representing
- Break the problem down into smaller steps.
- Analysing
- Use logical reasoning, and make calculations.
- Interpreting and evaluating
- Consider appropriateness and accuracy.
- Communicating and reflecting
- Communicate their findings effectively.

# Teacher guidance

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 cm

^{2}) + (9π = 28.27 cm^{2}) = (34π = 106.81 cm^{2})Assuming 12 pies cut from fist rectangle, remaining area = 518.23 cm

^{2}Theoretical maximum number of pies: 16 (1800 ÷ 34π = 16.85)

Actual maximum number of pies: 15