# Fruit Pies

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

# Practical details

Suitability
National Curriculum levels 6 to 8
Time
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.

• 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