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 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