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The Farmer's Field - Investigation

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activity of the week 15 - The Farmer's F
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Key Skills and Concepts

Optimising GCSE

Topics covered:

Area and Perimeter

Mathematical and Spatial Reasoning

Investigation Skills

Adding, Subtracting, Multiplying and Dividing

Equipment needed:

The image shown above (on screen is fine)

Some paper (plain or squared)

Pencil and a ruler (if you have one)



Mathematical Investigations are great ways to show children how mathematics is not as simple as answering questions given to you by a teacher. It enables the child to take control of their own learning and explore an in depth problem using mathematical skills and reasoning throughout. They should be encouraged to question and alter the rules of the problem and think about how they can improve their answer further. This problem involving shape and space will hopeful have children realise that the mathematical knowledge they have can help them reach the best possible answer. It also uses Area and Perimeter with a real world problem.


The objective is to design a fence enclosed field using exactly 30m of fencing. Read the instructions on the image below and ensure your child knows the difference between perimeter and area. If you have squared paper you can draw accurate fields and count the squares to work out area, or you can use the various formulas for different shapes.

Eg: Area of a rectangle = Length x Width


After answering the initial questions ask your child if they can make another rectangle using the 30m of fencing that would have a larger area. Then allow them to lead the investigation themselves using diagrams to show the different fields they think of.


Key Questions:

“What does the perimeter of a shape mean?”

“How would you work out the perimeter of a rectangle?”

“What does the area of a shape mean?”

“How would you work out the area of a rectangle?”

Key terms to try and use: Length, width, perimeter, area, space, metre, square metre


Questions to Ask to help them extend the investigation:

“Can you make a field with a bigger area?”

“Are you sure that is the largest possible field?” – “How do you know?”

“Does the field have to be a rectangle?”

“Does the length and width of the field need to be integers (whole numbers)?”

Extensions (SPOILER ALERT):
The extension should be led by the child but the optimal solution for this problem actually ends up with a circular field, which requires some grade 5 GCSE mathematics to work out accurately. In terms of primary level mathematics a square would be the best possible solution. However, it is encouraged that you ask the question about whether other shapes could give a greater area as this will give them all the more enthusiasm when it comes to learning about the area and circumference of a circle later on.



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