# NRICH PROBLEM SOLVING AREA AND PERIMETER

Isosceles Triangles Age 11 to 14 Challenge Level: Fence It Age 11 to 14 Challenge Level: What actions could they perform on a shape without changing its perimeter? Cubes Age 7 to 11 Challenge Level: Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle.

Area and Perimeter What can you say about these two shapes? I’m thinking of a rectangle with an area of Shaping It These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. How many shapes can you draw on the grid which have that area or perimeter? I think students need to realise that there is a whole range of numbers out there not just integers and start to realise that fractions, decimals, surds etc are all just numbers. Through the Window Age 7 to 11 Challenge Level: I want my students from early on to realise that these things are numbers and to feel comfortable working with them.

# Nrich – Can they be equal? – Mrs Mahoney

Tilted Squares Age 11 to 14 Challenge Level: One answer given was a 6 by 3 rectangle which all of my students accepted and said yes they agreed this was indeed an answer. Age 11 to 14 Challenge Level: Areq Squares Age 7 to 11 Challenge Level: If you move the tiles around, can you make squares with different coloured edges?

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Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle.

In how many ways can you halve a piece of A4 perimeeter Keep adding as few pebbles as necessary to double the area. I think students need to realise that there is a whole range of numbers out there not just integers and start to realise that fractions, decimals, surds etc are all just numbers.

## All about Area and Perimeter

All about Area and Perimeter. My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you find rectangles where the value of the area is the same as the value of the perimeter? Matthew from Parkgate Primary School focused on the first two shapes in the problem. You could investigate your own starting shape.

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How many different squares can you make altogether? These practical challenges are all about making a ‘tray’ and covering it with paper. These rectangles have been torn.

Different Sizes Age 5 to 11 Perrimeter Level: Overall, I think this is an excellent activity to undertake in lesson. How have “Warmsnug” arrived at the prices shown on their windows? Can you draw a square in which the perimeter is numerically equal to the area? The first part of the problem is below: How many extra pebbles are added each time?

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Area and Perimeter What can you say about these two shapes?

Identical squares of side one unit contain some circles shaded blue. Bashayer from Kingsbury Green Primary also found this solution. Working on this problem will give students a deeper understanding of area and perimeter, and how they change as a shape is altered. Fitted Age 7 to 11 Challenge Level: In a right-angled tetrahedron prove that the sum of the squares of the areas of the probelm faces in mutually perpendicular planes equals the square of the area of the sloping face.

This problem combines both area and perimeter by inviting students to consider the different possibilities for the perimeter when the area of solvkng rectangle is fixed.

# All about Area and Perimeter :

Thomas didn’t give any units in his solution. Isosceles Triangles Age 11 to 14 Challenge Level: Register for our mailing list. Pick’s Theorem Age 14 to 16 Challenge Level: Can you rank these sets of quantities in pegimeter, from smallest to largest?

You could investigate your own starting shape.