# NRICH PROBLEM SOLVING AREA AND PERIMETER

Can you find rectangles where the value of the area is the same as the value of the perimeter? This problem challenges students to work systematically while applying their knowledge of areas of rectangles. Blue and White Age 11 to 14 Challenge Level: Can you rank these sets of quantities in order, from smallest to largest? 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. What is the largest ‘ribbon square’ you can make?

Read more at https: How can you change the area of a shape but keep its perimeter the same? This problem allows students to consolidate their understanding of how to calculate the area of irregular shapes, while offering an opportunity to explore and discover an interesting result. Measure problems at primary level that require careful consideration. Shaping It These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. Pairs could then explore the shapes on the remaining cards and you can challenge them with the specific questions given in the problem itself.

Brush Loads Age 7 to 11 Challenge Level: After going perumeter one basic example of how to find the area and perimeter of a rectangle and how I wanted them to set the work out, I introduced them to this problem. Understanding how areas and perimeters change as we change a shape is important not just mathematically but also in solving many real-life problems.

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# Perimeter and Area :

Through the Window Age 7 to 11 Challenge Level: Once the comments had been made I challenged one of the students: Shape Age 7 to 11 Challenge Level: Perimeter Possibilities Age 11 to 14 Challenge Level: Pick’s Theorem Age 14 to 16 Challenge Level: This problem allows students to consolidate their understanding of how to calculate the area of irregular shapes, while offering an opportunity to explore and discover an interesting result.

Can you help William to work out its area?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. These pictures were made by starting arwa a square, finding the half-way point on each side and joining those points up.

## All about Area and Perimeter

Can you provide convincing evidence for your rankings? Torn Shapes Age 7 to 11 Challenge Level: What are the possible areas of triangles drawn in a square?

Have a go at creating these images based on circles. Age 7 to 11 Challenge Level: Register for our mailing list.

# Area and Perimeter :

To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. If you move the tiles around, can you make squares with different coloured edges?

Fence It Age 11 to 14 Challenge Level: This problem challenges students to work systematically while applying their knowledge of areas of rectangles. How have “Warmsnug” arrived at the prices shown on their windows? If all the vertices must have whole number coordinates, how many is it possible to draw? A task which depends on members of the group noticing the needs of others and responding.

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An activity for high-attaining learners which involves making a new cylinder from perieter cardboard tube. Fitted Age 7 to 11 Challenge Level: Investigate how the four L-shapes fit together to make an enlarged L-shape.

Fence It Age 11 to 14 Challenge Level: This problem encourages students to use coordinates, area and isosceles triangles to solve a non-standard problem. Area and Perimeter Age 7 to 11 Challenge Level: Once again students got to work trying out different rectangles and trying to find the answers.

Perimeter Challenge Age 11 to 14 Challenge Level: In this problem students consider the relationship between them. How many squares did each one have inside it before it was ripped? Here we explore areas of triangles Perimeter Challenge Age 11 to 14 Challenge Level: