### NRICH PROBLEM SOLVING AREA AND PERIMETER

P is 16 , a is 9 Thomas didn’t give any units in his solution. Matthew from Parkgate Primary School focused on the first two shapes in the problem. Isometric Areas explored areas of parallelograms in triangular units. Cylinder Cutting Age 7 to 11 Challenge Level: Start with the smallest. Are these statements always true, sometimes true or never true?

So I continued to press on, is that the only defining feature of a rectangle? How can you change the perimeter but keep the area the same? Used a reflection worksheet by Don Steward this week with my year 7s. This problem combines both area and perimeter by inviting students to consider the different possibilities for the perimeter when the area of a rectangle is fixed. Pick’s Theorem Age 14 to 16 Challenge Level: When these students were confident that they could use a decimal they were soon on their way. Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Pythagoras for a Tetrahedron Age 16 to 18 Challenge Level: Perimeter Possibilities Age 11 to 14 Challenge Level: This problem offers students a chance to develop strategies for organising and understanding mixed up information within the context of calculating areas and perimeters of rectangles.

Can prob,em find them all? It also encourages students to realise that unless a question stipulates that an integer must be used then they can use an array of numbers and hopefully build their confidence with these numbers. Area and Perimeter Age 7 to 11 Challenge Level: Keep adding as few pebbles as necessary to double the area. The perimeter is always bigger except for one Shape G.

Age 7 to 11 Perimdter Level: At the end of the allocated time for the task I asked the students to share their findings. If all the vertices must have whole number coordinates, how many is it possible to draw?

# Nrich – Can they be equal? – Mrs Mahoney

Is there more than one? Can you work out how they arrived at these prices? Matthew from Parkgate Primary School focused on the first two shapes in the problem. But can you work out how many of each? Thomas went on to investigate how to make the area of a shape go up but the perimeter go down.

Shape Draw Age 7 to problfm Challenge Level: Exit tickets — Plenary idea. To find all possible solutions they will need to work systematically. Register for our mailing list.

## All about 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.

A colourful cube is made from little red and yellow cubes.

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Understanding how areas and perimeters change as we change a shape is important not just mathematically but also in solving many real-life problems. These pictures were made by perimster with a square, finding the half-way point on each side and joining those points up.

solvin What could its perimeter be? Measure problems at primary level that may require resilience. What are the dimensions of the rectangle? Register for our mailing list. Can you find rectangles where the value of the area is the same as the value of the perimeter? These rectangles have been torn.

## Area and Perimeter KS2

This problem challenges students to work systematically while applying their knowledge of areas of rectangles. Do they all have the same volume? You could investigate your own starting shape.

Shaping It Age 5 to 11 Challenge Level: Identical squares of side one unit contain some circles shaded blue. Perimeter Challenge Age zrea to 14 Challenge Level: