#### NRICH PROBLEM SOLVING AREA AND PERIMETER

Tiling Age 7 to 11 Challenge Level: These rectangles have been torn. How would you move the bands on the pegboard to alter these shapes? Have a go at creating these images based on circles. What are the possible areas of triangles drawn in a square? All about Area and Perimeter. This is a brilliant way to challenge the misconception that so many year 7s posses.

Making Boxes Age 7 to 11 Challenge Level: Identical squares of side one unit contain some circles shaded blue. How many different squares can you make altogether? Surface Area and Volume This selection of problems is a great starting point for learning about Surface Area and Volume. Compare Areas Age 14 to 16 Challenge Level: Try with other numbers of cubes as well.

On the Edge Age 11 to 14 Challenge Level: Register for our mailing list. Once the first part of this problem was completed, students probldm onto the second part of this problem which is below: Thomas also sent us shapes that have the same area but different perimeters: Shaping It These pictures were made by starting with a square, finding the half-way point on each side and joining those points up.

When you gather the whole group together again, invite them to share not just solutions i. 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.

## Nrich – Can they be equal?

Once the comments had been made I challenged one of the students: 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. Brich problem challenges you to create shapes with different areas and perimeters. Can you deduce the perimeters of the shapes from the information given? Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

perimetter

# Perimeter and Area :

prlblem Surface Area and Volume This selection of problems is a great starting point for learning about Surface Area and Volume.

Pebbles Age 7 to 11 Challenge Level: Could you use it to estimate the area of a shape?

I do truly believe that this activity has a lot of value and I certainly encourage teachers to use this activity. Matthew from Parkgate Primary School focused on the first two shapes in the problem. Isometric Areas explored areas of parallelograms in triangular units. Cuboid Challenge Age 11 to 16 Challenge Level: What will happen if you try the other shapes?

# All about Area and Perimeter :

Thomas didn’t give any units in his solution. Shaping It Age 5 to 11 Challenge Level: Overall, I think this is an excellent activity to undertake in lesson. Measure problems at primary level that require careful consideration. What are the possible areas of triangles drawn in a square? This collection of rich tasks is intended to help you to develop these useful insights into area and splving. If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Can They Be Equal? Sometimes area and perimeter of solvlng are taught separately, and are often confused.

What is the largest ‘ribbon square’ you can make? How many shapes can you draw on the grid which have that area or perimeter?

## Search by Topic

Find the area of the square that could be inscribed in a circle of the same radius. Shape Age 7 to 11 Challenge Level: Cut differently-sized square corners from a square piece of paper to make boxes without lids.

Do they all have the same volume?