### NRICH PROBLEM SOLVING AREA AND PERIMETER

Find a cuboid with edges of integer values that has a surface area of exactly square units. I’m thinking of a rectangle with an area of As we approach the first maths GCSE exam of the year, just a reminder that last year I shared a set of breakfast warm-ups that can be used either on the morning of the exams or in the lessons leading up to them. Once the first part of this problem was completed, students moved onto the second part of this problem which is below: Can you find rectangles where the value of the area is the same as the value of the perimeter?

A colourful cube is made from little red and yellow cubes. What will happen if you try the other shapes? Numerically Equal Age 7 to 11 Challenge Level: We started drawing some quadrilaterals – can you complete them? Pick’s Theorem Age 14 to 16 Challenge Level:

If you move the tiles around, can you make squares with different coloured edges? 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. How are they related? Thomas from Colet Court examined the eight shapes which were drawn on the cards. Overlapping Squares Age 7 to 11 Challenge Level: Shape Draw Age 7 to 11 Challenge Level: Understanding how areas and perimeters change as we change a prroblem is important not just problsm but also in solving many real-life problems.

These rectangles have been torn.

## Perimeter, Area and Volume – Stage 3

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off? How have “Warmsnug” arrived at the prices shown on their windows?

This problem offers students a chance to develop strategies for organising and understanding amd up information within the context of calculating areas and perimeters of rectangles. It might also be helpful to nridh post-it notes so that pupils could attach details of area and perimeter onto each card, rather than continually having to re-calculate them.

Some students without prompting soon realised that the width needed to be 2. Shaping It These pictures were made by starting with a square, finding the half-way point on each side and joining those points up.

This is a brilliant way to challenge the misconception that so many year 7s posses. Different Sizes Age 5 to 11 Challenge Porblem What could its perimeter be? To which my reply simple is, is a fraction a number?

Are these statements always true, sometimes true or never true? Area and Perimeter What can you say about these two shapes?

Making Boxes Age 7 to 11 Challenge Level: Have a go at creating these images based on circles. Ribbon Squares Age 7 to 11 Challenge Level: In which of the four examples is the shaded area greatest? Finally, it stimulates good conversation about the properties of squares and rectangles and challenges that common misconception that year perumeter can posses, that a square is not a rectangle.

These rectangles have been torn. Triangles in a Square Age 11 to 14 Challenge Level: Leave a Comment Cancel reply.

# Area and Perimeter :

Wallpaper Age 5 to 7 Challenge Level: What happens to the area and volume of 2D and 3D shapes when you enlarge them? Cylinder Cutting Age 7 to 11 Challenge Level: Age 11 to 14 Challenge Level: After going through 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.

You could start with the whole group looking at the two shapes given at the beginning of the problem and nrichh learners to talk about anything they notice.

Can you find them all?