NRICH Perimeter, Area and Volume Key Stage 3
This list supports teaching of perimeter, area and volume in secondary mathematics. It provides investigations, problems and games from NRICH as well as classroom activities on the STEM Learning website that compliment them.
Here are some of the favourite activities selected by the NRICH team.
- Cuboids Find a cuboid (with edges of whole number lengths) that has a surface area of exactly 100 square units. Is there more than one and if so can you find them all?
- Warmsnug Double Glazing A variety of windows and frames are presented on a grid, together with prices. The challenge is to find out which window has been priced incorrectly.
- Cuboid Challenge A square sheet of paper 20cm by 20cm has a square cut from each corner and is then folded to make an open box. The challenge is to find the maximum possible volume.
- Perimeter Possibilities The investigation starts with finding possible perimeters for a rectangle with an area of 24cm2. The investigation is broadened to consider a rectangle with fractional perimeter but a whole number area.
These are just a few of the activities on Perimeter, area and volume that you can find on the NRICH curriculum pages.
The activities below, taken from the STEM Learning website, complement the NRICH activities above.
Surface Area and Volume
This SMILE resource contains two packs of games, investigations, worksheets and practical activities supporting the teaching and learning of surface area and volume, from counting the number of cubes in a solid to find the volume to finding maximum volumes of a solid.
The materials are useful in preparing students for tackling the NRICH problems on surface area and volume.
Boxes and Bottles
These Cre8ate maths activities explore some of the mathematics behind packaging decisions taken by manufacturers.
'Stock cubes' asks students to design a box to hold stock cubes and poses the question as to which cuboid would they choose. This is a useful activity to use with students to prepare them for the NRICH 'Cuboid Challenge' activity.
'Folding cubes' is particularly helpful in preparing students for the NRICH task 'Cuboids'.
'How much does it hold' is an interesting exercise in estimating capacity.
Boxes
This Study Plus unit from the National Strategies develops an understanding of volume and surface area of 3D objects through exploring nets. The materials are particularly helpful to use in preparation for the NRICH activities 'Cuboids' and 'Cuboid Challenge'.
Simultaneous Equations
One way of tackling the NRICH activity 'Warmsnug double glazing' is to form simultaneous equations.
This Nuffield Foundation resource introduces students to simultaneous equations and demonstrates a rather unusual way of approaching the topic. This would is a useful resource to use prior to students tackling the NRICH activity.
Factors, Multiples and Primes
The NRICH activity 'Perimeter Possibilities' can be tackled by using factors of 24.
This video resource from 'Great Maths Teaching Ideas' provides an introduction to factors and is helpful to use in advance of tackling the NRICH activity. The video begins by defining a factor and then finds the factors of 12 with the aid of a factor bug.
