### A Chain of Eight Polyhedra

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

### Magnetic Personality

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

### Lighting up Time

A very mathematical light - what can you see?

# Cut Nets

##### Stage: 2 Challenge Level:

Hallie and Moira from Southbury Elementary in the US sent us the following:

When solving this problem, we found it easiest to look for similarities between the nets.  One of the most obvious pairs were nets ‘e’ and ‘k’ because they are the same shape, each with 3 squares of the same size, so you could infer that when folded into their 3-D forms they will form a cube.

Another easier one was ‘c’ and ‘p’, because they have rectangles that have the same dimensions as each other. You could use this strategy (looking for equivalent dimensions) for other pairs too such as ‘b’ and ‘f’, ‘l’and ‘m’, ‘n’ and ‘d’, and ‘o’ and ‘s’.

For sets like ‘r’ and ‘j’, ‘h’ and ‘a’ and ‘g’ and ‘q’, you find more similarity between the regular polygons such as the pair of trapezoids or hexagons.  We also find it interesting that about
half of the nine figures are pyramid shapes and about half are prisms.  We found it helpful to make a list and use process of elimination.  We also cut out the shapes and folded and taped them to check our answers:

Brandon and Rebecca from Oakwood Academy send in the following picture:

This is what their teacher wrote:

Two of our pupils at our SEN school have done really well with this challenge. They were given some support due to the nature of their learning needs.

Mia and Isabelle , from Fordingbridge Junior School, wrote

First we looked for similar 2D shapes and gently folded them to see if they created one of the finished 3D shapes. Then if it worked we would experiment to find out how the net would be put together. If it didn’t work we would choose another piece of net with similar 2D shapes until we
found one that worked.

With the last few shapes we looked at how many sides the main shape, like a square, hexagon, pentagon or trapezium had and found another piece of net that could cover all of the sides. For example to find out that A and H worked we looked for two pieces with trapeziums on. Then we gently folded them together and it formed a 3D shape.

We also had a number of solutions sent in from Cromer Junior School; namely Amy and Grace, Jacob, Owen and Ashley, Glen and Toby, Noah, Shannon, Aleesha and Brandon. Thank you for your good solutions.

Finally, Mr Arnold  from The Gerrards Cross C of E School  wrote:

Hi there. My class really loved working on Cut Nets. The attached file contains workings, reasoning and explanations on what they found, which they wrote themselves in small groups.

The Gerrards Cross C of E School.docx or The Gerrards Cross C of E School.pdf

Thank you everyone who sent in a solution. Keep up the good work and please send in further solutions to future live problems!