### Construct-o-straws

Make a cube out of straws and have a go at this practical challenge.

### Matchsticks

Reasoning about the number of matches needed to build squares that share their sides.

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

# Regular Rings 2

## Regular Rings 2

You might like to try Regular Rings 1 before having a go at this challenge.

Below is a picture of an unfolded piece of paper.
Can you work out what shape is made when it’s folded up using the crease pattern shown?

Click below if you want to see the shape.

Can you make one of these shapes with a new piece of paper?

Now make several of the same shape from A4, A5 and A6 pieces of paper in two contrasting colours.

Challenge 1

Make a pattern from your shapes, by laying them on top of each other, that fits both of these rules:
You must be able to see at least part of each shape.
All three shapes must fit inside the perimeter (outline) of the largest shape.

Challenge 2
Use a new large, medium and small shape to recreate the same pattern but in opposite colours from Challenge 1.

Place these two patterns next to each other and continue to fold and add to your pattern until you’ve made a ring.

Can you predict how many of your original Challenge 1 pattern you will need?

We would love to see photos of the ring you make.

#### Why do this problem?

This problem provides the opportunity to develop visualisation skills.  It requires children to solve the conundrum of what happens in between, when they are given a picture of a crease pattern and the finally-folded shape.

#### Possible approach

Just share/project/show the picture of the crease pattern first and allow children to talk about what shape they think it might make when re-folded.

Then share the picture of the ready folded shape (or a real one you made earlier!) and ask children to talk about what they think now.

Give each pair of children a piece of A-sized paper (A4 is easier for smaller hands or beginner folders, but any A size will work) and ask them to try and recreate the shape. They can of course un-do their folds at any point in order to check whether their crease pattern matches the one in the picture.

Here are some examples of regular rings made with pentagons by children at Abbot's Hill School in Hemel Hempstead, which you may or may not wish to share with your class:

#### Key questions

What do you notice about the different types of fold on the crease pattern?
What order do you think the folds were made in?
How could we check what we’ve done so far?

#### Possible extension

Pairs given one piece of A-sized paper could take it in turns to give an instruction whilst their partner carries out the fold.  The instructor must do this with their hands on their hand, (no handling of the paper or pointing is allowed) in order to develop the accuracy of their descriptive and positional language.  Children might be given larger A-sized paper (A3 for example) to act as a model for the rest of the class, as folding with larger paper is more difficult and requires more accuracy.

#### Possible support

Give children a piece of paper each to work with in order to allow them to practise their motor skills more independently.  Then ask them to compare what they’re doing with their partner and to compare shapes for accuracy when they have completed the shape.