# Year 7 Enrichment

## Networks

The worksheets are available to download.

The answers are available for you to check your solutions.

Part 1
Part 2
Part 3
Part 4
Part 5

The activities at the end of sections 1, 2 and 3 are detailed below.

### Part 1 - Möbius Band

Follow the
instructions down to number 5 from http://pbskids.org/zoom/phenom/mobiusstrip.html.

Now try the ‘Cutting
Tricks’ section from http://math.cofc.edu/mobius.html.

There is a little
information on Mobius strip uses at http://scidiv.bcc.ctc.edu/Math/Mobius.html.

There
is a larger version of the classic piece of artwork here http://www.worldofescher.com/gallery/A29L.html

Try
searching for Möbius using http://www.google.com.

Now record what you have learnt about the Möbius Band. Ask your teacher for
some paper to produce a poster, so you can tell others the weird and wonderful
properties of the strip.

### Part 2 - Three-dimensional solids

We'll use the five 'Platonic solids'. There are interactive pictures at http://mathworld.wolfram.com/PlatonicSolid.html.
(or http://www.3quarks.com/GIF-Animations/PlatonicSolids/
if the pictures don't work). Try to use the pictures to count how many faces,
edges and vertices (corners) each of the shapes has. Put your results in a
table.

Now check your answers using http://www.enchantedlearning.com/math/geometry/solids/.
How are the three numbers connected? How does this compare with networks?

As you did with Part 1, you can now record your findings. A display with the
five solids and the relationship between faces, edges and vertices would be
ideal. The link http://www.enchantedlearning.com/math/geometry/solids/
has printable templates for making the solids, your your display could become
three dimensional!

### Part 3 -The Bridges of Könisberg

Follow this link http://mathforum.org/isaac/problems/bridges1.html
for a little background on the problem. You should be able to convert the river
and bridge diagram to a network and solve the problems (Problem 1 and 2) using
what you've learnt about traversable networks. (There is some help in the
conversion here http://math.youngzones.org/Konigsberg.html,
this site also has links to some useful background information for your write
ups.).

The final task is your write up. A display of what the Bridges problem is,
and a little about its history and how it can be solved so that others can share
what you've found out.