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.