Q:

Introduction to Topology for 11 year olds

I am planning a 1-hour lesson for a group of 20 11 year olds. I would like to expose them to topology, as an area of research-level mathematics that could be accessible to them. I want to convince them that maths can be visual and beautiful!
The pupils are struggling in Maths (for example are not confident with negative numbers, decimals, algebra, graphs). So an introduction to topology that requires as little machinery as possible would be ideal.
I am thinking of discussing some of the following:

Genus
Definition of manifold (see Teaching manifolds to high schoolers for an existing discussion on this)    
triangulations (How can I demonstrate triangulations of surfaces with real hands-on objects?). Any tips on how to help pupils with the difficult task of accurately counting objects when exploring triangulation on difficult surfaces would be appreciated.  
Homotopy type (group letters in alphabet or various types of food up to homotopy class)

If you have tips or knows of any existing resources then I look forward to hearing from you! In particular, any tips on how to build models or use everyday objects (tasty donuts) to illustrate ideas.

A:

You could explore maps such as the London Underground where the actual distance and locations of stops are unimportant only their relationships. Perhaps this could be turned to a practical lesson somehow? Kids with playing the part of stations and holding string?  Design a similar map of their home city? Ranking maps? What makes a good map? You could take the theme in many different directions and return to a real world application.

A:

Two ideas.
(1) Form a Möbius strip out of paper. And then cut it down the middle.
Restart and cut it at a third of its width. See, e.g., "Explanation for cutting a Möbius strip at one-third its width."

     

     

(Image from Kidzone.ws.)

(2) You already cited the previous question about triangulated surfaces,
presumably for verifying Euler's $V-E+F=2$.
In the absence of (expensive) construction materials (like polydrons), you could fold polyhedra
from nets, e.g.:

     

     

(Image from Minieco.co.uk. Note the tabs for gluing.)

A:

Thanks everyone for your tips! I thought I would share what we decided to go for in the end.
We had far more material than this (it naturally extends to the investigation into mobius strips, but in an hour this is a good amount of material. Even for top set Year 8 students, who we also did this lesson with in the end).
What surface is the game "snake" played on?

As a class on the projector, we played snake, both with the walls turned "on" and "off".
After discussion of what shape the snake might be living on when walls are off (consensus was it was a sphere), pupils each given strip of paper, told to attach one pair of opposite sides together (first predict, and then do - hard to work out it is a cylinder in advance!) What would this correspond to in the snake game?
Next, pupils did "cross activity" see 5.13 in video, after good discussion on what might happen when we cut along the centre of each loop (how many bits will the paper fall into? what shapes will we see?)
Played a video, pausing it before giving the game away.
At this stage (same point in the three lessons we did with different pupils), pupils able to work out living on doughnut (we didn't call it a torus). 
Lesson finishes with one pupil travelling as a snake around a square, while teacher mirrors the movement on an inflatable ring (this allows for a dramatic unveiling of the inflatable ring from its hiding place - nice)

