Seeing through these problems

At our school in Toulouse, the classrooms have one wall that is almost entirely glass and big double glass doors on the opposite wall. This makes for a lovely light a spacious room but sometimes leaves us short of wall space! Imagine then my delight and discovering 'Window Markers!' My classroom walls are now becoming adorned with lovely maths problems! Here are a couple of problems that are on the door at the moment....

Can you solve the problem on the door of P5? #istlive pic.twitter.com/HnHkSMub8J
— Mr Noble (@MathsinP5) November 18, 2014

I am sure many have seen this problem before, but Mathematics is never going to run out of things for us to spend more time looking at. I picked this up from a friend's daughter's homework they were asking me about. The problem has a couple of particular fascinations for me based on playing with it myself and putting it on my classroom door.

1. That there are some quite different ways to approach it
2. That there is significance difference between asking students or a particular unknown length and a more general 'given the diagram, what else can you tell me that is true?' approach

That last thought has occupied me for a while....

Here is another one!

Another problem on the door of P5 #istlive pic.twitter.com/W5J9nblp1U

— Mr Noble (@MathsinP5) November 19, 2014

This took even more thought! and even prompted +Simon Gregg to write this blog post when he first saw it!

No solutions here as that would spoil the fun!