Midair Maths and a Marvellous Mistake

On the fourth week of maths club my teachers gave to me: four miles of line, three piles of rocks,

 two logic puzzles, and information on a dead genius!

Today in Maths club we made a giant number line. The students were each assigned an odd number and wrote it in the middle of a piece of paper. Then they taped their papers together in order and wrote the even numbers over the cracks. This ensured that all of the whole numbers were evenly spaced:

They eventually added halfs and negative integers:

The finished product was very, very long:

Then we jumped! I can only jump by 5's but some students can jump by 10's!

If you look closely at the above picture you will notice the biggest learning opprotunity (a.k.a. mistake) made during the creation of the line. The team assigned to making the negative integers originally made them in the order "-1, -2, -3..." rather than "-3, -2, -1...", etc. To affix them to the rest of the number line they had to realize their error and turn the whole negative part upside down. That is exactly the kind of productive negative experience that, taken as a challenge and approched creatively, leads to a rich understanding of concepts. I felt like I was inside my Philosophy of Education textbook!