Route to Infinity

Why I like this problem: It is a great review of coordinate plane attributes. Many avenues can be taken to solve the problem, and the questions of increasing difficulty make it ideal for all levels of thinking.

Observations from class: Seeing the animation on the Nrich maths website was very helpful to students. Without it, some of them thought that the path remained in the 6X6 square pictured in the poster. Seeing the animated version showed students that the area covered was not restricted, and extended to coordinates (1,7) and (7,1) and so on. A lot of students were intimidated by the last task of finding the 1000th coordinate and did not attempt it. They enjoyed trying to figure out the patterns of the points that will be reached.

Follow-up questions I asked: 

1. What patterns do you notice?
2. Can you find a system that will allow you to predict the nth point that will be crossed?

Required skills / content: Understanding of how coordinate planes work.

Links: PNG / Google Doc

Source: https://nrich.maths.org/