1. On which blade of grass will the grasshopper land on the spider’s web?
Shared by John Scammel, Learning Through Problem Solving - February 11, 2011 session at the North Central Teachers’ Convention
Teacher’s Notes: This problem should LEAD the lesson – let students work together, struggle with the problem and, after working on it for 5-10 minutes, share the methods they used. Present a short lesson on a strategy that makes solving this problem easier.
Source: Andrew Shores at

2. Problem Extensions
Can the grasshopper start on any particular number (not counting shaded boxes) and be safe by taking hops of 4?
What if it took hops of 5? 6? 7?
What if the spider webs were on perfect cubes? What if they were on triangular numbers? Fibonacci numbers? etc.
Source: Andrew Shores at

3. Grasshopper Problem Debrief
What mathematical concept is covered in this problem?
What methods worked well for you?
Where did you struggle?
If you were to solve a similar problem again, what would you do differently?