The Soggy GrassHopper – A Twist on Zeno’s Paradox

This month we are going to highlight an activity called “The Soggy Grasshopper”, which comes fromĀ Fostering Mathematical Thinking in the Middle Grades with Casio Technology Ish Zamora (@seemathrun), one of Casio’s ACE math teachers has created a whole lesson package centered around this activity, which includes a paper, a YouTube video on using the activity, and I am attaching the PDF of the activity for those of you who want things written out and might be using a hand-held device. Though don’t forget, is a free web-based software where you can do all the math – i.e. calculations, graphing, statistics, writing out explanations….all of which are needed as part of this lesson.


The Problem

A grasshopper is on the ground and notices that it is beginning to rain. It wishes to hop to a spot beneath a tree to get out of the rain. It aims for the tree, but finds it can go only halfway on its first hop. As the grasshopper gets wetter, it finds that it can only hop half the remaining distance each time.

In this investigation, students will explore the grasshopper’s journey.

The Math

This problem involves collecting data, so setting up a table, to collect the numbers of hops and distance traveled and the distance left. Students will look for patterns and write formulas for the fraction of the distance remaining. Students will create scatterplots of their data and use the table and graphs to answer questions about the grasshoppers journey.

The Resources

  1. You can find the PDF of the complete activity here: The Soggy GrassHopper
  2. You can find the paper here: The Soggy Grasshopper (created by Ish Zamora)
  3. You can find the YouTube video on the activity, narrated by Ish Zamora, here: How-To Activity: The Soggy Grasshopper