Raindrops down windshield is a maze that has students comparing values of numbers.


Start with raindrops on any of the top numbers.


We will start with 856 in the middle. On each move down the windshield choose the largest number one row beneath and touching your raindrop’s current location.  In this example 597, 638, and 404 are the three possible numbers to move to. Which is the largest?


Of 597, 638, and 404 the largest is 638 so we will move there. Repeat. Can the student in the back left of the classroom tell me where the raindrop goes next?


441 is correct. Can Ms. pink headband with white frills tell me where the rainbow goes next.

PS.  I often do not see students frequently enough to remember their names. They don’t mind me referring to their clothing. I joke my way of naming is superior – because they can change their name each day.






Students should be stopped and asked to pose some questions. Two sample questions:

  • Do all the raindrops end up at the same space at the bottom of the windshield? Answering that for each maze would be interesting.
  • We are choosing the largest number each time. If we choose the smallest number each time could we end up with the raindrop in the same space at the bottom?


Students should be stopped and asked to pose some questions. One of the ones that I’m hoping for is:

Do all the raindrops end up at the same space at the bottom of the windshield. Figuring that out is the objective of this puzzle-maze.





Do all raindrops starting at the top end up on 697?

Students might ask what to do if two numbers under your current position are the same. The answer is that I made sure this wouldn’t happen. The numbers are not totally random.

Students in later grades might ask what dimensions of Windshield means that waterdrops starting from the top will end up on the same bottom space half the time.

Raindrops Down Windscreen

(MathPickle, 2016)

Raindrops Down Windscreen gives students practice with ordering numbers. These puzzle sheets give students practice 0-9, 0-99 or 0-999.

Joshua Greene made this clickable version for use in front of our class.

This puzzle inspired Uncut Spaghetti which is one of my favourite pattern discovery puzzles (it’s better than Raindrops down Windshields.)

Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

MP1 Toughen up!

Students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

MP2 Think abstractly!

Students take problems and reformat them mathematically. This is helpful because mathematics lets them use powerful operations like addition.

MP3 Work together!

Students discuss their strategies to collaboratively solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

MP4 Model reality!

Students create a model that mimics the real world. Discoveries made by manipulating the model often hint at something in the real world.

MP5 Know the tools.

Students master the tools at their fingertips - whether it's a pencil or an online app. 

MP6 Be precise!

Students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

MP7 Be observant!

Students learn to identify patterns. This is one of the things that the human brain does very well. We sometimes even identify patterns that don't really exist 😉

MP8 Be lazy!?!

Students learn to seek for shortcuts. Why would you want to add the numbers one through a hundred if you can find an easier way to do it?


Please use MathPickle in your classrooms. If you have improvements to make, please contact me. I'll give you credit and kudos 😉 For a free poster of MathPickle's ideas on elementary math education go here.

Gordon Hamilton

(MMath, PhD)