Round Tower Drill and Kill, is not a typical MathPickle’s puzzle-sheet. It helps with multiplication speed memory.

If students have most of the multiplication table already memorized*, they compete in pairs – One student is defensive the other offensive. They both get identical puzzle-sheets (downloadable at the end of this slide show). The defensive student must try to find the protective ring around the round tower – skip counting back and forth through the multiplication table…

*If students are not as strong they work collaboratively to find this defensive ring around the tower.


For example – this defensive player here must use the multiplication table for the number seven…


14… 7… 14… 21… 28… 35…  is acceptable.

14… 7… 0… 7… 14… 14… 21… 35… is not acceptable because each skip must be by exactly 7.


Here the loop has almost been completed, but the student will need to double back…



Meanwhile – the other student is trying to break into the tower as many times as possible before the first student completes their loop. This second student has the disadvantage of not knowing which numbers (1-12) to use…

This is a lot harder. Students just learning addition should ONLY play the defensive role.


Here is an example of 8 being used to breach a large section of the outside wall…


Here are all six of the breaches. They use the numbers 4, 5, 6, 8, 9, and 11.

There is no need to identify winning conditions precisely unless you want to. The students just need understand that one is trying to make a protective loop before the other can breach the wall too much.


One last thing. Each puzzle has a single block on the exterior that cannot be breached. If you are pitting a weaker student (the defensive player) against a stronger player… make it so the stronger player MUST find this single brick.

Download puzzle-sheets with and without multiplication tables here.


Round Tower – Drill and Kill

(MathPickle, 2015)

Joli Barker’s photo of a round tower being stormed.

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)