Klingon Attack 

The Earth is being attacked by Klingons. It is your job to shoot the enemy spaceships out of the sky using our single ion cannon. Download a pdf of puzzle-sheets here.

Much thanks to Ex Astris Scientia for their permission to reprint their engaging starships.



To save Earth we must fire our ion cannon - starting at the rear of the ship. Ask the students how long they want to wait before they target the upper left deflector. They might say "10 seconds." You re-phase it "time 10" so students understand that this puzzle can be played slowly.

A new student is asked to supply the time for the disk below. At this point, the students do not know the rules. Our first objective in to engage. If you start by trying to teach rules you will lose 10%-15% of the class. You engage students by asking them to contribute...

The next student says "time 15."

The next student says "time 8."

No hands are raised. You methodically go through all students.

The next student says "time 12."

The numbers in the next row must be either the sum of the two numbers behind - or a factor of the two numbers behind. So ask the next student what they want for the number in front of the 10 and 15.

10 + 15 = 25... so 25 is a possible answer.

5 is a common factor of both 10 and 15, so 5 is another possible answer.  (1 would be another possible answer.)

Let's say the student says "time 5."

The next time in that row could be 1 or 23.

Let's say the next student said "time 1."

...and for the last one a student might say either 8 + 12 = 20 or 4 (4 is a factor of 8 and 12), or 2 or 1.

It may need to be emphasized that low numbers are better (I have not told you why yet.) A wise crack student who insists on a huge number (like 1,000,000) needs to be dismissed without giving them attention - and the next student chosen.

The student chooses "time 20."

Just let's skip forward quickly to the end...

So we have finished! How long did it take us? What is the largest time?

Let's say back at this shot we chose differently. We chose the 4. Let's step forward to the end...

So this might look better. It looks like we have 15 as the highest number which might mean that we would save Asia. Unfortunately that would be wrong. What's wrong here?


At time 5 we are confused. "There are two places we have to shoot! The enemy ship penetrates Earth's defences - the Earth is destroyed! Drats."

Duplicate numbers are not allowed.

Negative numbers are not allowed, but zero is allowed (however students might discover something interesting if they use zero.)


Download a pdf of puzzle-sheets here.

Klingon Attack

(MathPickle, 2014)

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)