There are only four slides in this compact presentation so before heading on to the next one, your students and you should study the image and come up with conjectures about how the images are created and what to expect on the next slide. This first slide has too little information to speculate wisely… so start speculating with the next slide.

This is an example of a mini mathematical universe. It is to be used to teach the scientific method in the math classroom.

Download the high resolution pdf here.

What is going on here?

Your students and you should make conjectures about what is going on and what will appear on the next slide.

List observations from your class. Here are examples, but do not show them these (download the pdf here.) Examples:

  1. All twenty of the images are composed of four squares.
  2. All squares in an image lie on a vertical axis.
  3. If squares intersect – they intersect at two points – never an edge.
  4. These are Venn diagrams.

The last student idea is wrong, but you would put it up on the board for discussion without passing judgement. What do your students expect on the last slide? Perhaps students will manage to predict the bottom left figure? Maybe the whole left column which will have 10 figures.

Look at the vertical axis going through each clump of squares. It is intersected at regular intervals by exactly one square. Did your students find that? More difficult by far is to figure out how the squares are organized.

Square Dance

(MathPickle, 2016)

This mini mathematical universe is used to get your students generating and discussing true and false conjectures. Make sure to reward true AND false conjectures. If students are hesitant to come up with false conjectures you should suggest your own or prod them into making one.

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!

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

MP3 Work together!

This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

MP6 Be precise!

This is where our 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!

One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.


Please use MathPickle in your classrooms. If you have improvements to make, please contact us. We'll give you credit 😉

Gordon Hamilton

(MMath, PhD)


Lora Saarnio