The City (Unit)

Main Concepts


Direct Proof, Contrapositive Proof, Proof by Contradiction, Proof by Cases, Pigeon hole principle

Cardinality of infinite sets…


Individual activities may take as little as 10 minutes. (Kahoot: 25 minutes / Unjumble activity 10 minutes / Mindmap 4-8 hours) The unit as a whole requires about 8-10 weeks.

Summary of Activity

Teaching and learning is often a linear process where teachers and students discover concepts in a pre-determined order. In this unit about proof techniques, I attempted to break that linearity and let students choose their path more freely. I did my best to analyze the different orders that sections in the “Book of Proofs” by Dr. Hammack could be learned, and ended up with a general diagram. Have a look at the file “Diagram (Sections)” to get an idea.

In addition to this diagram, I imagined that it would be more palatable for student if there was a form of storyline, so in this unit students impersonate a tourist visiting a foreign city. Each section is associated with a “tourist sight” in the city… You can see the city arrangement in the second diagram called “Diagram (City)”. The first two locations are compulsory, but after that students are allowed to visit the city in the order they wish. Each time they pick a location, they are exposed to the material in a way that corresponds (more or less) to the location, and they are assigned a variety of tasks that they can complete independently. As a result, each student may be studying the material in a different order. At any given time, each student might be learning about a different section. The tasks allow for independent work. (Our students here at KIS are usually very disciplined and organized, especially those who ) Before moving on to the next location, a student always has to check in with me. Obviously there are some graded formative and summative assessments sprinkled around too.

Notes and Insights

The Intro pages linked above are samples of what a city location looks like, with the storyline, content and list of tasks students need to complete before moving on to the next one. 

Contact me if you want more information and more documents about this unique unit.