Skyscrapers

I spent a lot of time thinking about what activity I should do with my grade 10 applied students on the first day of semester 2. I wanted them to be engaged in mathematical thinking, preferably with something hands-on (but nothing that would cause complete chaos!) and I wanted them to work with someone else in the class. What I ended up choosing was Skyscrapers from BrainBashers - here is the link to their site. These are logic puzzles with only a few rules:

A completed board would look like this, where the numbers in the grid represent the height of each skyscraper:

I first learned about these puzzles from Alex Overwijk last year and I'm fairly certain that he heard about them from Peter Liljedahl (I spelled that correctly this first try!). Alex let us try them at our math PD day last year using linking cubes as the skyscrapers.

I set up the skyscrapers ahead of time for my class, using a different colour for each height so that it would be easy to see if they had more than one skyscraper of a particular height in the same row or column. It turned out that I found this feature more useful than them as I circulated and checked their work.

Each pair got their first puzzle and these:

Here is an example of one column. We reasoned through the fact that there is only one way to place the skyscrapers if you can see all 4.

Here are a couple of views of the completed puzzle:

I had printed out 6 different puzzles for them to work through, each on a different colour of paper so that I knew which one they were working. I also had the solutions printed on the same colour of paper to make checking their work faster. I checked the first two and then let them go. I should have printed some harder ones as some groups flew through these. I did have blank ones for them to make their own, but I really think this could have been a much richer experience if they had tried some of the harder ones, like these:

This is what I tweeted out:

What you may not realize is that very few grade 10 applied students ask for more "work", so it was awesome that they wanted more! Day 1 was definitely a success. I got to interact with all my students and see a little of how they think, whether they are able to follow directions easily, and how they work with others. It was a good day and a great start to the semester.