Many math educators have come to realize how important it is for students to play in math class. Whether for finding patterns, building curiosity, experiencing math as a beautiful endeavour, or as a source of meaningful practice… games and puzzles are excellent ways for your students to experience mathematics.
Last year I published a number of templates to play a game/puzzle called Skyscrapers (see here for templates) that involved towers of connected cubes. This year, I decided to make an adjustment to this game by changing the manipulative to Relational Rods (Cuisenaire Rods) because I wanted to make sure that more students are becoming more familiar with them.
Skyscraper puzzles are a great way to help our students think about perspective while thinking strategically through each puzzle. Plus, since they require us to consider a variety of vantage points of a small city block, the puzzles can be used to help our students develop their Spatial Reasoning!
How to play a 4 by 4 Skyscraper Puzzle:
- Build towers in each of the squares provided sized 1 through 4 tall
- Each row has skyscrapers of different heights (1 through 4), no duplicate sizes
- Each column has skyscrapers of different heights (1 through 4), no duplicate sizes
- The rules on the outside (in grey) tell you how many skyscrapers you can see from that direction
- The rules on the inside tell you which colour rod to use (W=White, R=Red, G=Green, P=Purple, Y=Yellow)
- Taller skyscrapers block your view of shorter ones
Below is an overhead shot of a completed 4 by 4 city block. To help illustrate the different sizes. As you can see, since each relational rod is coloured based on its size, we can tell the sizes quite easily. Notice that each row has exactly 1 of each size, and that each column has one of each size as well.
To understand how to complete each puzzle, take a look at each view so we can see how to arrange the rods:
If you are new to completing one of these puzzles, please take a look here for clearer instructions: Skyscraper Puzzles
Relational Rod Templates
Here are some templates for you to try these puzzles yourself and with your students:
4 x 4 Skyscraper Puzzles – for Relational Rods
5 x 5 Skyscraper Puzzles – for Relational Rods
A few thoughts about using these:
- How will you introduce these puzzles to your students? Would you use the cube version I shared first? How much information about strategies and tips will you provide? Will this allow for productive struggle, or will you attempt to remove as much of the struggle as possible?
- Would you use these as an activity you give all students, or something you provide to just some. Why? (Something for students who finish early or something for everyone to try?)
- How would giving a puzzle to a pair of students be different than if you gave it to individuals? Which were you assuming to do here? What if you tried the other option?
- How might using Relational rods be different than paper-and-pencil or electronic versions? How might it be different than the version with cubes?
- How will you orchestrate a conversation for your class to help consolidate the learning here?
- What will you do if students give up quickly? What questions / prompts will you provide?
A belief I have: Teaching mathematics is much more than providing neat things for our students, it involves countless decisions on our part about how to effectively make the best use of the problem / activity. Hopefully, this post has helped you consider your own decision making processes!
I’d love to hear how you and/or your students do!
Thinking Mathematically 