Skyscraper Templates – for Relational Rods

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:


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!

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Zukei Puzzles

A little more than a year ago now, Sarah Carter shared a set of Japanese puzzles called Zukei Puzzles (see her original post here or access her puzzles here).  After having students try out the original package of 42 puzzles, and being really engaged in conversations about terms, definitions and properties of each of these shapes, I wanted to try to find more.  Having students ask, “what’s a trapezoid again?” (moving beyond the understanding of the traditional red pattern block to a more robust understanding of a trapezoid) or debate about whether a rectangle is a parallelogram and whether a parallelogram is a rectangle is a great way to experience Geometry.  However, after an exhaustive search on the internet resulting in no new puzzles, I decided to create my own samples.

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Take a look at the following 3 links for your own copies of Zukie puzzles:

Copy of Sarah’s puzzles

Extension puzzles #1

Extension puzzles #2

Advanced Zukei Puzzles #3

I’d be happy to create more of these, but first I’d like to know what definitions might need more exploring with your students.  Any ideas would be greatly appreciated!


How to complete a Zukei puzzle:

Each puzzle is made up of several dots.  Some of these dots will be used as verticies of the shape named above the puzzle.  For example, the image below shows a trapezoid made of 4 of the dots.  The remaining dots are inconsequential to the puzzle, essentially they are used as distractors.

trap


If you enjoyed these puzzles, I recommend taking a look at Skyscraper puzzles for you to try as well.