Skyscrapers
Players: 1 or more
Ages: 6 and up
Cost: Free!
Math Ideas: logical deduction, spatial reasoning
Questions to Ask:
Can you create your own Skyscrapers puzzle?
How can you tell where the tallest towers go?
Sign up for the Games for Young Minds Newsletter!
This week's game is a combination of two of my favorite elements of a game.
First of all, you play with physical, tactile objects that you must analyze with 3-d spatial reasoning.
And secondly, the game is totally free!
The game is called Skyscrapers.
How to Play
I first found Skyscrapers on Mark Chubb's website. Mark is a teacher who is fully on the Spatial Reasoning Bandwagon with me. Expect more of his resources to be highlighted in the future!
Anyway, let's take a look at a 4x4 Skyscraper puzzle. Think of the game board as a city block, full of different skyscrapers. The goal of the game is to fill the board with towers of different heights.
Since it's a 4x4 game, you'll need to build four 4-block towers, four 3-block towers, four 2-block towers, and four single-block towers.
You can make these towers out of LEGO bricks, Cuisenaire rods, or any stackable blocks. Ideally, you can color-code them so that each height has its own color.
To fill in the board, you use the typical rules from Sudoku or any other Latin Square game: each row, and each column, must contain all four heights.
But how do you solve the puzzle? How do you know where to place your towers? You use the numbers that run along the perimeter of the board.
Those numbers tell you how many towers you'd be able to see from a ground-level view, if you were walking past this city block on the sidewalk.
In the image here, you can see two towers in the leftmost row, then four towers, then three towers, then one tower.
If you find a way to place all your towers so that they follow these simple rules, congrats! You've won.
You can find templates for Skyscrapers at Mark's site. He has some larger templates for generic blocks or Unifix cubes, as well as smaller templates for Cuisenaire rods. Many of these pictures come from his very helpful blog posts, so thanks to Mark!
Where's the Math?
Like most Latin Square or Sudoku puzzles, Skyscrapers requires a lot of logical deduction. Your child might be stuck at first, but as soon as they are able to place their first tower, this information helps them deduce the location of another tower, and another. Before long, they've solved the whole thing!
But Skyscrapers has a unique spatial reasoning element: the perspective-taking necessary to view the puzzle from above and from ground-level on all four sides. The interaction between these perspectives is a challenging and fun element of spatial reasoning.
Think of the pyramids at Giza for a moment. From the side, they look like triangles. What do they look like from above? Can you imagine that perspective without flying over the pyramid in a helicopter?
This skill, of imagining 3-d objects from different perspectives, is essential to many aspects of geometric thinking, but it's also a beautiful and magical part of art, design, and engineering.
If your child can mentally place themselves at different perspectives and imagine what an object looks like from that perspective, they will have a much more robust mental framework for thinking about, playing with, and designing 3-d objects.
Questions to Ask
A great way to play Skyscrapers with your kids is to take a single area and discuss it deeply. Let's look back at that game board again.
See that top left corner? There is a 1 above it, and to its left. That means that, if you were standing at ground-level on those 1s and staring at the city block, you'd only be able to see a single tower.
So ask your child "Which towers could be in this spot?"
The beauty of the game is, since your child will have the physical towers, they can try out all their options. They will eventually conclude that only the tallest tower could be in that top left corner. If you placed any smaller tower there, then you'd also be able to see the tall tower farther down the block, and the 1s would be wrong.
Once they've placed a single tower, you can ask them "What new towers can we figure out now?" Usually, each new tower gives you information that can help you place the next tower, and the game progresses until all towers have been placed.
Or, you could switch up the game! Ask your child "Can you invent your own Skyscrapers puzzle?" Give them a blank sheet of paper and see what they come up with!
There are two challenges in this exercise: First, they have to place all the towers using Latin Square rules (the same tower can't appear twice in any column or row)
Secondly, they'll need to correctly identify how many towers can be seen from each perspective. They'll probably end up crouching down, circling the table, and generally doing a whole bunch of awesome perspective-taking.
For a final challenge, you can ask your child "Can you solve a Skyscrapers puzzle without the actual towers?" This is the true master-level game. Without the physical objects, your child will be forced to visualize the towers' relationships with each other entirely in their minds. It's tough, but if they love the normal puzzle, you might print out an easy one for them to solve with just a pencil and their mind.