Games don’t have to be complicated to require some good thinking skills. We all learn tic-tac-toe when we are younger. We soon learn how to always come to a stalemate with an equal opponent. Once you get the strategy, it can get a little boring… But what if we add a layer (or two) of moves. What does this do to the strategy of the game? Is it so easy to predict your opponents next move?
This week I recommend learners create a tic-tac-toe board that has tic-tac-toe boards in each square. Here is a video of how to play:
My learners contemplated:
How many times can you nest the game before it’s too complex?
With each layer added, how much longer and more difficult would it be? (how many moves are there?)
How is this like a fractal?
Could you keep a game going with one move a day for how many days with 2-nested?, 3-nested, 4?
What does the game tree look like?
How many ways can you play tic-tac-toe vs ultimate tic-tac-toe?(think combinations). What is the combinatorics calculation look like for this?
If you are wondering how I was able to do this in the time of Covid… I use a digital white board and label squares so it is easy to say the next move. You can also use a shared google drawing or a google spreadsheet to play (here is one for you.)
Another blog (Games for Young Minds) that does a great post on this game is here. Math with Bad Drawings also has a great post here. As you can see, this is a fun game with us mathy folks everywhere.
After teaching this a few times this week, I created a video for those that missed it or want to go back. We made two different origami toys that have some flipping fun. Feel free to contact me if you have any questions.
After teaching this a few times this week, I created a video so those that may want to pause and draw at their own pace while playing with isometric paper. Feel free to contact me if you have any questions. I love doodling on Isometric paper – enjoy! Here is a link to the isometric hands-on math activity and here is the paper.
Let’s get out our pencils, isometric paper, and thinking caps this week! Isometric drawings are often used in engineering and design as a way to display 3D ideas. They can also be used to create optical illusions and escheresque works of art.
To start, print some isometric paper, or set your digital drawing program to isometric drawing guides. Start by drawing simple objects, like a cube, and play with shading.
Once comfortable with basics, start making skeletons for shapes, linking sides that don’t make physical sense, and thinking about objects that would allow you to go up and down at the same time. Below are some examples and videos to play with:
Sometimes the simplest things have wonder hidden within. This week, learners can play with the angles of polygons. How many degrees are in a triangle? In a quadrilateral? In a hexagon? Is there a pattern?
Here is a warm-up activity:
Draw a triangle (any triangle), and cut it out.
Next, rip the corners off:
Now, here is the fun part… put the pointy angles together. What do you get? Try it with lots of triangles and see if you always get a straight line. Rather than lecturing or telling learners that triangles have 180 degrees (or pi radians), let them discover. They can even create art ( I like to make my angles into perspective path doodles.)
Now do the same with a four sided shape. What do you notice? Is it the same for all the ones you can create?
Now do the same with 5, 6 or more sided shapes. There is a rule to be found. Try to discover it if you don’t know. I will put the rule at the bottom of this post.
I did this twice last week with virtual classrooms through the Covid-19 isolation. Students from kindergarten to middle-school ate it up. We used it as a warm up activity (10-15 minutes) prior to doing some loop-doodle math and/or other activities.
The rule for simple polygons is that for n sides there are 180(n-2) degrees. Or you add 180 degrees every time you add a side.