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.
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.
I am trying to tell my 15yr old daughter that an elective high school credit in Graph Theory would be fun next year. Of course I do this as subtly as possible – I start drawing coloring sheets for this post on my iPad and then carefully shade them in. All three of my children slowly sneak up behind me and breath in my ear.
“You know that it will never take more than four colors” I state.
“Really?” I hear my oldest daughter say with a sense of wonder in her voice. “Can I make one?” she asks reaching for my device.
She takes over the iPad. I go for a run. I clean up a bit. She is still designing, thinking, coloring. A wave of gratitude flows over me “Thank God that coloring isn’t just for kindergarten.” We are so blessed to have the abundance and time to be able to color, play, and contemplate.
She finishes her design. “It looks like the beautiful cobbles on our Oregon beaches.” I think, then say.
“That’s what I was going for.” She says. Then gets up and goes back to her school work.
This week I challenge learners to play with coloring sheets. Make your own. Share them. Color them. Contemplate them. Can you restrict the coloring to four colors? It may take some problem solving for more complex sheets.
In graph theory, there is the study of graphs that are made up of nodes (vertices) that are connected with lines (edges). Create a graph for one of your coloring sheets, where the regions are nodes and lines connect the regions that touch.
You could also create a graph with nodes and edges and then the coloring sheet to go with it.
Below are a couple examples (some blank for you, my readers, to use):