Week 32: Isometric Drawing

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:

Opal’s sketch (13yrs old)

Week 24: Pastel Diagrams and Plots

Hyperbolic Paraboloid

Sometimes math diagrams, plots, and examples can be a little dry in our books and on the board. This week learners will be taking a diagram or plot that they want to improve upon and sketch it up with pastels, paints, or other media. Color, composition, and artistic embellishments can be added while, keeping the overall concept in tact. Ask them what a math textbook would look like if they created it. Would you have a cheshire kitty in the mix? Would you turn each chapter in to a different land or island?

These sketches don’t have to be fancy, I recommend small pieces of paper and having fun with it (most of these are around 3×5 inches and took a few minutes.) Most of all – have fun!

Binary, powers of two, exponential…
D6, cube, hexahedron, volume, probability…

Week 22: Tessellations – Paper Method

This week we will do tessellations that fit together through translation (moving without rotation). We will look at reflection and rotation in other weeks. There are a few different ways to do this, but we will use the paper method today. I always start the class by talking about what different kinds of shapes can tessellate (triangles, trapezoids, hexagons, rectangles, etc.). We look at the tessellations around us (bricks, floor tiles, fabrics, etc.)

If you have never made a tessellation before, the easiest way is to use a rectangle sheet of paper, with a pencil, scissors and tape. Here are the instructions:

  • Step 1: Sketch a curve that stretches from the bottom left to the bottom right corner of your rectangle
  • Step 2: Cut out your curve and move it to the opposite side of your rectangle. Tape it together as perfectly as you can.
  • Step 3: Sketch a curve from the top left of your rectangle to the bottom left.
  • Step 4: Cut out the curve on the left and then tape it to the opposite side (again as perfectly as you can).
  • Step 5: Trace your shape on a sheet of paper and add some fun details:

Week 16: Geometric Sketching – Hummingbird

I love to incorporate drawing skills into math education. This week I encourage learners to start seeing birds (or other animals/people) as shapes. Heads are circles, torsos are ellipses, beaks are triangles, wings are long ellipses…

Sketching is a skill. A skill is something that you can master in time (think growth mindset). This week I challenge learners to start a daily doodle routine. Just doodle something (anything) for 1-2 minutes a day.

Here is an example of the activity. I will use a hummingbird as guidance, but please feel free to pick any object/bird/animal. I tried to do this as a quick sketch example:

Some of the concepts and discussions around sketching can include proportions, ratios, what shapes fit best, etc. I encourage learners to research and dive deeper into sketching skills and drills. I truly believe that art and spatial awareness can be beautifully integrated into learning math.

Additional activity: For high school students in Algebra 2 or higher, they can use Geogebra to sketch the shapes for an animal. How do you plot a circle? an ellipse? triangles? etc. Desmos can be used at a precalculus and calculus level.