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.

https://www.geogebra.org/graphing/x6k9wnag

Week 2: Spiral of Theodorus

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This week the Spiral of Theodorus can be used to enhance understanding of the pythagorean theorem, right triangles, pi, and more. The spiral goes by many names (square root, Pythagorean, or Einstein Spiral) and approximates the Archimedean Spiral.

Stop animation of sketching process

Instructions:

1.) Create a right isosceles triangle where the sides that are the same measure 1 unit (I used inches).

2.) Add a 1 unit line segment perpendicular to the hypotenuse of your first triangle and then connect it to create another right triangle.

3.) Add another 1 unit line segment to the hypotenuse created in step 3 and connect it to the center to create another triangle.

4.) Repeat step 3 as many times as you wish to expand your spiral.

5.) When your done, you can transform your work into a fun sketch:

Possible reflection/discussion questions:

  • How does the Pythagorean Theorem apply here? What pattern do the hypotenuses make?
  • Can you create a function that would reflect the rate of growth for the hypotenuses?
  • There are so many ways to say “right angle” – can you say it three other ways?
  • Can you create an algorithm for making these spirals?