Octahedrons are such a fun shape. This week we are going to learn an important fold in origami that can be used to make so many mathematical shapes, puzzles and works of art. We are going to learn Sonobe. Below is a video of how to create the basic fold and then assemble the octahedron. You will need 12 sheets of origami paper. I have done this project with 7yrs and up. My high school students have folded in teams to make larger polyhedra. In future weeks we will be making other structures and sonobe will be an option.
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.
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?
Welcome to 52 weeks of math! I will be posting a new activity every Wednesday for 52 weeks of hands-on math. Week 1 is one of my favorites – drawing with thread.
In this activity, learners will play with their rulers (or thread) to create curves with lines. The idea is to have students draw straight lines close together with various slopes to create curves. For younger ages anything goes! For middle school and up, it is a great intro into lines and the Cartesian Plane. Below is an algebra video I made for a class back in 2016. It gives you the basic idea. I also have modifications and additional ideas below.
Possible reflection questions:
Line segments – what are they? How many points do you need to make one?
What is a tangent line? What can have a tangent line?
Do the distances change with each line? Why?
Middle school (use the questions above as well):
What is slope-intercept form?
How can you change the outcome of your art if you change the axes of the graph to have angles other than 90 degrees?
How does the slope change? What observations can you make about the ratios?
How do the slopes change when a quadrant’s set of lines is reflected over an axis?
Algebra (use the questions above as well):
Is there a pattern to observe if the lines are written in standard form or point-slope form?
What type of curve do you think you have approximated?
Can you write a function for the change in slope?
Geometry (use the questions above as well):
When creating reflections over an axis, are there any patterns with sets of parallel or perpendicular lines?
Can you write a function for the change in distance for each line?
Where do you see rotational symmetry, translations or reflections in you art?
Trigonometry (use the questions above as well):
Could you create a similar work of art using polar coordinates?
Can you write a function for the change in angles for your art?
Can you write a trigonometric function for a pattern in your art? Are there any periodic behaviors?
Calculus (Use the questions above as well):
Can you create a function for the slopes? If so, what is this function in relation to the curve you created?
Can you determine the function for the curve you created?