Week 7: Cartesian Coordinates

This week learners can get hands on with plotting. I encourage learners to investigate the history behind the Cartesian Coordinates (it’s interesting – I was just reading about it in Infinite Powers by Steven Strogatz).

The idea is to plot with D&D figures, chalk, legos, or watercolors. Make art out of plots! This is a great activity for pre-algebra and algebra students. Younger students can learn as well but can focus more on finding ordered pairs (x,y). Below are four activities for plotting:

Activity 1: Hit the monster (game it up!)

  • Use a gridded mat (like what is used in D&D), large graph paper or overhead projector
  • Draw Axes on the grid and define the quadrants and scale
  • Place or Draw monsters throughout the plane
  • Have students devise functions that can hit/intersect monsters
    • This can be timed or not timed
    • Students can work in teams
    • This can be a D&D math mission if you are gamifying your lessons
  • If there is only one or two learners then smaller graph paper can be used

Activity 2: Cartesian Lego

  • Decapitate as many minifigures as possible for this activity (other round 1×1 pieces will work as well.
  • My students used a large gray sheet and black flats for the cartesian coordinates
  • Make plots of various functions and then see if others can “name that function”

Activity 3: Watercolors (or other art media)

Create plot families using watercolor flash cards

  • add characters, color, and comics
  • label the backs with the family the plot belongs to.

Activity 4: Plotting in a large room

  • With masking tape in a large room you can make a grid
  • Have students plot functions with beanbags or rope
  • Students can toss a beanbag and then try to figure out the coordinates
  • This can work at an outdoor park if you can grid off an area without creating a tripping hazard

Week 6: Randomness using pi

Pi with Lux Blox

This week learners will create a work of art using pi. The goal here is not to understand pi, but to play with randomness. We will dive into the ratio of circumference and diameter on another week. Pi’s decimals go on forever and without pattern. Here are some ideas to play with that randomness:

  • Build a skyline with your favorite building toy using the digits of pi
  • Use graph paper and shade a skyline of pi
  • Assign a note from 0-9 on instruments or bells and have the learners play the digits in order to hear the randomness
    • Example: C = 0, D = 1, E = 2, F = 3, G =4, A = 5, B = 6, C = 7, D = 8, E = 9 (where you use more than an octave. You can also use sharps, flats, or skip notes)
    • You can also assign chords to each digit rather than notes
  • String or circle art with pi (you can do a circle with 10 points)
Pi using a circle with a point every 36 degrees
Students’ pieces

Week 5: Tell a Tale (or comic)

No matter what grade/age, stories are fun. This week I encourage learners to read and write math stories. Take a concept and illustrate it through the art of story. Write comics, picture stories, murder mysteries, fantasies, plays, etc. Students can act their story out, create a stop animation, or illustrate. I often encourage learners to write about a concept they love or think they can teach.

Learners I have worked with have enjoyed sharing their stories with each other and friends. Encourage this through a google classroom, open mic, etc.

Some fun ideas if you come up blank:

  • Powers of 2 – the magic of multiplying (like in Demi’s One Grain of Rice)
  • The algorithm for long division as steps to a mystery or spy mission
  • A solar system of various Euclidian Solids
  • A geometrical mission through space with specific angle requirements
  • The route inspection problem – what is the shortest path for the mail to get delivered with a specific layout of houses?
  • Comics on how to learn or do concepts in math
  • Mystery characters that emulate mathematical properties (Logical Lucas, Divisive Desi, Manipulative Mike, etc)
  • Super heroes that have mathematical powers and must solve mathematical problems
  • Fractals – Create a world, character or story that is iterative and infinite

Please note that one of the ways I support this website is through affiliated links. As an Amazon Associate I earn from qualifying purchases from the links above.

Week 4: Polyhedra Study

Opal’s sketch (11yrs old)

Leonardo da Vinci was an amazing mathematician, inventor and artist. His sketches in The Divine Proportion are a wonderful collection to study. Spacial awareness and being able to draw what we see is a skill that can be mastered through practice.

This week, I encourage learners to sketch polyhedra from cubes to tetrahedrons to dodecahedrons. Use charcoal, pencils or watercolors to create works of art. You can model with clay, paper, glue and sticks, or building toys and then sketch. Play with various forms of lighting and shading. Move beyond the numbers this week and look for math in the objects/polyhedra around you.

You can combine this study with history and architecture. Go out and look for polyhedra around you. Can you make a pyramid scene? What is a soccer ball? What is the shading like at different times of day for a favorite building? Are there planes of symmetry for your sketch? How many vertices are there?

Week 3: Sonobe Octahedron

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.

The best resource for Sonobe I have found is here: https://www.amherst.edu/media/view/290032/original/oragami.pdf

Week 2: Spiral of Theodorus

This image has an empty alt attribute; its file name is image.png

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?

Week 1: Embroider Curves with Lines

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:

  • Elementary:
    • 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?