# 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 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?