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:
Poetry forms are like a puzzles. You have to take the words you want to say and rearrange them, find synonyms, and reformulate them until they can fit in a form. This problem solving is so similar in math.
One of the first forms to play with is the Haiku. It is a three line poem with no rhyming scheme that fits a syllable pattern of 5/7/5. Traditionally there is a season mentioned (Kigo) and a cutting word to compare two ideas (Kiru). Learners can try to do a traditional Haiku, or they can just work with the syllable pattern to start. This can be done in any classroom to contemplate the concepts that are being learned in a different way. When we relate these abstract ideas to our inner beings, we remember.
Once poems are complete, maybe a work of art can complement it.
This week learners can dive deep into their imaginary worlds (or real world inventions). The project this week is to create a map, castle, spacecraft or invention. The math focus will be on developing a sense of scale. Younger learners may practice scale with proportions in their drawings. Older learners may add units and measurements to their designs.
Offer various materials for their designs: graph paper, extra large sheets, engineering papers, isometric, or hex. Facilitators can supplement learning by looking at maps, blueprints, and patent designs that learners are interested in.
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?