I love thinking of mirror images when I am block printing. I will never forget the time I printed SPARK backwards on accident for a summer art camp and my kids laughed at the reverse phonics. This week I encourage learners to take a math concept, tessellation, or shape and create a print.
Ways to create plates for printing:
For younger learners, foam boards easily take impressions.
For those that are semi-comfortable carving, potatoes, apples, or rubber blocks can provide semi-soft mediums to carve.
For those that are skilled with sharp objects, wood or lino-blocks may be preferred.
When I teach I say these words at least a few dozen times:
Do not ever force a blade.
Do not cut towards yourself or others.
Keep your tools sharp and cleaned.
Be in control.
If you are going to carve on a block, foam, or rubber sheet:
Sketch a design on paper with a pencil. (Keep in mind the size of your carving surface.)
Transfer the design by rubbing the pencil onto the carving surface.
Carve your design. (You can either carve in, tracing your lines, or around them.)
Roll ink on the block with a brayer.
Place a sheet of paper (or fabric) on the block and burnish (or rub) it with a flat surface to make sure that it makes contact with the block.
Peel the paper/fabric off. (This can take a few tries to get it right.)
For this post I carved a circle composition with the Fibonacci sequence in mind. I think I run faster with math shirts, so I printed one as well:
One of my children jumped in and we did a Sierpinski potato triangle. To use potatoes: Draw a sketch on the potato, cut out the design, and then treat it like a stamp.
This week I encourage learners to play with their animation skills. Take a math concept, problem, or design and play with ideas to animate it. Start simple to warm up and then build on the ideas. Flip books are fun. I recommend using thinner paper that can be seen through so it is easier to draw on top of the previous frame. Try the paper out before spending the time to draw. Flip books are an analogue GIF.
Here are the basic steps to drawing a flip book:
Decide on your math topic to animate. (Fractals, projectiles, growth, decay, etc.)
Draw the starting frame:
Draw the next frame by tracing and/or using the previous sheet as a reference:
Repeat the process of making new frames by referencing the previous:
Once your frames are complete – flip it!
There are other ways to animate as well. There are apps such as iMotion to make stop animation films. I also enjoy using Procreate and Looom to create animated GIFs. Learners may prefer to use technology for their animations. I plan to cover this in some STEAM posts at some point. Please share your animations!
After teaching this a few times this week, I created a video so those that may want to pause and draw at their own pace while playing with isometric paper. Feel free to contact me if you have any questions. I love doodling on Isometric paper – enjoy! Here is a link to the isometric hands-on math activity and here is the paper.
Let’s get out our pencils, isometric paper, and thinking caps this week! Isometric drawings are often used in engineering and design as a way to display 3D ideas. They can also be used to create optical illusions and escheresque works of art.
To start, print some isometric paper, or set your digital drawing program to isometric drawing guides. Start by drawing simple objects, like a cube, and play with shading.
Once comfortable with basics, start making skeletons for shapes, linking sides that don’t make physical sense, and thinking about objects that would allow you to go up and down at the same time. Below are some examples and videos to play with:
Sometimes math diagrams, plots, and examples can be a little dry in our books and on the board. This week learners will be taking a diagram or plot that they want to improve upon and sketch it up with pastels, paints, or other media. Color, composition, and artistic embellishments can be added while, keeping the overall concept in tact. Ask them what a math textbook would look like if they created it. Would you have a cheshire kitty in the mix? Would you turn each chapter in to a different land or island?
These sketches don’t have to be fancy, I recommend small pieces of paper and having fun with it (most of these are around 3×5 inches and took a few minutes.) Most of all – have fun!
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:
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.