Doodling and math? Yes, we can play with doodles and see what patterns emerge. Finding patterns and problem-solving is a big part of math. For this week’s hands-on-math, learners are going to draw a loopy doodle where they start and end at the same point without lifting the pencil (or pen). Try to make sure that crossings are recognizable (not on top of each other). Once a doodle, or masterpiece, is created, then I encourage learners to color it in. Make lots of loopy doodles and see if any patterns or behaviours emerge. This is a great activity for discovery. Create birds, people, or city scenes with loops. Instead of coloring it in, learners can make knots by going over under, over under (erasers are good for this.)
The patterns that emerge with these doodles are fun. What do you think of the negative spaces that are created? My daughter sat down for hours last week and drew one doodle after another after another and said, “Mom, no matter how I draw these, only one color will touch the outside.” I smiled and we talked about how important discovery is. I love that we have the precious time for doodles. She was excited (and not surprised) to hear that there is a whole area of math that looks at how to shade various maps, shapes, and even doodles. My daughter’s drawings are below (with her permission – the butterflies aren’t part of the knots, but definitely needed). She gets credit for picking this week’s math activity.
Do you ever need more than two colors to shade these in?
If you tangle more than one loopy doodle together, does it still work out for shading? What about knots?
Can you classify some of your knots? (count your crossings)
This week break out your blocks (or whatever building toy you enjoy). We are building a Sierpinski cube (Menger Sponge) or Sierpinski tetrahedron. I would also encourage learners to create their own shape and expand on it to create a self-similar sculpture or fractal (think what each iteration would look like).
2.) Use toothpicks and gumdrops, cardboard, paper, aluminum foil or other handy building tools in the house.
3.) Use lego (I try not to show learners pictures of the tool they are going to use. I think it’s important to figure it out and discover.)
4.) Try Lux blox – this took us quite a while for the third iteration, but it was fun. We found that for the first three sides we needed to build inward to “figure it out.” My daughter built the last two sides while I build inward. It was a lot of fun.
5. Goobi toys are great and my kids and I have built many fractals with them as well. Below is the Sierpinski tetrahedron.
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.
KMUZ’s Steven Slemenda interviewed our family in a two part series for a wonderful program called Poetry on the Air. Thanks to KMUZ and Steve Slemenda for sharing. This show is in the archives on their website, and with permission I am posting it here. My children were appreciative of the experience for the interview. It was such a wonderful exercise for them to reflect on. We are grateful for a way for voices to be heard in our Salem Community.
One of my hobbies is to take completely non-math related games and modify them for classes. I don’t know what to call this game, it is probably a variation of “psychiatrist” or something, but here is how it goes:
In a group of at least 4 players, ask one player to leave the room and go out of earshot.
Tell this person that when they come back they can ask as many questions as they would like to figure out the rule.
Next, the remaining group creates a rule that answers must follow.
This can be a logical rule
truth then lie then truth
always tell the truth
This can be a number of words rule
always answer in two words,
anwer in one, then two, then three words
This can be a sequence rule
include the next number of the fibonacci sequence in your answer (A1- I had one good fish, A2 – One reason I don’t like questions, A3 – Two of a kind, A4 – I really only like tricycles in threes, etc.)
This can be a sound pattern rule (like syllables, rhymes, etc)
Or whatever crazy rule your class/group comes up with.
once the rule is guessed or the player gives up, play again!
There are lots of amazing paper Möbius strips that are fun. You can cut down the middle, twist multiple times, make a Möbius paper chain, and try it with various materials. For a basic paper tutorial, I found a good one here.
Rather than creating the classic paper strips, this week learners will be creating Möbius strips with clay. Using a polymer or air-dry clay, encourage the creation of these wonderful mathematical shapes with a sculpting medium. A clay extruder can come in handy, but isn’t necessary.
I have had students make pendants, infinity signs, and amazing patterns with their projects. For advanced sculpting, learners can create a paper strip first, and then sculpt the same curves.
Matt Parker with Standupmaths also has a great video on these fun strips and how they can make linked hearts: