Week 17: Sierpinski in 3D Building Toys

My Building partner and our Menger Sponge

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).

Here are a few options for building:

1.) Use this link for a paper model (good for a short class or quick project).

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.

3 iterations

5. Goobi toys are great and my kids and I have built many fractals with them as well. Below is the Sierpinski tetrahedron.

Week 16: Geometric Sketching – Hummingbird

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.

https://www.geogebra.org/graphing/x6k9wnag

KMUZ Poetry on the Air With the Family

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.

8-20-19: Interview with Sophia’s Children
9-13-19: Interview with Sophia

Week 14: Guess the rule – math game

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
      • always lie
      • 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!

Week 13: Clay Möbius Strips

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:

Week 12: Galileo and Gravity

This week we are going to take a look at applied math. Learners will be given a ramp (this can be a ruler), a ball that fits on the ramp, measurement device (ruler) and a timer. With these instruments learners can investigate the relationship between distance and time as the ball rolls down the ramp. I encourage teachers and facilitators not to give too much procedure here and let students come up with the way they will execute an experiment and record their data. I usually go with a 10-15 minute “sweat-it-out” period before I give them any hints.

This exercise is a great intro into calculus concepts like “instantaneous velocity” and derivatives of functions that model falling bodies. I think this is fun to do with middle schoolers and up. You can plot your functions and then draw the tangents to the curve and find slopes (this is fun in groups).

If students are stuck, hints may look like this:

  • Have you set up an experiment that you can repeat to get multiple samples?
  • What time intervals are you going to try to record? how far has the ball rolled with zero seconds? 1 second? 2 seconds?
  • Once you have your data, can you plot it to see if there is a relationship? Is it a direct variation?
  • If you plot the relationship, what type of curve is it? Can you create a function for that curve?

Here is a sheet I had for a class that students received after completing their experiments:

Week 11: Soma Cubes

I love Martin Gardner’s work and books that brought math to so many people in a fun and engaging way. One of the topics he covered was Soma Cubes. This week learners can create and play with this wonderful seven piece puzzle that was invented by Mr. Piet Hein during a lecture on physics. I love this puzzle because there are so many questions to ask and ways to solve it. There are a few options for creating your own:

Option 1: Wooden cubes

I ordered wooden cubes and found they aren’t perfect, but do the job with students. You can get them at craft stores or amazon (affiliated link).

Option 2: Sonobe Origami

You can make a Soma cube with a lot of folding. I would recommend doing this with teams and older students (or as an adult). The folds need to be exact. That being said I have seen 9 and 10 year olds do beautiful origami Soma cubes. The best tutorial that I was able to find is on the Luck Paper Scissors Blog here.

Here are some questions/exercises:

  • How many unique ways can you solve it? Is there a systematic way to track your solutions?
  • Are there combinations that will never have solutions (ex: starting with one or two pieces in a particular way)
  • What other symmetric constructions can you create?

One of the coolest links to all of the solutions I have found is here on GeoGebra by Michael Borcherds.

Another unique page devoted to Soma is here.

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