I’m kicking around the idea of doing a “notice and wonder” project for 4th and 5th grade Family Math night next week. I’m expecting about 20 kids and families and I think I have enough prints to make it work, although this type of hour long activity is something that I’ve not tried before.

The idea would be for the kids and families to circle through 6 stations writing down what they noticed and wondered about the various shapes. I’d let that go for 30 min and they we could talk in a group about the shapes.

The 6 stations would be:

(1) Two shapes made with intersecting cylinders plus the shape from Quanta Magazine’s contest based on Laura DeMarco’s work. The 3d print for the shape was designed by the contest winner, Yoshiaki Araki:

(2) Various forms of the trefoil knot made by Laura Taalman and by Henry Segerman:

(3) Penrose tiles and Gosper Islands

The tiles were designed by Laura Taalman and the Gosper Islands were designed my Dan Anderson:

(4) Incredible 3d shapes –

The Sierpinski pyramid was designed by Laura Taalman (and was our first ever 3d print!) as was the space filling curve. The Gyroid and the evolving space filling curve were designed by Henry Segerman (I think – can’t remember for sure where the gyroid came from).

(5) 4 dimensional cubes:

The “balloon” version was designed by Henry Segerman and the red version is “Hypercube B” by Bathsheba Grossman.

I will also include the version of Hypercube B that we made from our Zometool set. Even though it is not an exact replica of Grossman’s shape it is still pretty cool:

(6) Squircles and an really fun shadow-casting shape

The sphere was designed by Henry Segerman and is on the front cover of his book:

The thin squircle came to us via Dave Richeson and Brenda Landis, and I’m not sure of the origin of the other one:

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Good ideas and good organization. Personally, I would pick notice & wonder as the single best activity for changing attitudes toward math (on top of being useful skills to practice whenever we can).

In both my classroom time and with my own kids at home, I’ve found that notice & wonder takes some effort and repetition to get them to really understand and participate. My guess is that your format (stations, writing comments, parent + kid teams) will dramatically shorten the time for participants to understand.

You might consider giving some examples at the beginning, say a notice & wonder for a simple shape that you don’t use in one of the stations. For example, a square drawn on a chalkboard might prompt the following

I notice …

– it is flat

– it has four sides

– it has four vertices

– the angles are right angles

– the sides are the same length

– it is a square

– it has an inside and outside

– it is white (or whatever color your chalk is)

– it isn’t perfect (the drawing isn’t a perfect square)

I wonder:

– what is the area?

– what is the perimeter?

– how far is it from a perfect square? Leads to questions about error measures for side length variation and deviation of angles from 90 degrees

– how many circles of a given radius we can pack inside? How does that number change with the radius?

– what radius circle would have the same area as the square?

– etc

Excellent idea – thank you. I don’t have a chalk board since the event is in the school’s gym, but I’ll find something to hold up in front of the group.