In my capstone class for future secondary math teachers, I ask my students to come up with ideas for *engaging* their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Kristin Ambrose. Her topic, from Geometry: introducing the terms parallelogram, rhombus, trapezoid, and kite.

How could you as a teacher create an activity or project that involves your topic?

An activity I could do with my students is to have my students sort the different shapes into their own categories. Without letting them know the terms for these shapes, I could give my students several cut-outs of different parallelograms, rhombi, trapezoids, and kites, and have them sort these into four categories. Then the students could discuss how they grouped the shapes, and with the teachers guidance the students would come up with a list of the key characteristics each group of shapes had. Only at the end would the teacher reveal the official terms (parallelogram, rhombus, trapezoid, and kite) for these categories, and by this point the students would already know the characteristics for each shape since they previously listed the characteristics before they knew the official terms. I believe this would make the process of learning about these shapes more meaningful and interesting since the students would have discovered the characteristics of these shapes on their own.

How has this topic appeared in high culture (art, classical music, theatre, etc.)?

Geometry often appears in art, and therefore shapes like parallelograms, rhombi, trapezoids and kites can be found in pieces of artwork. I was able to find a website (http://fineartamerica.com/art/all/geometric/all) where they sell geometric artwork. On this site I was able to find a few pieces that contained parallelograms, rhombi, trapezoids, and kites. Here are a few pictures of artwork that contains these geometric shapes:

These shapes can also be found in other forms of art like jewelry, like this trapezoid necklace and kite earrings:

Students may find it interesting to see how geometric shapes can be used in different forms of art, and it may even inspire them to create their own forms of geometric artwork or crafts.

How can technology be used to effectively engage students with this topic?

On YouTube, the channel Vi Hart has a video where they create geometric shaped cookies. Here is the link to the video:

During the first two minutes of the video they create √2 rhombus cookies. Then they are able to create other cookie shapes using the rhombi cookie dough. It’s interesting to see the different ways they cook with the geometric shapes, and it could even inspire my students to create their own geometric-shaped cookies. After viewing the video, I could discuss with my students what characteristics they noticed about the rhombus-shaped cookies and this could open up a discussion about what the definition of a rhombus is. After discussing rhombi, we could move on to discussing other kinds of geometric shapes like parallelograms, trapezoids, and kites. We could also discuss the similarities between these kinds of shapes, and how they connect to each other.

References:

Geometric Artwork:

http://fineartamerica.com/art/all/geometric/all

Vi Hart Video:

https://www.youtube.com/watch?v=_n1126GoxbU&list=UUOGeU-1Fig3rrDjhm9Zs_wg

Fractal Geometric Dog, artist: Budi Satria Kwan

http://fineartamerica.com/featured/fractal-geometric-dog-budi-satria-kwan.html

Red Parallelogram art:

http://www.wetcanvas.com/forums/showthread.php?t=601147

Trapezoid necklace:

https://www.etsy.com/listing/53449025/brass-trapezoid-necklace

Kite earrings:

https://www.etsy.com/listing/168803451/modern-geometric-earrings-of-angles-and?ref=market