Line & Rotational Symmetry

This year is my first teaching line and rotational symmetry.  I taught this lesson in one class period.  I believe my students learned line and rotational symmetry at some point in elementary school, so the lesson went smoothly.  (However, my past students also learned that 1 is a prime number, and that rhombuses are tilted squares in elementary school.)

I put my students into groups of 4.  With their groups, students filled in their interactive notebook insert.  It was a table depicting each shape with space to list how many lines of symmetry and how many degrees of rotational symmetry each shape has.

Each group had a sheet of cardstock with seven shapes printed and labeled on them (square, rectangle, parallelogram, trapezoid, isosceles trapezoid, regular hexagon, and regular pentagon) and seven-ish sheets of patty paper.  Students were able to trace each shape, and then fold the patty paper to determine the number of lines of symmetry.

 

Each group also had a manila folder.  Inside the folder I had taped down seven 360-degree protractors, and then cut out each shape and attached it to the folder through the center of the protractor with a brad.  (It was also super handy for holding each group's materials.)  Students were able to spin the shapes to determine the degrees of rotational symmetry.  (This was very helpful for the pentagon and hexagon.)

Overall, it was an easy set-up and totally worth the little bit of time it took.

Constructions Tech Tip

My first year of teaching constructions was a disaster.  I never learned constructions when I was in high school, so I had no frame of reference of how to teach them.  We constructed circles.  That was it.  In college, I learned about constructions with Geometer's Sketchpad, but it is so different from doing constructions by hand.

My second and third years of teaching constructions was much improved because I'd discovered http://www.mathopenref.com/tocs/constructionstoc.html.  I was able to play animations of constructions while helping individual students that needed more help.  There are still some drawback's however.  Firstly, we don't use the same type of compass presented in the animation.

Our school has these:

(These compasses are the worst.   The red part that is for the pencil slides while you're trying draw arcs.)

We used to have these:

(We still do, but we only have 15 or so, which isn't enough for one class, let alone for everyone to use on our state test.  These compasses are the best.  They have a locking mechanism so arcs can be drawn without any issues.)

We currently use these:

(They're not my favorite, but they get the job done, and I find that the flat compasses are easier for students to handle than the standard compasses.  The biggest bonus of these is that they are cheap.  I have enough for all of my students have their own, which means that they can do constructions for homework.)

The second issue with the animations is that they don't always show exactly what I need them to.  Sometimes they show extra steps, and they make partial arcs instead of full arcs.  These are small differences, but they are enough to confuse students.

So now that I am in my fourth year of teaching constructions.  I found another solution, and it was right under my nose the whole time.  I am one of those teachers that cannot imagine teaching without a SMART Board.  I have been trained in the use of SMART Notebook during my undergraduate education.  I knew that SN had construction tools available for awhile, but I never fully explored them.  It was daunting, and I had a mile-long to-do list, so I forgot about it.

This year, I needed to show my students a construction, but it was too different from the one available on Math Open Reference.  I took a look at the tools, and found that the compass was so much easier to use than I ever imagined.  I thought it would be helpful to show a brief tutorial on using the compass on the SB.  It takes some practice, but I think it's going to make a big difference in how I teach constructions next year.  Take a look at the compass directions I have posted below.