We began last week's class by each collecting a randomly selected shape, then finding a group of people in the class with a similar shape. At this point we discussed what it meant for a set of elements to be similar or congruent. The idea that similar shapes shared the same proportions was put forth, and congruent was decided to be exactly the same. This was extended to the question of colour---do two items have to be the same in colour to be congruent? I would argue yes, as otherwise they aren't exact replicas, though the argument of relevance was also put forth.
There was then discussion about classifying shapes. In elementary school we glossed over the idea that a square was a rectangle, but a square is also a rhombus, parallelogram, and a quadrilateral. Any more terms we could label it with? Probably. Maybe this topic was avoided---like the time I asked whether peanut butter would be classified as a solid or a liquid---because we were bratty kids, or maybe because it could confuse some students, but these distinctions (or lack thereof) represent a deeper understanding of the material.
Class seemed to fly by---perhaps because I was somewhat distracted by tangrams. Oh, how I love tangrams. We did them almost every day in grade 4, trying to replicate shapes from a grainy photocopy. The activities for the day dealt with patterning and spacial relationships. The first involved finding the relationship between a a string of numbers. I liked the activity as a whole, as I really enjoy trying to find patterns in every day scenarios. Unfortunately for me, the activity was aimed at a grade 4 level, so it wasn't particularly challenging, but I still appreciated it. The second activity involved transformations on a grid, and used the example of moving a car from one point to another. I felt it was pretty straightforward, however other members of my group had some trouble following the transformation steps for the first part. Students were unclear about where to rotate the shape and how far to do so (instructions said rotate a half turn at the nose of the craft), and what line to use when doing a reflection. For the grade 7/8 level, I felt the instructions were probably appropriate, and students having had instruction on these concepts might not had had the same issues that we saw at our table. The next activity was about navigating bus routes in Hamilton. I thought this a rather practical idea, and liked how a map could be used to find parallel and perpendicular lines. My only concern was that the map was difficult to make out (Garth St. was missing entirely), and if students are unfamiliar with the area they might not be able to fill in the blanks.
The last activity dealt with drawing reflections. While this seemed like a simple task, it would be good practice for the grade 4 level at which it was aimed to draw reflections and identify lines of symmetry. What I particularly liked about this activity was the differentiation! Materials were available for both left and right-handed individuals, and students were provided with a mira should they not choose to free-hand the drawings. I chose to use a mira and it was actually quite surprising to see how badly my drawings turned out with it. They are probably more accurate than if I chose to free-hand, but the lines are very shaky and uneven, giving it a very crude and unpolished look. I thought this was interesting because while I was using assistive technology, I was finding that my work was not necessarily being improved by it. It highlights how not everything works for everybody and how we cannot just give students a single tool, selected by us, and assume it will work. Also, the music was a great addition for the grade level!
