This past week we’ve been doing some geometry work in class. The grade 2 curriculum expectations for geometry are fairly simple: name, sort and make 2D and 3D shapes. In general, children arrive in grade 2 already knowing most of these. The more common the shapes are in the natural environment, the more likely this is true. Octagon and hexagon usually give everyone a hard time with their tricky names, but by the end of grade 2 few children can’t recall these names. In grade 3, we have to do a few more things. The vocabulary is increased (quadrilateral, angles) but again other than folding and unfolding nets of 3D solids, it’s nothing too complex. Of course, I say that from this point of view – some kids do find it a bit tricky. In all, however, it’s about 1 week’s worth of expectations. I like to teach them early on because there are a lot of problem solving opportunities that can involve geometry and once we have the vocabulary learned the problem solving comes more easily.
This week I had rubber bands on hand. That’s not actually something that happens all the time. Since we had them, I pulled out the old geoboards. Lack of rubber bands is actually one of the main reasons I don’t always pull them out. The virtual geoboards, available here, here and here, are so much more reliable. And nobody can shoot a virtual geoband across the room at somebody.
In the activity shown below, our Friday lesson, students were asked to make some shapes according to a rule. Then their classmates had to figure out the rule. Was the rule: shapes that have 3 sides? Shapes with 4 corners? Shapes I enjoy making because they create cool patterns? Here are some of our results:
A few years ago I remember reading an article about how important it is for students to have a real experience with a manipulative before they move to the virtual version. I tried to find that this morning and couldn’t. My brain doesn’t remember the source! So I put it out to my virtual PLN (Professional Learning Network) on Twitter, and found a lot of teachers agreeing with my thinking. Reflecting on our week today, I was so glad that I had used the real geoboards. There was some really interesting stuff that happened.
First, students were making shapes of different sizes over and over in different ways. On the apps, they tend to get busy playing with other tools – like changing the colour of their geobands, or colouring the shapes in with a variety of colours. They get focused on the wrong things and come up with rules like: Shapes that are orange. And I’m sorry, but orange is not a geometric attribute.
Second, I noticed that some children were struggling to stretch the bands across the pegs. Some of the rubber bands are smaller than others, so this became a problem solving challenge. I feel like they were motivated by the task to work through the challenge and find a new rubber band or change the perimeter of their shape. This simply doesn’t present as a challenge to be worked through in the virtual environment. I had forgotten about this part! Developing learning skills needs to be embedded in every part of our day, and I’m glad they got this chance to work on some problem solving skills.
Finally, there were some social things that we could work on. Sharing is always an issue for 6 and 7-year-olds. They had to cooperate and collaborate to share the rubber bands on their table, and to decide who would get which geoboard. I tried to make sure that every board at least matched the other boards in a group, but I didn’t always make that happen. Again, students had to talk through this because everyone wants the one that is different, and therefore special.
Now that we have spent some time with the geoboards, they can become one of the activities students can do during a Math Workshop session. I can put them on a table with some task cards, or the students can request them to help solve a problem. When we move on to perimeter and area (after we spend some time working with number lines for the next 3 weeks!) I can incorporate questions about shapes and feel confident that everyone knows the shape, and can work with the shape. And I can add some