Geometry

In this week's exploration of geometry there were two activities in particular that really stuck out for me. The first activity is a toothpick puzzle game as a way of reasoning with edges and vertices and how changing one affects the shape as a whole. The second activity, No Pegs Allowed, is similar to the first in the sense that it explores how changing a part affects the whole, but it uses geoboards and requires students to find all triangles that have no pegs within them. And the last thing I want to reflect on this week is a game I found while observing a grade 7 class.

Toothpick Puzzle

When presenting the toothpick puzzle it is important to make the learning goal of the activity clear before they start, that way they understand why they're doing this activity and will have the learning goal in mind while they work through the puzzle and will likely be better able to make the connections we're hoping for them to make. 

The puzzle works by presenting the students with a toothpick formation (that they recreate on their desk) and then asking them to change it into something specific but by only removing/moving a certain number of toothpicks. Below are two examples: 

MacCuish (2015).  

MacCuish (2015).

This activity gets students to start thinking outside the box in terms of what make up a shape and how they can manipulate it. This is part of the Ontario curriculum for grades 7 in the third overall expectation for geometry and spatial sense: describe location in the four quadrants of a coordinate system, dilatate two-dimensional shapes, and apply transformations to create and analyse designs (page 103). For grade 8 they would need to take it one step further and formally analyse the shapes which is part of the geometric relationships expectation under geometry and spatial sense to determine, through investigation using concrete materials, the relationship between the numbers of faces, edges, and vertices of a polyhedron (page 114). 

No Pegs Allowed

The second activity I really connected with was called 'No Pegs Allowed' which encourages students to focus on the properties of triangles by having them make as many triangles on a peg board they can without having any pegs in the triangle. Here are a few examples: 

MacCuish (2015). 

MacCuish (2015).

MacCuish (2015). 

Similarly to the first activity, students are working with manipulating shapes (specifically triangles). This activity would be appropriate for grades 6-8, however into grades 7 and 8 students will need to do a little more work with each. For example, by the end of grade 7 students must be able to decide if two shapes are different, so in this activity they would have to figure out what qualifies as a unique triangle from the ones they've already created. For example, in the image below, students must be able to determine and explain why these two triangles are the same.

This concept is called congruence and is outlined in the curriculum for grade 7 on page 103, but it would be a good refresher for early grade 8 as well. 

Prodigy Math

The last thing I want to mention that I've come across this week is a program called Prodigy Math. This game gives teachers control over the types of questions students have to answer as part of their 'quest'. My associate teacher is using the program in his classroom and he says students really enjoy the game and it gives him a weekly report of each student's progress and game time. He typically uses it when they have math class last period and allows them to play once they've completed their math work for the day.

I think this is an excellent strategy since the teacher can monitor progress and it is an on-going game throughout the year. I don't think it should replace any of the other games we've explored, but it's definitely something I plan on incorporating into my lessons during my practicum.