Intermediate Mathematics Courses

As mathematics teacher candidates, we are often told that we will be teaching grade 9 and 10 course for the first couple years of our career. Once we have a permanent contract, it is extremely likely that we will not be teaching senior mathematics courses until we have had a few years of experience with intermediate courses. Therefore, I plan to learn as much as possible about these intermediate courses in order to be confident in my first few years as a teacher. This week, my peers presented some activities that would provide students with excellent learning opportunities. 

Speed Dating

I can honestly say that this was one of the most exciting activities that I have ever done in a mathematics course! I can only imagine how much grade 9 students would enjoy this activity and I am so excited to try it in my future classes. The activity was based on sketching linear functions based on slopes and y-intercepts. The desks were set up in a U-shape and there were students placed in pairs on both sides of the desk; just like in a speed dating situation. Everyone was given a piece of paper that stayed with them during the entire activity. For example, my piece of paper stated that my graphs would have a slope of 1. Every new student that sat in front of me would have a different y-intercept and we would put both pieces of information together to form a line. If this line went through a heart, we were a match! Throughout the entire activity I was engaged and excited for the next person to sit down. The only thing that I would add to this activity would be to incorporate the concept of parallel lines. Half of the students ended up with a sheet that looked similar to mine (only with different slopes) so it would be an excellent introduction to parallel lines.

Interior Angles of a Triangle 

The next activity that we completed was an introduction to the sum of interior angels in a triangle. We were asked to draw any triangle on a piece of paper and cut the triangle out. This demonstrates that this theory holds true for any triangle since it will work for all of the students in the class. We were then asked to cut of each tip of the triangle, which is essentially cutting off each ‘angle’. We rearranged the angles to form a straight line which proves that the sum of the interior angles in any triangle is 180! It was a fantastic way for students to be able to visualize the sum of interior angles in a triangle. When I learned about this topic, I was simply told that the sum of any triangle was 180 degrees but I never understood why or how that was true. Using this activity demonstrates why the interior angles add to 180 degrees and it allows the students to find this information for themselves, rather than being told. I plan on using this activity in my future classes because it will allow the visual and kinaesthetic learners to understand this property.

Inquiry-based Learning

Inquiry Based Learning is a method of teaching where students are at the centre of the learning. They are presented with a problem and must use problem solving strategies (often in groups) to work through the problem by making connections to prior knowledge. Although the students are typically the ones leading their own learning, the teacher is also a valuable member of the process who facilities discussions around the mathematical conversations. This type of learning creates an engaging environment for students and they are motivated to learn because they want to solve the problem. Rather than a teacher simply telling students how to solve a mathematical problem, they are launched right into the task and asked to solve it themselves. This creates a rich mathematical discussion among students and it usually generates many ways to solve the problem. Inquiry based learning is also an excellent way to encourage students to develop critical and creative thinking skills. 

Many of the activities that were presented this week in class were inquiry based problems. The presenters allowed the students to work through the problems while facilitating some discussions, whether during the activity or once it was completed. 

Stick Man

The Stick Man activity was essentially a scavenger hunt based on rotations, translations and reflections in the cartesian coordinate system that was meant to be used in a grade 8 course. I loved how this activity got students out of their seats and presented a typically dull topic in a fun and exciting way. We were put into groups of about three people and were told to start at one of the eight stations around the room. We had to solve the problem in order to find where the stick man was on the cartesian plane. Once we solved the problem we needed to find his next location in the room. What I liked the most about this activity was that it gave each group a different final location, rather than one group finishing first and telling everyone else where the stick man ends up. Once we completed all eight stations, we sat down as a group and figured out how to get the stick man home again which was the consolidation portion of the lesson. We were also asked to write a story about the stick man's adventure based on our own scavenger hunt. This was an open-ended question that allowed for creative thinking skills. If I were to use this activity in my own class, I think I would have made a couple less stations and allowed for more time to complete the consolidation. However, overall it was a great activity!

Holes

I loved the movie 'Holes' when I was younger so when the activity began with a clip from this movie I was hooked from the start. We were asked to compare the volume of two character’s holes and to find out how many times one characters extra dirt could fill another character’s hole for an entire year. In my opinion, this question would be considered a thinking question because there were many steps involved in solving this problem. I believe students would find this engaging because they are given a problem that applies to a movie that many of them would have already seen. The students are also motivated to solve this problem because it is an authentic mathematics problem from the movie. I would love to do something like this activity with my class in the future because it will engage students right from the beginning. One difficulty that we faced with this problem was that the movie used inches and we were asked to work in metres. This caused some confusion and I could imagine that grade 7 students would also be confused. Therefore, if I were to do an activity like this in my class, I would use the same units that the movie used or find a scene with units of measurement that I know my students would be able to work with.