Workplace Mathematics

In my last placement, I had the opportunity to observe and teach a few lessons in a Grade 11/12 Workplace Mathematics. What I loved about this course was that it taught students very valuable mathematics that will assist them for the rest of their lives. I found myself wishing that I could have learned about these topics in my secondary education experience. They learned topics such as banking, travel and investing money. One main thing that I noticed while observing this class was that there was lots of time spent doing research on the topics and finding the information themselves. This also teaches them how to research and search for accurate information in the future.

Planning A Night Out 

The first activity in this class was about planning a night out with your friends. We were asked to choose between going to the movies or going bowling. I liked how students were given the choice of which activity they would like to do because they will be more engaged. There were 6 sections of the activity to be completed; budget, destination, transportation, cost of activity, food and beverages, and a reflection on costs and budgets. I could imagine the students at my placement enjoying this assignment because it relates to what high school students may be interested in. The next activity was very similar as we were asked to plan an ‘adventure’. We were essentially doing the same calculations, however, we were also required to use the 24 hour clock. Many travel schedules use the 24 hour clock and converting between the 12 and 24 hour clock is a valuable lesson for students. 

Since this concludes the presentations, I can confidently say that I will be using many activities within my future classes. The ideas were very creative and many lessons turned typically dull mathematics topics, into interesting inquiry-based activities! I look forward to using these activities.

Authentic Activities

The activities that were presented in this class were all extremely authentic and useful in students’ lives. Each activity was presented in an interesting way and I can imagine that students would enjoy all of these lessons. The first activity was about interest rates which is something that everyone will need to be able to calculate in the future. The second activity was about calculating the probability of getting a 21 in black jack. Although not all students will play black jack, it was an interesting way to demonstrate odds and probability within a senior level mathematics course. The last activity, which I will be focusing on in this post, was about remodelling a home. 

Remodelling

Our group was handed many different types of material such as carpet samples, hardwood samples, laminate samples and paint chips. Each material had a different price attached to it which made it feel more real. We were all very excited to get started because we had never seen this activity presented in this way. As teacher candidates, we have all seen the activity where you must calculate the area of floor in a room and calculate how much the material will cost. However, we were never given manipulatives and given the opportunity to choose which materials to use. This made the activity much more realistic because you always have options when remodelling a room. I loved this activity and I plan on picking up some samples of my own to use in my future classroom. This is a great lesson that can be used in many grade levels and I hope that students will enjoy this activity as much as my group members did. The one aspect of the activity that I would change would be challenging the students to stay within a certain budget.

Engaging Activities in Grade 12 Courses

Deal Or No Deal 

This past week, we were introduced to an activity that was based on probability for a grade 12 Data Management course. We were essentially playing Deal Or No Deal while learning about theoretical probability. We were asked to work in partners, however, our group ended up working in a group of 4 people. We found it was much more engaging working together because we had to make the decision as a group. This would be a great teaching decision because it allows the teacher to assess living skills and the discussions that were taking place at each table. After we opened each set of ‘cases’, we were asked to calculate the theoretical probability of leaving with a larger amount than what was offered from the ‘banker’. This was an authentic way for students to practice probability calculations and we all had fun in the process. I plan to use this activity because students always want to know when mathematics will be useful to them and this game show is one example of when mathematics can truly help you!

Logarithm Dominos 

We were also introduced to an activity about logarithms which was meant for a grade 12 Calculus course. I would have never imagined that there could be an activity that was this engaging about logarithms, yet here it was. We were given ‘dominos’ with expressions written on both ends. We needed to first understand the concept of logarithms in order to complete this activity so this would be an excellent way to consolidate a lesson. We were essentially playing dominos with the answers of the expressions and we had 45 seconds to place a domino on our turn. I thought this was an extremely engaging activity because we were truly having fun and learning about logarithms at the same time. The only part that I found confusing was the actual rules of dominos since I had never played before. However, we were helping each other, with both the rules and the mathematics, rather than competing to win. Completing this activity made me wonder if this could work for other concepts as well. For example, I can picture using this activity with linear expressions focusing on the slopes specifically, then another round using the y-intercepts. Within my next block, I plan on taking what the students are learning about and incorporating this game within a lesson. 

Senior Mathematics Activities

The activity that I presented to the class was an introductory lesson on exponential functions that is meant to be for a grade 11 university course. I put students into groups of about 4 or 5 people and set up three different stations around the classroom. The first station was about a zombie attack within the city that was spreading at a rate of four new zombies every day. The second station was about folding a piece of paper and counting the amount of sections that it created. The third station was about the ice bucket challenge, where each person that was nominated would nominate three more people to complete the challenge. Each group was given about five minutes at each station before we would rotate to the next station as a class. There were red counters (at the zombie station) and blue counters (at the ice bucket station) to allow the students to visualize how the zombie attack or the ice bucket challenge was spreading. I believe the counters worked very well because it was an easy way to picture how the numbers were increasing. All of these scenarios represent exponential functions, therefore, the students were able to see how exponential functions are used in real-world (expect for the zombies!) situations. Some groups were confused by the wording at some stations, therefore, I plan to ensure that more thorough instructions are placed at each station in the future. With that being said, all of the students seemed very engaged throughout this activity and I plan to use this activity in my future classroom. 

The Ambiguous Case of the Law of Sines

Another activity that was presented was about triangle properties. We were given three strips of paper that were either fully attached (stapled) or movable (on a brass fastener). The strips of paper were also either cut off straight or in the shape of an arrow which meant that the length could be changed. I thought that this could be an excellent way to demonstrate the ambiguous case to students. During an observation day in my last placement, my associate was teaching a lesson on the ambiguous case of triangles and it was clear that many students were confused. These triangles would be the perfect way to demonstrate the ambiguous case because it is a visual representation of both triangles. As you can see in the picture above, if you move the yellow piece of paper, two triangles will be formed. I plan to recreate something like this in the future when teaching students about the ambiguous case triangle. 

Graphing Calculators

In high school, I remember using the graphing calculators once in every unit and we were even told that we would not be tested on using these calculators. Therefore, before we even began, we all knew that this was simply a mandatory aspect of the curriculum and we did not have to worry about the lesson.  I did not enjoy these lessons because I would often get confused about how to use the calculators and then I would fall behind in the lesson. With all of the new educational technology that is being used in classrooms, I often forget that graphing calculators can also be used since they are usually not the most engaging piece of technology. However, using CBRs with the graphing calculators can completely transform a lesson and make it interesting for students. 

Calculator-Based Ranger (CBR)

We used the CBRs in an introductory lesson about rates of change. Rather than use the technology to simply fill a mandatory expectations, this activity was truly engaging and I believe students would enjoy this exploration. We were asked to replicate the given graphs with the CBR in groups of about 4 or 5 people. Our group had an amazing time trying to match the graphs perfectly and realized that we were learning about rates of change in a truly authentic way. What I found interesting about this activity was that it was very memorable. For example, I would remember how my group members or I walked (or ran) to match the given graphs much more than if a teacher simply told me what they would look like. This activity involved hands-on experiential learning that would get students fully engaged in the learning. The consolidation portion of the lesson was also very valuable because it ensures that the students understand rates of change and how this can be applied to linear functions. I would definitely use this activity in my future classroom.

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.