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.