Mixed Mathematics Class

This week we completed activities that would be completed in the grade 12 mixed math class. The first activity was about domain and range of a function. First four stations were set up around the class: inequalities, words, number line and list of numbers. Then each student was given 3 pieces of paper that represented one of the stations. After this, the students from each station then collaborated to match there equivalent statements that were represented in the different ways. This allowed for collaboration and for students to actively see that a range of numbers can be represented in four different ways. At the end we were given a hand out with graphs and students would state the domain and range using two different notations. This then allowed students to apply what they just demonstrated in the beginning of the activity.

The next activity we did was about investigating exponential functions. To begin the activity an example was shown using an email chain. The first person sent the email to one person the email to two people, and then those two people sent to two more people and then all of those people sent the email to two more people etc. Everyone who got an email stood at the front of the room in a line for each group of emails, It was shown that in the first group there was one person, then two, then 4 and then 8 (figure 1). This was then graphed using Desmos to show that it is an exponential function of y=2^x. This was a great way to visually show how exponential growth works as well as get the students up and moving. Then a handout was given and students were asked to use their personal devises to access Desmos and graph three groups of exponential functions. One group exponential growth, the other was exponential decay and the third was 1^x (a horizontal line of y=1). This was a great way to visually see the graphs and see how the variable a in y=a^x affects the graph. This was another great and engaging activity that incorporates technology. 

Engaging Activities

This week we completed 3 activates in class from the different presentations. The first activity was for a grade 10 applied math class and the activity dealt with measurement. In this activity we were first asked to estimate the conversions between the metric system and the imperial system. Then we were asked to measure various body parts with a partner using a meter stick. This was great for the students, especially applied level, to get them up and moving and actually physically measuring and seeing the measurements.

Next we completed an activity about triangles and using trig laws along with sine and cosine law. First we worked in small groups to complete a few simple problems using soh cah toa and cosine and sine law. After each question was complete we were given a pile of letters and once we competed all of the questions we had to unscramble a word that completed a sentence. This was a great way to motivate students to complete each question quickly because they would be excited to complete the word and phrase. Lastly we were given a real world problem that incorporated the students’ names and interests. My group’s problem was about measuring the distances of ships to a dock, to see which one was closer, only being given the distance between the boats and two angles. Since it was not a right angle triangle we used sine law to solve for the two unknown side lengths and discovered that the red ship was close to the dock than the blue ship. We then shared our solution with the class using chart paper, which can be seen in figure four. Using students interests and names in problems is a great way to get the students involved in a math class, this makes the students more excited about the problems and I think intrinsically motivates them to complete it.

The next activity was completed using graphing calculator and motion detectors. In this activity we were to recreate a circle graph using the detector. At first my group thought we simply just turn in a circle but then realized that the motion detector needs to stay fixed on one thing. We then realized that we can just move the motion detector in a circle by holding it close to you and then going around so your arm is stretched out in front of you and then back close you to you, all in a circular motion. Graphing calculators are definitely a great way to incorporate technology into the math classroom but I personally find them difficult to use, which is probably just due to my lack of experience. I think computerized graphing technologies such as desmos and/or gizmos seem to be easier to understand and are more user friendly. It is definitely important to some sort of graphing technology into the classroom, if it is available, as I think it really helps the visual learns as well as prepares students for post-secondary school. I remember getting to University and having to use graphing software in many of my math and physics classes and it was a huge learning curve since I wasn’t really exposed to a lot of it in high school.