Week 14: Trigonometry

During week 14 we looked at different trigonometry topics in the math curriculum. In grade 10, students learn the primary trigonometric ratios. I remember being in grade 10 and being taught trig ratios by memorizing SOH CAH TOA.  The activity we looked at took a much different approach to introducing students to the concept.

The activity introduced the primary trigonometric ratios using a hands-on inquiry method. The first trig ratio being introduced was tangent, but this same activity could be used with sine or cosine. Students began the activity by measuring and recording the length of the sides of triangles that were drawn on the classroom floor using tape. These triangles were drawn so that there were 3 sets of similar triangles. Students would then calculate the ratio of the opposite and adjacent sides and talk about what they noticed and wondered about the results. Students would see that the similar triangles had the same ratio results and questions could then be asked about finding values for triangles other than the 3 similar triangles.

I really like the idea of this activity because I feel like students would gain a better understanding of what they are doing and connect it to their previous unit on similar triangles.  I think it is easy to introduce a topic like primary trig ratios by simply providing the formula for ratios and not provide students with the opportunity to understand what it is these ratios mean. This is an activity I would really like to try with a future grade 10 class.

Another strategy this activity reminded me of was taking time in lessons to ask students what they notice and wonder. By asking these questions students are able to really think about the problem being presented, connect their thinking, and ask questions. I hope to be able to use the I notice and I wonder prompt during my next teaching block.

Week 13: Grade 12 Mathematics

The 3 courses that were covered in the learning activities this week were Data Management, Calculus and Vectors, and Advanced Functions. All of the activities were fun and engaging, and resources I want to keep in mind if I teach these courses. 

Vector Snakes and Ladders

http://www.codewithc.com/snakes-and-ladders-game-project-c/

Using the concept of traditional snakes and ladders, a vector version of this game was played, using concepts from the Calculus and Vectors course. The new game board contained different vectors that we need to calculate. It was fun to complete the calculation not knowing if it would be a snake or ladder right away. This game was very engaging and a great way to practice the concept of adding vectors.

Permutations and Combinations

The second activity completed involved exploring the concept of permutations and combinations, which is found in the Data Management course. Using examples of ice cream flavor choices and purchasing sale clothing items, we worked in groups to figure out the different ways to arrange these. I really liked that the activity started using visuals to determine the different options. From there, we were able to develop formulas for permutations and combinations. I thought that this activity was a really good introduction to a topic that can be confusing for some students.

Math Escape Room

The last activity we completed was a math escape room that involved review questions from the Trigonometry unit in Advanced Functions. This activity was also completed in groups and required us to solve math problems and riddles to find the location and numbers to unlock the final prize box. I thought this activity was much more interactive than a typical review and would have students very engaged and moving around the room. This activity could be used in many different subjects and I hope to be able to try it out during my next block. 

Week 12: Grade 11 Mathematics

There are four different math courses that grade 11 students can take: University, University/College, College, and Workplace. In the first three courses the common topics are quadratics, exponential, finance, and trigonometry. The learning activities during week 12 focused on grade 11 college and grade 11 university/college curriculum expectations. 

Personal Finance: 

http://www.wadeinsurance.net

The grade 11 College activity we completed was from the personal finance unit. In this activity, we worked in groups to determine what the cost benefit was for a new driver who took a driving course on their insurance. The activity was presented so that groups were working together to determine the solution. This activity allowed us to solve the problem different ways and could be differentiated for students. It was interesting to see the different values found and how changing features (like car, gender, age) affected the end cost. This activity also provides students with context and relevant information. Overall, I think this activity would be engaging and fun to investigate with students. 

Trigonometry:

https://illuminations.nctm.org/Lesson.aspx?id=2870

The grade 11 university/college activity we completed looked at the relationship between the sine ratio and sine function. This hands-on activity allows students to create the sine function using their previous knowledge of the unit circle and the sine ratio. Using spaghetti, we measured the value of sine at different angles around the unit circle. These pieces of spaghetti created the sine function graph. 

This activity also has students look at key features of the graph (for example the amplitude, increasing and decreasing intervals, and maximum and minimum values). Although this activity was presented for the 11 University/College course, it could also be used in the grade 11 University course.

Overall, these are both activities that I hope to use with grade 11 students in the future.

Week 11- Grade 9 and 10 Applied Math

Week 11 started off looking at the academic and applied streams of math. A difference noted in the descriptions and curriculum expectations were the increased emphasis on hands-on applications in the applied courses. This was well demonstrated in the two learning activities presented.

The first activity was a dice area activity for grade 9 applied math. This activity was played in partners and involved rolling two dice and creating rectangles on graph paper of the corresponding size. The activity also required us to determine the perimeter and area of the rectangles.

https://www.vecteezy.com/miscellaneous/21212-red-vector-dice

I enjoyed this activity and felt that it was a great introduction to the topic of maximizing area with a set perimeter. I also think this activity would provide students with practice on finding area and perimeter of shapes without having to complete a more standard worksheet. The supplies for this activity were minimal (only requiring dice, graph paper, and a recording sheet) so this could easily be used throughout the unit as an activity when students were done other work.

http://www.c-sharpcorner.com/uploadfile/75a48f/tic-tac-toe-game-in-c-sharp/

The grade 10 applied math activity was on the trigonometry topic. In 2 groups we first had a relay style races to complete a game of tic-tac-toe. Then, when divided into two groups based on height, we had to determine how to make the game fair. From this, we calculated stride length and determined the new starting distance for each group to make it fair. I really liked this portion of the game because it did not seem like we were doing much math, were, in reality, there was math and problem solving involved. The second portion of the game involved throwing the rings to a target and then using trigonometry to calculate the different distances. I think an applied math class would like this type of activity, but the classroom space would have to allow for such an activity.

Cup Stacking

Cup Stacking 

An activity we did this week involved cup stacking. We needed to figure out how many cups tall our instructor was.

The information that we were told was that 5 plastics cups=12 cm, 12 plastic cups= 20 cm, and the instructor's height. 

Trying to solve this problem was something I struggled with so it was helpful to see different ways of solving this problem. The method that I thought was most interesting was using the values given as coordinate points to determine slope, y-intercept, and then producing a graph. I had not even considered solving this problem graphically and was stuck trying to approach it in an algebraic way.

http://mr-stadel.blogspot.ca/2015/05/the-ultimate-task-for-vertical-planning.html

It was also suggested that students could complete this activity as a way of demonstrating direct and partial variation. I thought this connection was great visual since students in my placement grade 9 class struggled with the two.

http://mr-stadel.blogspot.ca/2015/05/the-ultimate-task-for-vertical-planning.html

A variation of this activity would be to use different types and sizes of cups, and looking at when the two stacks of cups are equal.

What stuck out from this activity was the variety of ways students could approach and solve this problem. It was also mentioned in class that this activity could be used as a consolidation of a concept, or as an introduction to the topic.

I found this activity to be fun and interactive, and hope to be able to try this out with a future class. 

Grade 7 & 8 Math

http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

Week 9’s class focused on looking deeper at the grade 7 and 8 Math curriculum. Even though I hope to be teaching high school math, it was very interesting to take a better look at the concepts being taught in grade 7 and 8. As a high school teacher, it will be important to know what knowledge students enter high school with.

A really interesting activity we did was developing a sequence of expectations from grade 7 through 9. We looked at the different strands and discussed where we thought expectations would be sequenced. It was more common to have grade 7 and 8 expectations sequences well, but it wasn’t always easy to find the grade 9 expectation for a particular topic. When teaching grade 9, I think this is going to be an important resource to remember and take into consideration when teaching. 

Making sense of division of fractions

https://www.pinterest.com/ranndomvariable/fractions/

Before this week, I had not considered why the method of invert and multiply works when dividing fractions. I was taught to invert and multiply and never questioned it. 

A concept like division of fractions doesn’t really seem like it would be that complicated to explain, but it certainly got me thinking. 

When being asked to divide 2 whole numbers, or even a whole number and 1 fraction, the use of a visual can demonstrate the process well.

However, when dividing a fraction by another fraction, it becomes a little harder. After thinking about this for a couple weeks, and seeing several different explanations in class, I now feel like I have an okay understanding of it. Looking at the division of fractions got me thinking about other concepts we tell students to do without explanation of why. 

Overall, I really enjoyed the task at looking deeper into my understanding of division of fractions.

Reflections from block 1 & Moderated Marking

Reflections from Block 1

My first four-week student teaching block was an incredible learning experience. I loved being able to apply the knowledge from our classes with students in a classroom setting. The four weeks went by so quickly and I am so greatful for having an associate teacher and group of students who welcomed me into their classroom. This teaching block reinforced my desire of becoming a teacher.

Some of the most rewarding moments throughout this blocked involved helping students succeed. For me these moments included having a student change their mindset about “not being able to do math”,  having students interested in the topic and having a student who was previously disengaged volunteer to answer questions.

One of the resources that I found helpful to have during this teaching block was 3 act math. I often used these as minds on activities.  In the grade 9 class, when learning about distance time graphs there were several different videos that were able to be used. 

One of the challenges I found during teaching block was finding a method to catch students up on material they missed while they were away. Attendance varied greatly each day and there were times when it was difficult to move on to a new concept when several students were away for the previous classes. During my last two practice teaching blocks I hope to develop a method to address this.

Moderated Marking

This week we did a moderated marking activity in class. In groups of three, we were given sample grade 9 math EQAO student responses from an open response question. We were also provided with the scoring guide which listed indicators associated with each level. We graded each example individually and then compared marks as a group.

It was interesting to discuss our responses as there were several problems that we did not agree on marks for. The discussion turned to be what components or processes of the problem are more important or worth more marks. It was also interesting to discuss what each of us thought were the key indicators of student understanding for a particular problem. 

A key take away from this process for me was to make sure my marking is consistent. As a new teacher, I hope to be able to participate in a moderated marking activity again.