Exciting Mathematics

Hi everyone,

This week was my final in-class session of my teacher’s college Mathematics course. This year has definitely flown by (way too fast) and I am grateful for the new insight and knowledge I am able to take away with me from this course. I am looking forward to implementing many of the activities we have explored throughout the year in my future classroom.

For the final lesson learning activities, the topics included: grade 9 and 10 Locally Developed and grade 11 Workplace. Similar to the presentations last week, I thought the activities were extremely practical and are designed to allow students to make real connections to their lives. Across all subject areas, it is critical educators take the time to create lessons that students deem both relevant and meaningful. If student’s can “see a purpose” to what they are learning, their engagement and motivation will increase and likely lead to higher levels of success.

Planning a Bowling Night

The first lesson learning activity I would like to highlight is Jenny’s “Friday Night Plans.” During this activity, students were required to plan either a bowling or movie night. Students were provided with transportation information for a cab, Uber and bus. Students set a budget and also had the opportunity to research where they wanted to go in terms of location. The activity we were completing was specific to Hamilton and this would obviously be adjusted based on your classroom and geographic location. With this being said, the activity became very real and relevant to students lives. Although a group of teacher candidates, you could still hear and see the excitement in the room about completing the activity. I can definitely see myself implementing a similar activity in the classroom; whether with a grade 11 Workplace class, or modifying it for a grade 9 or 10 Applied level class. Personally, I think this lesson models an ideal 21^st century learning classroom. The lesson fosters inquiry learning, technology, collaboration, mathematical reasoning and problem solving skills. As educators, we need to get our students excited about their learning.

World Records and Proportional Reasoning

Teaghan’s grade 9 Locally Developed lesson learning activity focused on proportional reasoning and beating the world record for clapping within a minute. Students were shown a short 4 second clip of the individual clapping and required to estimate the total number of claps. Students were then asked to make a prediction before the number was revealed. Again, a clip was shown and paused within the minute of clapping and students were asked to think about their predictions and adjust them based on the information they were provided. Throughout this process, students had the opportunity to discuss and reflect on their mathematical reasoning behind their predictions. During her lesson, Teaghan also used a “notice and wonder” chart, a new tool that really causes students to stop and analyze the task at hand. This strategy also allows the teacher to gather information as the students are “thinking out-loud.” Again, there was an extrmeley high level of excitement within the classroom and friendly competition for whose prediction would be the closest. I thought the activity was very engaging and will definitely have the same effect on students.

Over the past few weeks I have seen many exciting and insightful presentations and believe as future educators, we have all grown greatly over the past six months.

Until next time,

Rachelle

Meaningful Mathematics

Welcome back,

As my journey in teacher’s college is quickly approaching the end, I will admit it feels very bittersweet. I am very excited to take the knowledge and skills I have learned throughout the year in this mathematics course and apply it to my upcoming practicum.

This week the lesson learning activities presented included: Grade 11 Foundations for Collage Mathematics and Mathematics for Work and Everyday Life, Workplace. As I am not extremely familiar with the curriculum for these courses, I was very intrigued by the activities that were presented. One overarching and very important theme I was able to take away from the lessons was the connections being made to a real world context. Not only were all the lessons extremely fun, they also provided students with the opportunity to connect the mathematics to a real scenario.

“Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.” – Paul Lockhart

Personal Finance

During Kyle’s Grade 11 Foundations for Collage presentation, students were provided with information on either a debit card or credit card. In addition, each group was given information such as: interest rate, monthly transaction fees, benefits, etc. Using this information, students had to calculate the total cost of using their card and paying for an expensive TV. As a class, the groups compared their cards and discussed which credit or debit card company offered the most cost efficient solution. I really enjoyed this activity because it stimulated discussion about a real world problem many individuals will encounter. Although it may not seem necessary to teach at such a young age, I believe it is extremely valuable so students gain an understanding about how various methods of payment work. This activity is also very easy to modify. For example, if I were to use this activity, I might give each group a different debit and credit card to compare at their tables, as opposed to waiting for a whole-class discussion.

Remodelling

The next presentation I would like to highlight is Heather’s activity focused on proportional reasoning for Grade 12 Mathematics and Work for Everyday Life. As a group, we were provided with a floor plan, some dimensions and various samples. Our task was to remodel the floors based on the square footage of each room. I thought this activity was very engaging and my group members and myself found became “into” the activity. My group also used our problem solving skills to determine dimensions from rooms where they were not explicitly provided. Again, calculating the square footage and pricing of flooring is a skill many individuals will benefit from when trying to remodel. I can also see myself using this activity in the classroom. Considering how consuming the activity is, the only change I would possibly make is provide students with a few number of samples. 

In conclusion, I really enjoyed how all this weeks activities met the needs of various learning styles (especially tactile learners). I can see myself using these lessons in my classroom and would expect students to enjoy the activities as much as I did! 

Until next week, 

Rachelle

GrAdE tWelVe CoUrSeS

Welcome back! I hope everyone is enjoying the week thus far.

This week in class, my peers presented lessons on the grade twelve University courses: Advanced Functions, Data Management and Calculus. Taking on the grade twelve courses is not an easy task and therefore I congratulate them for taking on the challenge. I was very impressed with the lessons I saw and thought my fellow teacher candidates did an excellent job creating engaging and meaningful activities.

Dominos

For the Advanced Functions presentation, students were required to practice their Logarithm Laws by participating in a game of Dominos. Taking the rules of traditional Dominos, students are required to pick five different dominos, each containing a logarithm. When their turn approaches, they are required to build off the previous person’s domino, or if they can’t play, pick up. Each person has forty-five seconds to determine whether the numbers on their domino correspond to a played domino. I really enjoyed this activity as it’s a great way to practice fundamental skills while fostering friendly competition. Although the game is supposed to be played individually, my group decided to collaborate as a whole to complete the game. This may also end up happening in the classroom, which is perfectly ok. Simple and engaging activities such as this one are very effective in the classroom, especially with grade twelve students who often approach academic math classes with a higher level of seriousness.

Deal or No Deal

Reflecting upon my high school experiences, Data Management was my favourite Mathematics course. I remember it being ‘fun’ and interesting, with so many different activities that related to real-life scenarios. During this learning activity, our class had the opportunity to participate in a game of ‘deal or no deal.’ Although current high school students may be unfamiliar with this game show, students of our age group are able to relate to this activity.

The game involves different dollar amounts and twenty-six briefcases. Students are required to open a certain number of briefcases each round, revealing different dollar amounts. After opening the brief cases, the banker makes the contestant offer. As the contestant, it is your job to determine the probability whether or not you have a greater chance (or higher probability) of a larger dollar amount that could potentially be in your selected briefcase. I really enjoyed this activity because it demonstrates to students as to where they may use probability skills in a real-life scenario. Since the game is so fun, students can easily forget that they are working on their mathematical skills. I can see myself using this in my classroom as an introduction activity to probability. Being a group activity, it fosters collaboration and communication amongst students and therefore is a great method for building a sense of community within your classroom.

Often grade twelve mathematics classrooms can be  very stressful environments with many students trying to attain marks to get into University programs. Although it is critical to ensure they are provided with the fundamental skills they will require in University, I think it is equally important to take a step back sometimes and ensure these students are still having ‘fun’ in math class.

Bye for now, 
Rachelle

Zombies and Exponential Functions

Hi everyone,

In my teacher’s college math course, we are continuing to present lesson-learning activities and I am thoroughly enjoying all the creative and insightful ideas being offered. This week in class, my fellow teacher candidates had the opportunity to work with the grade eleven curriculum and being a course I personally enjoyed, I was extremely excited for their lessons. This week, I would like to focus on the learning activity where the class was introduced to exponential functions through a series of stations.

 

During this ‘action’ component of the lesson, the class was divided into small groups and instructed to move to a series of stations. As shown in the picture on the right, there was instructions and counters at each station. On the worksheet, students are required to create a table and graph and the lesson concluded with reflection questions that were taken up as a class. I really like how this lesson fostered student communication and problem solving skills. With my group members, I worked collaboratively to solve the problems while discussing our mathematical reasoning. I believe it is very important to encourage students to share their thinking process out loud, in addition to the traditional paper and pencil techniques.  

Regardless of the subject, it is important educators take the time to know their students in order to make content relevant and meaningful for the unique learners in their class. In doing so, educators are demonstrating their commitment to student success, as well as demonstrating they care about what’s going in their student’s lives. I thought this was exemplified exceptionally during this lesson. The activities included the themes of zombies, the ice bucket challenge, and folding paper (which was actually completed on myth busters). Although it may be ‘simple,’ by taking the time to invest in and understand your student’s interests, it’s the difference between a normal lesson and an engaging and interesting lesson. The only suggestion I can offer for this lesson is ensuring students understand that they are not adding on to the number of “something per day.”  While the instruction sheet clearly indicated that the table was based on the number of zombies each day, based on my groups knowledge of zombies (i.e. from movies or books) they had a difficult time not adding on to the number of existing zombies. Although extremely minor, this is something I would not thought of unless my group members mentioned it it. I personally do not always enjoy using manipulatives to demonstrate my understanding; I found the use of counters really helped me visualize the pattern from ‘day-to-day’ within the table. This activity reinforced the importance of differentiated instruction, as well as adjusting your teaching style to meet the varying needs of learners within the classroom.

Although a university student, I still found this activity extremely engaging and therefore is definitely something I can see myself using in my future classroom.

Until next time,
Rachelle

Taking Risks

Hi everyone,

This week, I was responsible for planning and presenting a grade 9 Applied-stream lesson. I really enjoyed the process of designing a lesson and I believe it was a good opportunity to consider different learning styles, anticipate student responses and incorporate technology. In my lesson I used CBR’s (Calculator Based Rangers) and thought they were engaging even with our skill base. Although I have heard of CBR’s in the classroom, I have never had the opportunity to implement them into my own teaching. Considering this, they are a great and simple tool and as demonstrated in class, foster collaboration, critical thinking and problem solving. My peers this week also presented grade 9 and 10 applied-stream lessons. I would like to comment on both learning activities as they were extremely well done!

Factoring Simple Trinomials

During this lesson (Grade 10 Applied), students are provided the incorrect solution to a factored trinomial. Working as a group, students are required to determine the correct solution, explain their mathematical reasoning and represent the solution using algebra tiles. I really enjoyed this activity because it fosters “math talk” in the classroom. While completing this activity, it caused my group members to engage in rich conversation regarding different methods. I believe this would also be the same case with students in the classroom because there are numerous methods for solving simple trinomials. Furthermore, the use of algebra tiles is a great manipulative for visual and tactile learners. Personally, I do not have a lot of experience using algebra tiles, however, I believe it's a great tool to use in the classroom. Groups also had the opportunity to present their solutions, fostering communication skills. I can defiantly see myself using this activity in my classroom and modifying it to apply to various mathematical concepts.

Solving First Ordered Equations

Solving first ordered equations is a straightforward concept, however, as demonstrated during this lesson, there are many fun and engaging activities to implement in the classroom. I thought it was extremely brave of Cobie to take on the task of using the Smart Board for the first time. Educators fortunate enough to have access to Smart Boards are fortunate for the wide range of activities and programs that can be utilized. During this lesson students had the opportunity to work through the problem within groups and at the Smart Board. I liked the idea of the entire group working together line-by-line to solve the problem. This allows students to think about the steps of solving the equation both before and after their turn. Again, this activity met the needs of various learning styles. It is important that educators find ways to make simple mathematical concepts for engaging and meaningful for students.

This week, there were a lot of “firsts” regarding technology. It is important that educators are willing to take risks in their classroom. Doing so allows teachers to reflect, modify and improve upon their lessons for the future, or the opposite can occur and you can scratch the lesson all together.

Enjoy the rest of your week!