Making Math Come to Life in a Grade 11 Workplace Class

Dear readers,

It has been a while since my last post. I'm sorry for the delay, but life got in the way! This post is dedicated to a fellow teacher candidate who goes above and beyond in her classroom. She is super smart, creative, and always comes up with phenomenal ideas for lessons and activities to use in the math classroom. As I mentioned in my previous posts, this semester is dedicated to learning about the different mathematics streams available from Grade 7-12. My classmate took on the Grade 11 Workplace stream and came up with a super awesome lesson that I cannot wait to try in my classroom-if I'm fortunate enough to teach Grade 11 Workplace that is!

As mathematics teachers, we constantly strive to find a way to make our units and lessons relevant for students; we need to make the math applicable to their lives, in order for them to want to learn. Otherwise, what is the point? We have questions like, "Why is this important? When will I ever need to use this? Why am I learning this?" A great way to answer these questions is to allow students to reflect and make connections between the math and real life. How could their learning be applied to the world? We know that reflection is the key to learning and higher order thinking, so we need to devote some time to student reflection.

In Grade 11 Workplace math, students are learning about budgeting and personal finance. Unfortunately, this can often be a boring topic for students, especially those who would rather spend their money, than save it. My candidate, Ms. T, designed an activity to allow students to learn about designing a budget, and planning an event, while giving them an opportunity to reflect on their choices and end result.



Ms. T wanted her students to plan a Friday night outing. She had two worksheets that the students could choose from: movies or bowling. When the students chose their outing for Friday night, they would work in pairs or groups of 3 to choose a budget for their night out. They would then figure out which movie theatre or bowling alley they would like to go to, while noting down the address in their workbooks. From there, the students will figure out how to get from their school to their choice of venue by choosing two modes of transportation and figuring out the cost of each. They will also calculate how much money it will cost them to buy a movie ticket or entry into the bowling alley; and how much they will spend on snacks or dinner. After they make each decision, they will reflect on why they made the choice they did. Finally, they will reflect on their overall budget: Did they stay within their budget or exceed their initial budget? What factors helped them stay within their budget or made them exceed their budget?



This was a really fun activity that is applicable to the students. They will all need to be able to plan and budget for a night out with their friends or family, so this activity allowed them to see the different aspects of their night that they need to account for, such as the destination, transportation, price of admission and additional foods and beverages. It also allows them to reflect on how they managed to stay within their budget or why they may have gone over their budget. I think that this activity will be something that they remember and use, not only when planning their Friday night, but when they are planning other trips and future events.

Mathematics Presentations Part 3: Grade 9 and 10 Applied

CBR

Welcome to another week of Math Presentations! This week in my Math Teaching course, I got a chance to see three more of my peers present on a lesson that they would use in either a grade 9 or 10 applied Mathematics class. My favourite presentation focused on a Grade 9 applied level class, learning about linear relations. This lesson could be used at the beginning of the linear relations unit, to introduce the slope of the line (rate of change) using a kinesthetic approach that students will love. The activity works by getting students into groups of 2-3. Each group receives a CBR, a calculator based ranger by Texas Instruments, along with a page of different graphs and their lines. A CBR is a calculator based ranger designed by Texas Instruments to track student motion using lines that will display on their TI calculators in a graph.

The goal of the activity is to have students try to replicate each graph by matching their motion to the slope of the lines in each graph. My group had a lot of fun figuring out which direction and speed to walk in order to match each given graph. By the end of the activity, we were able to understand the following:

1. Speed affects the slope of the line 

2. Walking fast produces a steep line 

3. Walking slow produces a fractional slope

4. Walking at a constant speed will produce a constant slope of 1. 

5. Walking away from the CBR will create a positive sloping line

6. Walking toward the CBR will create a negative sloping line 

I think that this activity would work really well in a grade 9 level applied classroom because it introduces the concept of linear relationships the students in a way that is fun and engaging. The students can literally graph their movement electronically to make their own linear path! They will be able to learn math, while getting some exercise in at the same time. I love this idea, and I would love to try it out in my own classroom! 

Math Presentations Part 2: Grade 9 Academic

Hi fellow bloggers! This week in my Math Teaching course was round 2 of math presentations. Four of my peers went up one by one to present on a math activity that they would do in a Grade 9 Math classroom. All of the presentations were excellent, and I found myself taking notes, so that I could try these in my Math placement. However, there is one activity in particular that I would like to focus on for today's blog. The topic was Grade 9 Geometry and the students would be learning about how to find the sum of the interior angles in any shape ranging from a triange (3 sided figure) to a myriagon (10,000 sides)!

In order to help students figure out an equation to solve for the sum of the interior angles, there was a guiding example that helped students make the connection! The teacher (Mr. F) would ask the class to draw any triangle that they wanted; it could be as small or as a big as they would like. The next step would be to figure out where the interior angles were on their triangles. When they found these as a class, he would instruct them to draw the angles in. They would then take a pair of scissors and cut out the triangle, before cutting out the interior angles. The key to this example is the interior angles. When the students have their 3 interior angles, they need to find a way to fit them together to make a semi-circle. Mr. F would guide them by asking what shape they just made; when they understood the shape, he would ask them to pull out their protractors and measure the angle of the semi-circle. It was 180 degrees! Even though each student drew a different triangle, they were still able to get the same result, which proves that the sum of the interior angles of any triangle will always equal 180 degrees. How cool!

Once the students had this knowledge, he passed out a guiding worksheet for the students to work on individually or in pairs. Even though it was an inquiry based worksheet that helped students to explore how to find the sum of the interior angles for any shape, it also provided some guidance to ground student thinking. It instructed students to try to make the smallest number of triangles from a single point A to any other vertex in the shape! I thought that this was a great way to keep students on track, yet keep it open enough so that they could experiment and try different things before coming to a solution. Finally, the students would have to fill in a chart to identify the relationship between the number of sides of a shape and the smallest number of triangles that they could draw inside of it. Overall, this was an outstanding activity!

I think that students from any stream (academic, applied, and possibly essential) could complete this activity because while it was geared towards students exploring and playing around with an abstract concept, it was also concrete in its guiding questions and semi-circle example. Students would be able to make the connections between the sum of the interior angles of a circle, the number of sides of a shape, and the number of triangles inside the shape. If students needed any more guidance, the teacher could provide one-on-one support, or more guiding questions, to help scaffold student learning. I will definitely try this in my class!

Math Presentations Part 1: Grade 7 or 8

Hi everyone! It's been a long time since my last blog post, but I am back for the new semester! Last week in my Math Teaching course, we were given the opportunity to present on a lesson activity that we would do in a grade 7 or 8 classroom. One of the presentations that really stood out to me was geared towards a Grade 8 level class learning about plotting coordinates (x, y) on a coordinate grid.

In order to spice up a traditionally dry mathematics concept, Ms. J decided to try something different. She took a kinesthetic approach to her activity by having students move around the classroom from station to station. She had eight stations set up around the classroom, so she divided the class into 8 groups and directed each group to a different station. At the first station, students would be given the coordinates for a stick figure's head and bottom. They would plot their stick figure on their coordinate grid, and they would fill in the accompanying chart to decide whether the stick figure was standing upright (head to bottom) or upside down (bottom to head). Once each group had figured out their man's initial position, they would be given a clue to help them find their next coordinate. Ms. F was helping them figure out transformations such as reflections and shifts, so each clue would focus on transforming Mr. Stick Figure's position in some way. When the students had completed their transformation and had the new coordinate position, they would need to look around the classroom to find the station that had their matching coordinate. At the next station, students would find their next transformation clue, complete the transformation, obtain the new coordinate, and move onto the station that had a matching coordinate. Students would proceed around the classroom like this until they had completed each of the eight stations.

As a reflection/consolidation of what they had learned, Ms. F would ask her students to take Mr. Stick Figure's current position, and help move him back home, so that he could go to sleep. In order to complete this task, students would need to know his last coordinate position, whether he was upright or upside down, and the coordinates of his house. They would need to find a transformation that would help get into a sleeping position (sideways) in his house!

I thought that this was a great activity because it got students moving and thinking, two things that are essential parts of learning. As teachers, we know that students cannot sit down for long periods of time because it's hard for them to sit still and concentrate; therefore, having them move around the classroom, while still doing math was a great way to promote student engagement, and give them an opportunity to stretch their limbs. I also loved the way that Ms. F helped students understand the transformations that were happening to Mr. Stick Figure because they could clearly see when he was shifting, reflecting, or moving from an upright position to an upside down position. If I ever get the opportunity to teach grade 8, I would love to try this in my classroom! However, I think that Ms. F also taught me that this lesson or concept of a scavenger hunt through the stations, can be applied in different grade levels and subjects across the curriculum. I am looking forward to incorporating movement and fun scavenger hunt activities in my math classroom!