Day 12 - Annuities Exploration Day 2

Today students continued to work on the annuities exploration that they started yesterday. We had a good teachable moment because the definition for "annuity" that Google gives is not a very good one and so today I spent more time trying to explain to students why it isn't a good definition. It is a good instance of students seeing an "answer" online that isn't actually correct. Hopefully they will think more critically in the future!

I explained to students that their answers should have detail, that I should be able to read the answers aloud to students in a different class and they should be able to understand the answer. I don't have a full complement of iPads today, so I realized that I could not use Explain Everything today. I will collect this work, but not mark it. I think what I might do, is get them next week to use what they have learned to make a video explaining annuities and mortgages. That might get what I wanted out of it while being able to move on for now.

Tomorrow I will not be there but students will have a supply teacher. They will be working on conditions of annuities:

They have a filled in version of the lesson that they will read through and then they will work through the homework:

I will, on Monday, talk to students about the big picture questions that relate to this topic:

1. If you are investing, what would you look for in the conditions of your investment? (i.e. interest rate, compounding frequency, length of time of the investment etc.)

2. If you are borrowing, what would you look for in the conditions of the loan? (i.e. interest rate, compounding frequency, payment frequency, length of time of the loan etc.)

3. When you go to a bank, the amount of money that they say you can borrow may be really high. Is it a good idea to use the maximum? Why or why not? What would they be basing their decision on? What do you need to think about when you go to buy a house?

I will not be writing tomorrow so have a good weekend readers!

Day 11 - Annuities Exploration

Today students went online and researched annuities and mortgages.

This is an old activity that was created by some folks at OAME. I especially liked the first table where students had to decide which situations were describing annuities and which were not. Most could do this without trouble but there were a couple sticking points. If you search "annuity" in Google, the definition that comes up is "a fixed sum of money paid to someone each year, typically the rest of their life". This definition is not a very good one when students are trying to understand an annuity in a mathematical context. The table that follows on page one allowed students to see examples and non-examples, in a borrowing and investing context. If students needed to look up the definition, this table allowed them to deepen their understanding and be able to understand beyond the Google definition.

The challenge is getting students to write more. I want them to give me complete answers. I think that I need to be more creative in that. Maybe I need to have them take their answers and make a video on Explain Everything that will allow them to expand on their answers and show me what they really know instead of the one word answers that they are giving me. Either way, students definitely need more time. I had to leave early but because of discussion that we, as a class, had at the start of the period, students did not get through this. I will give them an extra period to work on this. I think it is worth my time! So stay tuned for how day 2 of this activity goes!

Day 10 - Review/Preview to Investments and the TVM Solver

Today we reviewed the use of the TVM solver and the terminology required for investments:

Students definitely needed the review! They did get the hang of it fairly quickly but their investment math was definitely rusty. In particular, students needed help figuring out the difference between a compound interest problem and an annuity. There was some difficulty figuring out what numbers go where but they helped each other with this. By the time they got to the work, it went quickly and they definitely worked together. I am finding that if the work doesn't look too daunting, and it is somewhat challenging but not too overwhelming, the students will do the work well in class. They are all using class time well. Perhaps this is the honeymoon period but I am feeling pretty good so far!

Work:

Day 9 - Optimization Problems

Today students worked through optimization problems:

Students worked through this well and I will collect their work on Tuesday. This makes me feel better about the last few days! It is very much "old school" practice but students are a little bit challenged and are doing well. They clearly got the concepts I needed them to get from the previous lessons. They are also working really well together and are largely focused. Wow am I a lucky teacher!

Day 8 - Optimizing a Cylinder

Today we worked on optimizing a cylinder:

I worked through this activity more like a note, but I think I would change it up next time I do it. I might try a GSP activity or if there is a Gizmo I might try that instead. This activity required students to think of a number squared times another number that gives 500. There are a couple easy answers but it is not easy for students to work through that. I would rather they get the mathematical idea but by dragging something that gives the dimensions and surface area for them. It didn't go badly but I think it could have gone better. Live and Learn!

Day 7 - Optimizing Rectangular Prisms

Today we optimized 3-dimensional shapes. Today we only tackled the rectangular prism:

I was happy to get back to an activity with this class. Activities, especially hands-on with manipulatives work better with this group for sure!  Also, getting them to understand how to make multiple prisms with a volume of 48 cubic units would be impossible without the linking cubes. While groups did not make all their prisms with the cubes, they almost all started the activity with them.  Some student work:

Finding the surface area was trickier than I thought it would be, but I was missing a few students yesterday and the students who missed finding the surface area and volume of composite shapes yesterday definitely had a harder time. Because students had done a similar activity with 2-D shapes, the graphing was much easier:

They definitely came away with the idea that a cube will make the optimal shape, which was the important idea of the day!

Day 6 - Volume and Surface Area of Composite Shapes

Today we worked on the surface area and volume of composite shapes:

We started with an example and we only did one. I liked that I didn't try to do more. They did understand it well and their attention really only lasted in doing that one example. There were lots of practice questions:

I tried a strategy that I learned from one of the books regarding learning mathematics and discussed at our last Mathematics Learning Communities meeting - I asked students to do the easiest and the hardest question from each section. They also had to explain why they made the choice that they did. That way they have to look at all the questions but only put pencil to paper for a few. I felt like this strategy worked the way I wanted it to. Students put more thought into what they would do to solve the questions and actually got started. In the past, faced with this work, students would be daunted and not even start. This wasn't the most exciting of lessons, but it seemed to work well. I wanted to have a bit of practice under their belt before they get to do something fun with this concept.

Day 5 - Optimizing Triangles and other Shapes

Today we looked at optimizing shapes other than four-sided rectangles:

I did change a few things: Under "Practice", 1c asks for a right-angled triangle, but I took out the right-angled. Since we discovered that an equilateral triangle is the "best" shape, I felt it best they get a chance to practice this.

I would change this lesson next time to be honest. I think I would take out the questions about circles and add more practice questions that they could do on their own. I felt that I had to get them started. It had been too long since they had done any optimization and so it would be hard for them to recall it. Students were not nearly as engaged in this as they had been previous days and I think it was because they did not feel as confident. I don't mind stretching their minds but this was asking them to remember concepts from grade 9 without reminders. Perhaps if this activity had been in a different place in the course?

Overall, week 1 was still a success!

Day 4 - Cagey Problem Part 2

Today we did a short optimization activity that followed directly from yesterday's work. We optimized a rectangle with a fixed area:

Again, this activity took students at most half an hour. They completed it easily but it was a little harder than yesterday's work. Once they got how it worked, they filled out the table well enough. We noticed that while we got a perfect parabola yesterday, today the graph did not look that way:

We discussed briefly why it did not give us a perfect parabola, but students were keen to get back to their floor plans.

Day 3 - Cagey Problem

Today students worked on optimization review. We worked on finding the maximum area with a fixed perimeter:

I used a similar activity with grade 9s last year and remember that they didn't really know what to do with the Q-tips (I used Q-tips instead of toothpicks so students couldn't stab each other). I started them out by giving an example of one rectangle on the board. They quickly got the table filled out:

Students then needed to make a scatter plot:

While a few made a couple mistakes at the start, soon I had some pretty nice looking parabolas!

This took very little time. I could have done Day 3b, but I remembered from yesterday that students were going to need more time for their floor plans. While they made nice looking floor plans, they did not take into consideration their scale. Their plans needed to be for a floor plan that is roughly 1200 m2. If they didn't keep their areas in mind as they were working, then finding their scale after the fact is hard. So I decided to just take it slow (especially since I added 2 more students to my class list today!) and give them more time for their projects.

Day 2 - Designing a Cottage Floor Plan

Today students designed their own floorplan:

Students got creative!

Some students had more details than others but they all made a good start on this activity. I think more class time will be required but overall it was successful. I did need to remind students that though some arcs look nice, if it isn't a recognizable section of a circle it would be hard.  Also students needed to be reminded that if the scale is 1cm = 2 m, then 1cm2 = 4 m2.

Cycle 1 Day 1 - Area and Perimeter of Composite Shapes

The project we are starting with is a "New Job, New House" project. We started day 1 with introductions and just did an activity where students found the area and perimeter of a composite shape (i.e. a cottage). This is one of the great activities I got from Ms. McClennon-Sowchuk.

I found that the students at first thought that this was going to be an easy activity but when they got into it, it was much more challenging. Yet they were engaged in it for the whole period and talking to each other about how to do each part of it. There measurements were good and few students needed a formula sheet but there are parts that are definitely tricky.

Tomorrow I will take up parts of it and the students will get to design their own floor plan and find the area and perimeter.

Introduction

Hello and Welcome! My name is Pamela Chun and I have been a teacher of Mathematics for 12 years now. This year I am trying something new, with a colleague (Shout out to Deanna Ward!) with Grade 12 College Mathematics (MAP4C).

Do you find that students in this course lack motivation? Have you thought about spiralling but don't know how to get started? Do you want to add more activities more than traditional lessons? These are the questions we tackled in the summer. We designed the course around 4 or 5 projects (instead of units and tests). We tried to add a relevant purpose to each one so that students could see where they might use each concept learned. We know that this won't work for all expectations, but the projects do cover most of them and we can throw in a couple expectations at the end with a more traditional test. Deanna did this last semester and I am trying it this semester. I have a keen group but I do have a disclaimer - I have 13 students, all boys and all interested in a tech program when they finish high school.

In addition to working with Deanna (and therefore getting a lot of materials from her), I would also like to acknowledge Ms. McClennon-Sowchuk. We shamelessly used her materials that we found online for this course. Some were modified and others were not. I don't want anyone to think that all of these were made by me! However, I hope that by reading this, you get some of your own ideas or it helps you in some way.

All the best and good luck in all your teaching adventures and experiments!