Cycle 2 Day 1 - Pythagorean Theorem

And on to the next cycle! The geometry we are doing in this cycle is mostly trigonometry so we are going to start the cycle in this vein. The project's theme is being a Research Assistant and starting a lab. So they will have to help build it (and need to do some trigonometry and decide on an optimal shape and dimensions of things), determine proper dosage and how much of the drug is needed in various circumstances (data management and algebraic models), and decide what kind of loan to get and how to invest profits (personal finance).

Today we worked on the Pythagorean Theorem. They have been seeing this since grade 8, so this is very much a review. The mistakes that often get made with the Pythagorean Theorem are that students try to use it with non-right triangles as well as they tend to forget that the hypotenuse is always the "c" (or always the side by itself on the one side of the = sign). So to address this, I started with the following activity:

 I am hoping by starting with this, students got the idea that they have to be careful which side they sum the squares of the other two sides and also that they cannot use the Pythagorean Theorem with any triangle. I pulled it together by finishing the lesson with page 3 and students worked on page 4 to finish the class:

Students flew through this and really seemed to understand. In retrospect, I might in future combine this with a review of SOH-CAH-TOA. We'll see!

Day 24, 25 & 26 - Cycle Project

For the last few days students have been working on their Cycle Project. The theme was "First Job, First Home". It covered all the concepts that I covered in the course to date in a "culminating activity" kind of format. It was 3 booklets, so too big to post here, but if you want a copy, just send me a note!

The first day, students did not take well to it, even though they had been told about it. However, by day 2 and 3, they got into the groove and felt confident. From the work I have seen so far, it seems pretty well done, but I will give a final note when I have marked them all! I definitely felt better about administering this than tests I have done in the past with this type of class. It was more relaxed. It was a lot of work to make and put together because everything had to fit in the theme, but since I did the bulk of that work in the summer, my time now isn't too strained.

Day 22, 23 - Cycle Review

We are finally at the end of Cycle 1! Today we reviewed what we have covered to prepare for the first project. I made a Powerpoint Presentation with review questions, and students worked through them at the White Boards around the room. (Yes I know that the buzzword is "vertical non-permanent surfaces" but let's be real - these are white boards or blackboards! Geez. Anyway.) Students worked in pairs and on the harder questions, pairs got together.

This worked really well for about 2/3 of the class time. I think I needed to put a break in there and then try to get them to come back. Some students worked well the whole period, but others gave up. Having the students standing and working on stuff I could see definitely worked better than having students work at their desk, but working for an hour requires more concentration on math than they have yet.

I won't be posting for a while because this review will take a couple of days and Wednesday of this week I will be missing most of the class due to Heights Training for their SHSM certification. On this day the students who are here will be working on resubmitting work to improve their grades.  All the best folks!

Day 21 - Linear, Quadratic or Exponential?

Welcome back from March Break! I hope that everyone is happy and healthy, and also celebrated Pi Day.

Today I snuck some abstract math into my cycle by examining whether the relationships that we had been studying in finance (i.e. renting, annuities etc.) contained linear, quadratic or exponential growth:

This lesson was quite easy for the students. It was a fairly gentle way to bring them back from the March Break. Most of the students finished the work before the class was done:

This was the last lesson before this cycle is done. It was a really long cycle. I find the first cycle was long last semester as well when I taught grade 9 applied using spiraling because you have so much to cover to give the broad strokes of the course with a few specifics. I am not sure if this is always the case but I might try to shorten it next time a bit.

We will spend a few days on review (with one day where most of the class will be missing due to Heights Training) and then the students will work on the final project of this cycle.

Onward ho!

Day 20 - Renting vs. Owning

Today students thought about renting accommodations vs. buying their own place. We started with a think/pair/share:

They did *very* well with this. I did not need to add anything and was in fact surprised at how much they thought of. We are in the country so most of these students do not live in rental housing. From there, we delved a little deeper as a class:

This produced some more good discussion. Again, I was surprised with how much they came up with. We finished off with a little bit of homework:

This was not that challenging for the students. They were able to complete the work before they left for the most part. Since most students are gone tomorrow, this was, for them, the last day before March Break, so given that, it was a great class. Not really "mathy" but good discussions.

Remember to celebrate Pi Day on March 14, and have a good week next week. I will sign off until March 20.

Day 19 - Budgeting

Today we discussed budgeting. I started with students writing down their first thoughts about budgets:

Once they had worked on their own, they did a think, pair, share. We then discussed definitions and did a couple examples:

Their work was to make corrections to their original budgets.

The students are done their mortgage mini-projects and we have a few small topics to discuss before a "unit summative" (or cycle summative really). Almost there! Unfortunately we are almost at March Break, so the timing was not perfect, and I am finding that this cycle is long because I have a lot to cover in this one for the project summative that I had planned. However, we will make it work! Part of it is that I have to get used to much longer stretches between true summative assessments. I am used to having around 8 in a semester, and that gets cut in half when spiralling.  Anyway, almost March Break! I hope that everyone out there is well! (And enjoy Pi Day on March 14! I have only one more chance to remind you -- most of my class is gone to an auto show on Friday, so I have Thursday's lesson and that's it!)

Day 17, 18 - Mortgage Project Continued

I have looked at Part 1 for each of my students and the biggest issue was that students chose a house and then described what they think they might need in 10 - 15 years. What I wanted was for them to think of what they need, THEN find the house that fits their needs. I don't really know how to get around that other than have students brainstorm in class, maybe, before they get to the lab. They get so excited about finding their dream houses! Also, many students did not pick a house that was realistic. I am not really sure, for the purposes of this course, that I care. They may decide, through the course of the project that the house that they chose will likely be beyond their means. On the other hand, it is fun to imagine! As long as they do the work correctly, I think I will allow it.

I am doing this project in Google Docs and having students share their work with me instead of printing. Since they need to include an amortization table, I think this is the best way to go. It also lets me "mark" part 1 and 2 before the whole thing gets submitted tomorrow and they get feedback along the way that is easy to incorporate into their document. It is also faster for me since I type faster than I write! I would rather have a "starting mark" and then be able to improve it once they finish the whole thing. These kids definitely need their confidence boosted and so I am trying to do that at every opportunity.

One other benefit that I am getting from this is I really feel like I am getting to know the students a little better and see more of their sense of humour. Some students were really specific in what they wanted "the house has to be 1 km from all neighbours", "I am going to have 3 children, 2 boys and a girl", and some just said things that were worded in a funny way "the basement is going to be a man cave which will be permitted by my wife". This made me wish that I taught some English! I definitely got to see another side to the students. And allowing them to look at their dream homes also helped me see what they value most right now. I am enjoying that aspect for sure.

Day 16 - All about Mortgages!

Today students started a little mini-project to sum up what they know about mortgages:

Students will be spending a few days in the lab showing me what they know. They were given an exemplar as well to work off of. They will use Google Docs again and share the file with me. I can still check that way that they are on track and completing each section on time. This allows me to give them feedback, should it be needed, before the whole thing is done.

Once this is done, we will be spending a little bit of time on budgeting and then do this cycle project. This is one of the longer projects of the course and I am definitely looking forward to seeing the results! 

Day 15 - Making an Amortization Table

Today students went to the lab and made amortization tables:

I got this from Ms. McClennon-Sowchuck. I really liked it because in the past, I would walk students through and it would be painful. I would be slowing down some students and others would be lost. This way, students worked in groups and read through instructions and I was walking around helping students through it.

I did change one small thing. I had them work in their Google Drive, using Google Sheets. The formulas work exactly the same, but this way they don't need to print it. So one student had the instructions open, the other typed and then they could share the file with me and with each other. Then students had to change their files. Each group got different conditions:

They then shared this file with me. They did notice that they only needed to change the numbers at the top and the number of rows. They did not quite finish this activity, but they did finish it within the first few minutes of the next day. They also shared the file with each other so that they would have a starting file for the next activity!

This worked very well. Students struggled a little bit with the formulas at first and many did  not know how to "fill down". They learned some very useful spreadsheet skills as well! They definitely saw the value in doing this in a spreadsheet instead of by hand! They stayed engaged right until the end.

Day 14 - Conditions of a Mortgage

We are just about at making amortization tables ourselves but before we do that, we are going to delve a little bit more deeply into the terminology and the options when dealing with mortgages:

We started off nice and easy, with again finding payments and the total amount paid to reinforce what students already knew. They could quickly see the value in having a shorter amortization period. Then we got into the different kind of payment schedules that banks offer. We discussed why, if you pay the same amount in a year anyway, you still might want to choose the bi-weekly, semi-monthly or weekly payments. We also discussed the benefits of the accelerated weekly and bi-weekly. We then finished off with an example where students saw what kind of a difference making larger payments makes:

Students did have work:

Again, I chose to have students do a few questions that they could easily complete instead of many questions. I understand the benefit of students practice, but that only works if they do some of it!

Day 13 - Mortgages and Amortization

Sorry folks! If I miss a day I get out of habit! So I will write this blog pretending it is Monday. Today we worked through questions that students had about the lesson they worked through on their own on Friday that was about Conditions of an Annuity. From there, we moved on to Mortgages and Amortization:

Working through the first two questions solidified their understanding of solving mortgage questions. We then looked at a piece of an amortization table and worked through figuring out what each piece is.  This worked well. Then we looked at more of an amortization table:

What you don't see here is the discussion that we had as a class. I don't really know how to blog that. But we discussed the patterns and why an amortization table is useful etc. We talked about how each line is calculated and why the interest column goes down and the principal column goes up. It wasn't an exciting class but students were interested. They had already done some leg-work and understood some of the terminology and now we are just fleshing out more of the details. Once we finish this section, they will be able to read a bank's information about mortgages and really understand what they are reading. I think because they could see that what they were learning was useful, they were engaged without the bells and whistles. While we will see some of the formulas later in the course, I think that using the TVM Solver now freed them up a little bit so they were able to think big picture as well. I got that higher level thinking out of them. Onward ho!