Here’s the short version:

  • Everyone who wrote the Final Examination passed
  • One student dropped out of school mid-semester
  • One student was not successful

I didn’t quite meet my 100% pass rate, but it was very close.

Firstly, here is a comparison of Diagnostic Grades vs Final Grades:

Day 59 - Final Analysis 1

The Diagnostic scores were based on a combination of Grade 9 Final Grades and some diagnostic/observational data at the beginning of the semester. The distribution is clearly moving to the right, and the class average has increased from 59.5% to 70.4%… impressive!

However, it’s this graph that I believe is more telling:

Day 59 - Final Analysis 2

This graph is clearly showing the increase for all students but one (and Student T dropped from a 63% to a 62%). Nine students’ overall grade increased by over 10%, five of whom had increases of over 20%! The highest was Student G who went from a 53% to 81%! Wow!

I attribute this success primarily to Spiraling.

Having worked with these students for the past five months, I can also conclude that a lot of them learned more than Math. A lot of them gained some confidence in their ability in Math. Some overcame a degree of test anxiety. A lot of them took ownership of their learning and became leaders. Many learned to collaborate.

No, I am not saying that I ended up with a room full of model students, but they sure came a long way. I’m very proud of them.

As I was administering my other exams, it occurred to me that for my MBF3C class, their exam was their first assessment that contained a blended curriculum. All assessments that they had written were based on one unit of study… so no wonder they find it challenging! My MFM2P class had technically already written three exams previous to the Final Examination, so there was significantly less anxiety for them… and the results proved it.

think that I’ll be teaching MFM2P again next year, but in Semester 2. There is absolutely no question that I will be spiraling it again, only it will be better this time since I’ll be able to start spiraling from the beginning of the semester. And I’ll know what I’m doing this time 🙂

know that I’ll be teaching MPM1D next year in first semester, and I am definitely going to spiral it (I will not be blogging about it!). I am also teaching MBF3C first semester, and my plan is to develop a 3C spiral curriculum over the summer (with help!) and test drive it (I am hoping to blog about it). At this time I am also timetabled for MPM2D, but I’m not yet sure if I will spiral this course as well. I still have to give this more thought.

So thanks for reading my blog! I must give thanks again to Mr. Chris Hogg for all of his support, the support of my Principal, and I must also give credit to:

But most of all, I must give thanks to my students for buying in, and also for putting up with me for five months! Have a great Summer!




(aka Cycle 4 Test)

Ok, this is it…

… over the past week, I reflected on whether or not I was giving them an unfair advantage by allowing them to use the three exam review packages from last week, but then I remembered that when I’ve taught this course previously, I have always allowed (and encouraged) the use of a “Survival Guide”:

Day 58 - Survival Guide

My intention for the Survival Guide was a student-created resource, which was individualized for each student, based on whatever they felt they needed in order to succeed on assessments. Having said that, my philosophy in Math is that “I do not teach memorization. I teach problem solving.”

I have no issue with them using their review packages. Either they completed them, and therefore they are useful and they will be successful, or they did not complete them. I feel that this is really about learning to use the resources that are available to you.

Before we began, I reviewed each page, gave them a little pep talk, and said, “Worst case, you only need 30 marks to pass. Go find them.”

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What I noticed most about this exam is that there were pretty much no questions from the students… they all seemed to know what was expected of them in each question. Usually about half an hour into an applied/college level exam the hands start going up, but that wasn’t the case today.

They are all marked, and here are the results:

Day 58 - Final Exam Results

That’s right… everyone who wrote passed (two were very close)! I had one no-show, and one who is going to write tomorrow, but to be honest, these results are better than I had anticipated! I have found that Final Exams in applied and college level classes typically lower a final grade, but in this case, many final grades increased as a result of their Final Examinations.


Once I complete my report card comments and additional year-end paperwork, I will post one final blog entry to summarize the semester.


Last day!

Today’s review was of Quadratics – our last strand.

The first page went way back to when we first started with quadratic relations. While the exam will not have a regression, I thought it would be good to go through it one more time.

Day 57 - DESMOS 1

This seemed to go quite well considering that we haven’t done it in a long time. I was especially impressed that they were able to better make the connection between the results of the regression and the variables in standard form of the equation. Also, the substitution of x=20 to determine the number of toothpicks in Step 20 was well received.

Next, which step has 1300 toothpicks?

Day 57 - DESMOS 2

I like that we have done this several times in this course. Having taught MBF3C so many times, it’s a little frustrating that students aren’t familiar with this very useful tool – it’s especially helpful in finding an unknown exponent when dealing with Exponential Relations.

I think that because they have spent more time with Linear Systems, this idea of a point of intersection was now easier to relate to.

So Step 25 has 1300 toothpicks 🙂

On to factoring. We didn’t get to spend nearly as much time working with perfect squares and difference of squares in the course as I would have liked. Having never spiraled the course, I didn’t realize that they wouldn’t see it again (well, probably in Cycle 4 had I started earlier). I went as slowly and thoroughly as possible through this section, and hinted that they might see it again (wink wink).

From what I could tell, the idea of factoring and identifying the roots has improved significantly, as has their ability to sketch the graph given the three intercepts.

The last page was interpretation of word problems, which is probably their strongest area of Quadratics. They are also getting better at identifying a possible equation for these graphs.

Now that I’m finished the course, I can say that when I’ve taught MFM2P in the past, I’ve taken quadratics and factoring into more depth. I’ve combined factoring, such as 2x2-18, or had them factor h=-5t2+20t+25. I’ve also explored Step Pattern of quadratics (1, 3, 5, …), but having said that, in the 9 times that I’ve taught MBF3C, it seems like they’ve never even seen factoring before. Perhaps by only taking factoring as far as we did, this might help them next year – they might retain enough of it so that we can build upon it.

There is a chance that I might be teaching this same group MBF3C next semester, so I might just find out 🙂

Now they have until Tuesday to prepare for their “Exam”. I gave them a Practice Exam with the answers (just answers, not solutions) for those who wish to have more opportunity to prepare. We shall see.

So no more blogs until Tuesday, when I will hopefully have the final results of the course!


Again, no Warm Up today.

As mentioned, we started off the class with a bit of a review from yesterday – we reviewed some Pythagorean Theorem (aka Sum of Squares), and then completed the review of Trigonometry. This went much smoother than I had anticipated, which was great!

Today’s package was significantly shorter, plus this group is getting quite competent with Linear Relations.


I reminded them again that there are modified exam questions embedded throughout the review, and hoped that this might provide some encouragement for them to ensure that the packages are complete.

The timing was good today. We finished with a bit of time left over which just happened to coincide with an announcement for students to pick up their draft timetables for the fall.

I’m still chasing two, but here are the Cycle 3 results:

Day 56 Marks

We’ve had a couple fall off track over the last two weeks, and unfortunately this graph doesn’t paint a complete picture of some of the challenges, but also the successes that have been taking place in the room. Within those blue bars are some spectacular successes as well as some who sort of “dropped the ball” recently. Having said that, I think that nearly everyone is on board to put in some real effort in order to prepare for their exam.

But TEN over 70%!

Finally, I ran a quick analysis of where they are now as compared to at mid-term:

Day 56 - Grades

I find this interesting because I believe that if I hadn’t spiraled this course, the graph would be bi-modal – as in, there would be probably more failing, and then a gap in the 60’s with a second peak in the 70’s. So basically, I would have a group that “got it” and a group that did not (and had more or less “checked out”). With the nature of the group that I have, I am very pleased to see a bell-curve. This tells me that I’ve closed a lot of gaps from Grade 9, and have most of the students where they should be (more or less – there’s always room to improve!). Also, I am still chasing two for the Cycle 3 Test and so their current grades will be adjusted accordingly once they write the Final. It will likely just end up being a 30% Final for these two.

I’ve got a couple of good pieces of motivation for them as we prepare for the final:

  • You can bring your three review packages in to the exam as a resource.
  • The Exam is just another Cycle Test – and you’ve already written three of them!

Not sure I’m going to get that 100% pass rate that I was anticipating long ago, but it might just happen!


No Warm Up this week – I thought it best that we just get down to business.

I decided to present the class with three review packages – one for each strand. Today we would be working on Measurement and Geometry. If I’m not mistaken, this is probably the weakest area for this group.

Day 55 - MG Review 1

I designed each review to contain some practice problems so that they could practice the skills required for each strand, and then to also provide them with similar problems to the “Final Exam” so that if they complete all of their work, then they will be that much more prepared for the questions that are on the “Exam”.

Day 55 - MG Review 2

I am still surprised at how much they struggle with Volume and Surface Area. Definitely a mental note for the next time I teach this course using Spiral Curriculum. To be honest, I did skip one activity that would’ve helped a bit back in the first Cycle.

Day 55 - MG Review 3

We didn’t get to the Trigonometry today, and so we will start with that tomorrow. Tomorrow’s review is Linear Relations, which based on the last Cycle Test, they have a pretty good handle on, so there should be enough time for both.

I just about have all of the previous Cycle Test results compiled that I can present how they did 🙂


Last test! The only remaining assessment is the Final Examination.

Had I been on schedule (ie started Cycling from the beginning of the semester) I would have been able to run a fourth cycle, and had some sort of summatives during Moratorium. With the way things have unfolded, I think I will have this test count for 15% of their Final Grade, as it’s during Moratorium, and then the Final Exam will also account for 15%. This should work out well as I have lots of marks, and lots of evidence of what they’ve been able to do throughout the semester through Exit Tickets, Quests, and Tests. This satisfies the triangulation of  assessment that we are asked to provide for the board.

Looking through the test, it’s a good range of straight forward questions and some challenging questions. Leading up to this test, as I’ve already indicated, I was starting to get a little nervous, but after watching them work away this afternoon, I think we’re going to be ok. Sure, there will be a handful who may not be successful, but overall, there was lots of pencil on paper, and not a lot of blank questions that I could see (I haven’t marked them yet).

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I look forward to getting the results!


As much as I wanted to do the Would You Rather? that we normally do on Thursdays, I went with the Balance Bender instead in the interest of time.

Day 54 - Warm Up

Again, I incorporated equations at each step, and I think that as before, more connections were being made. I also appreciate that when students explain why, they are very good at providing sound mathematical reasoning and language.

I only gave them a few minutes to get organized, and then we got right into taking up the review. As there were a handful of absences yesterday, I wanted to make sure that everyone has a complete test review available to them during the test tomorrow should they opt to answer questions in pen.


While I really don’t like taking up a review when the students haven’t completed it, I didn’t really have a choice today. On the positive side, in taking it up I was able to propose strategies that I’m hoping will make the test less intimidating for those who are at risk.

I must admit that I am once again nervous as to the results of tomorrow’s test. With just four days remaining until Final Exams, I am really hoping that they are willing to give me their best. If they do, then I know they’ll get their credits!

Day 54 - Crossed Fingers

Math Is Awesome