As
I work through this way of teaching MFM2P I realize that some of my anxiety
stems from my need for structure. I like to know exactly what we will do
in each class, each day. Note that I am okay with controlled chaos too -
teaching shouldn't be all neat and tidy. Anyway, I have figured out that
if I record what we are doing in class either by taking pictures of the
whiteboard or by working on the SMARTboard, it helps me with that whole
need-for-structure thing. And this blog is in large part for me to refer to
when I teach this course again. Frankly, I can't believe that anyone is
reading it (really - why are you?!?)

Day 8:

We looked for patterns
(see day
7) and someone noticed that the area of the big square was equal to the sum
of the areas of the two smaller squares. We drew the squares on the
triangles to demonstrate this.

Somewhere
along the way we had to go over the fact that, in a right triangle, the...

And
we worked through more examples in the same way - notice there is no a, b, or c
here. No x either. We figured out the remainder of the table this
way, which took a bit of time as some had a hard time figuring out when to add
and when to subtract.

I then asked them to see
if they could find a pattern among some of the 9 triangles. They needed more to
work with so I gave them this:

It was interesting to
see that some noticed that the first number went up by 3, the second by 4 and
the third by 5, where I notice that the second row is a multiple of the first.
They came up with the other three triangles in the same family and separated
the remaining three triangles into 3 more families. (We also showed that we
could keep generating triangles within a family.)

Day 9:

Students started day 9
by drawing the 9 triangles in their comp books, with correct side lengths. They
then measured the acute angles - some needed to be shown how to use a
protractor correctly - and recorded them on their diagrams. They also had
to calculate the area of each triangle.

This is what it looked like:

Note: I will get them to
plot the areas of the triangles within a family based on scale factor and come
up with the relationship. Not sure when we will do that, but it's part of the
plan!

They quickly noticed
that the angles within each family of triangles were approximately the same.

We talked about the
properties of similar triangles. This was not very exciting for them or
for me. Less so for them, I think. (if you know of a way of making
it more interesting, please let me know)

Somewhere along the way
I realized (duh!) that we should have MEASURED the angles, not just stated that
they were equal (I am dumb sometimes) but I think we still got what we needed
done. And they had had enough after this!

Day 10:

Having received an email
from my principal reminding us that progress reports are just around the corner
(really? we have only had 2 weeks of classes!) I decided I better gather some
"evidence" of what my students have learned so far. I spent part of
my prep period this morning before class making a quiz to cover the types of
the linear and quadratic scenarios we had looked at. I made sure they knew that
they were allowed their comp books and any handouts for the quiz. There
was surprisingly little complaining and they got to work. They did a good job
showing me a lot of what they know, with a little help from me along with way.
There were a number of "I know this is wrong, but..." questions which
I responded to by telling them to write down what they had just said to me -
tell me that you know it's wrong then see if you can fix it. A couple of
students needed encouragement to get going or keep going, but overall the
results are fairly impressive - they worked for a solid 40 minutes!

I let them take a break
for a few minutes after the quiz the we continued with similar triangles. We
recapped yesterday's conclusions and started with the examples.

I suggested that adding
symbols to the diagrams to help identify corresponding angles would be a good
thing.

Happily most students
remembered the sum of the angles in a triangle so they had no trouble with the
next example. They did need some help figuring out how to tell if
triangles are similar if they are only given the side lengths. We will work on
that some more next class.

So there is the end of
last week. Yesterday (Monday) was Family Day here so today is day 11 and
I will try not to leave my blogging for so long this week, 'cause that makes it
so long!

To answer your question about why I would be reading this: It's great information. I'll be teaching 2P for the first time in a very long time. I want students to be more interested, more involved and hopefully take more away from the course. I wanted to try spiralling the course but I would have had no idea how to if I hadn't seen your work last year. I struggle a little with the 'how' and not really knowing what comes next, but your posts will help me overcome both of those concerns. Thank you so much for taking the time to put this together. I'd like to do the same with the 3C but maybe I'll take it one step at a time.

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