MFM2P - Day 18

Day 18
Today was about consolidating their knowledge of solving linear equations. We started by gluing some examples in the comp books and filing them in. (There was space between the examples.)

Then they spent most of the remainder of the class working through a handout while I circulated and helped. I am really impressed at how well they are doing with the algebra. I know, I know I was saying how poor their algebra skills were just a week ago, but I am surprised at how well they are picking it up.

The plan was to finish with one or more Estimation 180s, but my computer decided it needed to reboot so that plan was foiled. Instead we went over how to convert Mr. Stadel's height from feet and inches to metres. Not the fun ending to the week I had planned!

MFM2P - Day 17

Day 17
Instead of counting triangles or squares, etc. today, we counted vertices for the same shapes as yesterday. The handout looked very similar - they had to come up with three representations for the number of triangles (square/pentagons/hexagons) and number of vertices. They clearly did learn something yesterday as they had no trouble starting and many got the equations without any help. They were even using algebra to solve some of the questions! 

Next, we took up the two quizzes they have written. Well, I tried to but my SMARTboard decided it needed a break so we will go over the last two questions tomorrow.

We finished with a little Estimation 180 action. We started with day 1 and each student got their own small whiteboard to write their estimate. 

The twist I threw at them was that I wanted their estimate of Andrew's height in feet AND in metres. I asked them what information they needed from me. One student said he needed Andrew's height. Nice try! They asked for the number of feet in a metre and then for the number of inches in a foot. This was very informal - I did not check their calculations. It was meant to get them thinking about converting between units which is an expectation of the course. They held their boards up and for some, just doing that, was an accomplishment. I made them all hold their boards up whether they had a guess with both units or not - they had to make a guess. No one got his height correct though. We'll do another tomorrow.

MFM2P - Day 16

Day 16
We changed gears today and moved on to looking at patterns using toothpicks.

They readily came up with the number of toothpicks for each step and had little trouble creating the scatter plots, but had great difficulty finding the pattern. We used used step 1, step 2, etc. to try to help them relate the pattern to what there would be at step 0. It was a tough sell - they really didn't like that there was 1 toothpick at step 0. 

After we had gone over the pattern for triangles and squares they came up with equations for pentagons and hexagons and moved on to the questions.  The questions were all of two types - how many toothpicks would you have if you had <insert big number> triangles/squares/pentagons/hexagons and how many triangles, etc. would have you if you had <insert big number> toothpicks. As expected, they could solve for the number of toothpicks, but had a hard time working out the number of triangles given the number of toothpicks. In fact, several students got decimal values for the number of triangles. I know their algebra skills are weak so I grabbed this opportunity to work through solving equations algebraically (since doing it "their way" wasn't working).

I will continue to work on algebra skills with them throughout the course and hopefully eventually it will stick.

Finding my Groove

At my school those of us teaching the same course teach the same thing on the same day. That's the way it has been done so that's how it continues to be done. I am stepping out of the box with my grade 10 applied class this semester, spiralling through the curriculum while the teacher of the other MFM2P class teaches it in a more traditional way. Anyway, not to rock the boat too much, I am teaching calculus by units and in the usual "this is what we are covering today" way. I do many investigations with my classes (I have 2 sections of Calculus & Vectors). I try to make sure that my students understand the why, always. But I still felt like I could be doing better, even within the framework that we are using. 

Last year had added a "teamwork" portion to one of the lessons from last week - it was a more challenging problem that they worked on in groups on the big whiteboards. And, although this was not the first time I had done this, it struck me that this is what I am missing from the rest of my lessons.

These "teamwork" questions are harder questions, ones that make students think a little more, stretch them. They are the questions that when assigned for homework either get skipped or students copy a solution without understanding it. But they are the kinds of questions that students should be doing. The ones they must do. And now they are - every day! After we have gone over whatever concept we need to, the whiteboards and markers come out and the conversation gets lively. It is fantastic! Whiteboards are magical things in a math classroom. They give students permission to make mistakes and to try different ideas (and to draw pictures). They let students stand up, crowd around and point at what is good, at where there is a flaw in logic at something they don't understand and talk about the math! 

The added benefit to doing these "teamwork" questions is that it is (hopefully) helping prepare students for the unit tasks they write, usually the day after the unit test. I have been asked for years how students can better prepare for tasks and I think I have finally found the answer. Clearly I am a slow learner (!) but I'm very happy that I have finally figured this out and have found my groove in calculus.

MFM2P - Day 15

Day 15
Not an exciting day... I asked if they would rather do some more problems first or take the quiz first and they chose the quiz (that surprised me).  They worked away at it (open book) and I think did mostly good work. I will mark them later today. They worked on more word problems after the quiz and we took up a variety of them. That was it. Moving on tomorrow!

And since this is so short, here are my dogs. Not the greatest picture but, like taking pictures of children, it's difficult to get them both in the shot.

MFM2P - Day 14

Day 14
School buses were cancelled on Friday due to freezing rain. As 100% of students at my school are bused in, there were no classes - it was a wonderful day to get ahead, with a little Olympic curling and hockey action on the side.

Today we started by cutting and gluing three trig examples into comp books. Again, I want to ensure that they have an example of each type of question we do in their books as they will be allowed to use them for some tasks and for the summative. The good news is that they have a solid grasp of which side is opposite, adjacent or hypotenuse given a marked angle. Many correctly remembered how to solve for an angle.  A few remembered how to solve for a side in the numerator. And we went over how to solve for a side that is in the denominator together. I know this is still causing issues, but we will move forward and come back to it when we have done some more algebra work.

They spent the rest of the class working on problems relating to similar triangles, trig and sum of squares. Some of these are word problems that we have not done previously so I circulated helping them with their diagrams and figuring out what type of problem they were dealing with. It is good to see them "getting it" with a little nudge from me.

MFM2P - Day 13

Day 13
We spiralled back today and looked at similar triangles again.  I really wanted them to have a full example for similar triangles in their comp books so I quickly made one up for them to cut and glue.

They did pretty well matching up the angles and I heard some conversations about "scale factor" (yay!).  

Then we continued with trig. They started to have trouble when they realized that they couldn't just do the same thing for every question. They were okay with the difference between finding the length of a side and finding the measure of an angle, but solving for different sides caused problems. Their algebra skills, for the most part, are so weak that they don't have a foundation on which to develop understanding for these questions. They follow when solving an equation like:

and seem to understand why we are multiplying both sides by the denominator. However, when the variable is in the denominator like:

they have no tools to work with. I went over a case with just numbers with them... 14 divided by what gives 7? How could we write this another way? But they had a hard time transferring that to the example shown above. And they just want to memorize what to do if the variable is in the numerator and what to do if the variable is in the denominator. Sigh. I will see if I can figure out a way to better help them tomorrow...