Today was our third test of the semester. Just as they began, the school went into lockdown (it was just a drill). Needless to say, once we were cleared to get back to work, some of my students had a bit of a hard time getting focused. Overall, they worked well. Some said they didn't know how to do certain questions, but with the right prompting from me they persevered and showed a lot more of what they knew. As ever, they will be able to continue tomorrow. Or next Monday for the kids on a field trip tomorrow and on outdoor ed for the remainder of the week (sigh).
This post looks terribly boring without any pictures (I know, I know, it doesn't just look boring!). So here is a plug for next year's OAME conference which will be in Barrie, ON:
Keep up with news about the conference by following @oame2016 on Twitter.
The warm-up was a Balance Bender:
I am trying to encourage my students to "translate" these into algebraic expressions, which you see above. It is hard to convince students that they are actually doing all the algebra and just need to figure out how to write it down.
The remainder of the period was spent working on review for the cycle 3 test. Here is the handout and the solutions.
I was away at the OAME math conference last Thursday to Saturday. I was fortunate to have the teacher who is teaching the other section of MFM2P cover my classes, and she even sent me some pictures of what they did! (Thanks, Michelle!)
They started with this Would You Rather...
And this is what they discussed:
Then they continued with trig. The day before we had gone outside and collected data for the height of the tree/lamppost/hydro pole and for the ramp in the school's foyer. They spent some time on Thursday going through the calculations to find the height of their object and the angle of the ramp.
They spent the remaining time working through more trig practice problems.
Today's visual pattern asked for both the volume and surface area. They saw how the volume (number of cubes) grew, but had more trouble with the surface area. We used linking cubes to make the shapes which helped a lot. Next time I want to show them other ways of seeing it.
Next, on to trig. They have found both angles and side lengths of right angled triangles before using trig tables. Today I introduced them to SOH-CAH-TOA. I find it helpful to write it like this so that the ratios are more obvious:
Here is the handout they received. We got through example 3 together and then moved on to this. Yes! We were going to go outside! I showed them how a clinometer works.
I asked what data they would need to collect and we came up with this diagram:
I put them in random groups and told them they had 15 minutes to be back in class. Out they went (it was beautiful out) and started measuring. Some groups were finding the height of a tree, others a hydro pole and one group the light standard. They came back in the school to take measurements (as a large group) for the ramp then we all headed back to our classroom. They wrote the measurements they took for the ramp on the board for everyone to use:
And that was it. Tomorrow they will do the calculations and practice a little more trig.
I am home with 2 sick kids today and my class is likely being covered by a non-math teacher, so seat work it is :( Along with working on the pyramids handout from yesterday, I want them to do some trig again so I left this handout (which I know some kids already started a while back). I hope they will work collaboratively today...
Instead of starting with a counting circle today, I had them multiply two binomials. They haven't practiced this lately (and were really doing well with counting circles) so I thought it would be more beneficial. I have 8 of these ready to go on little slips of paper (found here) so we can do one each day this week and again later in the semester.
Next up, pyramids! Alex Overwijk and I had talked about creating a new activity involving tents in the shape of pyramids, but that hasn't happened. This week is crazy for me so I went with some not-very-exciting worksheets. We did start by building pyramids. I brought in the bins of G-O-Frames and asked them to build pyramids. That's all I said. Here is some of the collection:
There were a lot of tetrahedrons and some square-based pyramids. There is one hexagonal-based pyramid and one right-angled triangular-based pyramid. I asked what they noticed about the shapes and they said that the sides are always triangles. The base could be a variety of shapes. I asked how they could find the surface area of a pyramid and took a squared-based one apart. I asked the same question while holding up the one with a hexagon as its base. They seemed to understand the idea of adding up all the areas. I had them work on the first example from this handout and I circulated helping some of them get started.
I showed them the right-angled triangular-based prism and said that if we had three of them we could make a cube. I also showed them this video. I could have done the demo myself, but I would just make a mess and I wasn't up for that first thing on a Monday morning. I tried to really emphasize that to find the volume of a prism you take the area of the base and multiply it by the height because the height represents the number of "layers". To find the volume of a pyramid, you perform that same process and divide the result by 3. Again, I let them work through some of the examples before going over this one together:
Along the way we talked about the difference between vertical height and slant height. They figured out that the slant height of the pyramid is the height of the triangle. They also were able to determine that if you were missing one of the heights in a square-based prism, you could use the sum of squares (Pythagorean theorem) to calculate it.
We will do a little more with pyramids tomorrow and work on some trig again.
Today's plan: warm-up, one more cup stacking system, then move on to volume and surface area of pyramids.
The warm-up was this Daily Desmos, where they have to determine the equation of the line and we check it on Desmos:
I had them work in table groups on the big whiteboards. Here is some of their work:
Next, I had them go around the room looking at other groups' solutions and making comments on the work. Some fixed errors while others wrote comments like "where did this come from?" and "show your work". It was interesting. One group had a blank board (they were a little off-task) and they actually took the time when students were looking at each other's work to find the slope. We went over some of the errors and cleared up some misconceptions. I also had them go to Desmos on their phones to check their equations.
Next we went back to the cups. I put up the equations for the Styrofoam and red cups on the board. I assigned them random groups to answer this question: if the red cups started on the desk and the Styrofoam cups started on the floor, when would both stacks have the same number of cups and reach the same height? Many groups answered a different question - they made the height of each stack 76 cm (the height of a desk) and solved for the number of cups.
I let them struggle with this a little longer after explaining the difference between my question and the one they answered. I had my red cups travelling around the room with me as props to help me explain what I wanted them to find.
One group thought they had it solved so I pulled out the cups and we tried it out - and one stack came up short. Back to the drawing (white) board.
Eventually I had to stop the whole class and talk about what we knew and what we were trying to find. We went over what each of the numbers in the equation represented and whether it would change if you started the stack at a different height. We got to this point together and I let them continue in their groups:
Here is what they got:
The last picture, above, was for a group that calculated that they would need 65 Styrofoam cups to reach the desk so they were changing their Styrofoam cup equation by subtracting 65 from 7 - great strategy, but they did not finish : (
The consensus was about 133 cups and this is what it looked like:
Very close!
We still had a few minutes left and they clearly needed a specific task so I gave them this question to do as an exit card:
Based on the results, I think they understand how to solve these equations (yay!). So much for pyramids today. That will now happen on Monday.
