I wasn't sure if it was perfect timing or terrible timing when I realized that today's warm-up was this:
Given what we did yesterday, I expected to see a lot of boxes used to calculate this product. I did see more than I likely would have normally, but we got lots of different methods which we shared:
I showed them that you could double one of the numbers and divide the other by 2. I really like being able to see how my students think and having them explain their method to the class.
We then continued with the work from yesterday. We started by restating the zeros for each of the graphs and then tried to make sense of them.
I put up a different equation, y = (x + 7)(x - 9) and the student I asked told me that the zeros were at 7 and -9. So I pulled up the graph on Desmos and asked what he thought.
He opted to change his answer to -7 and 9. Then we talked about why they are called zeros - it was great to have the Desmos graph with the points showing the y-values as I did this. We discussed why the signs for the zeros are opposite to the corresponding numbers in the equation.
I'm not convinced they were all following (I should incorporate some formative assessment at this point next time), but they did at least all see that the signs were opposite.
They practiced multiplying binomials a couple more times as they added to their exercise books:
Then we moved on to a great matching activity, found here. This was created by the good folks at Sir Wilfred Laurier Secondary School. My students all did some cutting and some gluing but didn't finish anything so I got them to paper clip their pieces together and place their work in a large envelope so that we can continue on Monday.
As a side note, I know that some teachers don't like ending the class without finishing the activity. I have come to like it as it gives us a great starting point for the next class. There will be no need for instructions on Monday - just get back to it. It helps them remember what we were doing, ensuring continuity in their learning.
Today's warm-up was this Would You Rather:
They looked up the number of feet in a mile (likely a known fact to many American children, but not to Canadians) and then talked about how many days they have been alive. There were good conversations involving leap years and whether it was worth counting the number of days since their 16th birthday.
They all agreed that they wanted to have a dollar for every day they have been alive. It would be interesting to do this is a grade 9 class - just the right age to have both answers chosen within the class.
One of the few curriculum expectations that we have yet to tackle involved manipulating quadratic expressions. Not the most exciting topic and hard to make into an activity so we just work through this handout together (here is some extra practice for those who work a little faster). We start by multiplying numbers using the box method (none of these students learned to multiply in this way) and then move on to multiplying binomials. They get the hang of it and then we move on to making the connection between a quadratic equation in factored form and the zeros of the graph. They had just told me that they noticed that the numbers were the same with opposite signs when the bell rang today. We will consolidate that tomorrow.
My students finished up their test today. A few had finished it yesterday so they moved on to today's warm up and then to this trig word problem handout. I circulated and prompted as needed for the test. I am always amazed that some students are perfectly happy handing in a test with a number of questions unanswered. Blank. Not even a diagram drawn. And that these same students can actually answer the question fully with a little encouragement. So I encourage. Because I believe in them.
Today was the cycle 2 test, so I don't have much to say. They worked really well. I am very proud of my students. They impress me by thinking about the reasonableness of their answers ("I know this is wrong because...") and by not giving up even when they claim to have given up. A question or two from me and they are back on track and showing what they have learned.
Monday morning means counting circle. We started at -236 today and added 17. This was challenging for some so we focused on how to break up the 17 to make it easier.
On to review for tomorrow's test. Here is the handout. They worked, I circulated, helped point them in the right direction and encourage them. I emailed the solutions home so they can keep working on it tonight.
Today's warm-up got complaints because it was too easy. I will switch it out in favour of something more challenging next time.
Today was all about trig. I gave them a few minutes to work on some examples where they had to solve for an angle. We consolidated with this one, where they were given the lengths of all three sides so could choose which ratio to use. When I wrote the first student's solution on the board, some thought they had done it incorrectly until they saw the answer. It was good for them to see multiple ways of solving this question.
I let them work for about 10 more minutes on finding angles before we stopped to look at how to solve for a side. These are from their exercise books:
They seemed to understand quite well. When we got to the second example they tried multiplying the numbers together and we got about 5.4. I asked if that looked right and they said no! I loved seeing them realize that the hypotenuse had to be longer than 8 cm so we had clearly done something incorrectly. Upon their suggestion, we tried dividing and they thought the new result was much more reasonable. I have struggled in past years with this process - so many of my students have difficulty with algebra and get lost when you show how to solve these equations in a more formal, algebraic way. I have decided that I am okay with them reasoning through, possibly getting it wrong and fixing it.
They worked for the rest of the class on this handout while I circulated. Stickers were good motivators today and I was very impressed with the work I saw.
We did today's warm-up quickly as we had a lot I wanted to get done. Here it is:
I was surprised at how poorly some students understood what the numbers meant. A number of them divided the diameter by the number of slices and compared the results. I actually had to draw a circle, then the diameter and divide it up to help them make sense of what they had just calculated. Eventually they understood that we needed to compare areas. Here is one student's solution (he figured it all out on his own):
And my consolidation:
After the warm-up we talked about similar triangles. I asked what they knew about similar triangles. They said that they were the same only different sizes. Someone mentioned scale factor. I asked what the scale factor told you about the triangles. They replied that it was how much bigger the larger one was (I know it could go the other way). We moved on to doing a couple of practice questions (links to handouts are below). Here is the first one:
We went back to colour-coding corresponding sides which really does help some students. We found the scale factor, made sure everyone understood what that number meant then used it to find the missing side. The second example involved angle of incidence and angle of reflection, which they have learned about in science class.
They worked out the height of the statue after I demonstrated the process using a mirror. I then put them into random groups and set them on their way to collect data for two objects with inaccessible heights within the school. Some groups needed more guidance to correctly collect their data. They worked out the missing heights when they came back to class, although for many, their work ethic did not seem to make it back to class (the perils of letting them "loose"). Once done, they started to work on a trig practice sheet involving finding angles. I was pleased that they remembered to start by labeling the sides with "opposite", "adjacent" and "hypotenuse".
Here is the mirror activity handout and here is the practice worksheet for solving for an angle using trig. More trig on deck for tomorrow.
