MPM1D1 - Day 38 Equations of Lines From Two Points

Hoping to continue our work from yesterday on finding equations of lines we started with this pattern.(with students working in groups up at the board):

Most students are so good at these patterns. I really like their strategy of finding the y-intercept by seeing how much they are off by when the substitute a step number into their equation. I don't want them to lose that intuition but at some point the numbers will become challenging enough that it may be easier to use an equation. I had one group that really struggled with this question but eventually they sorted it out.

When they were done they moved onto the next bunch of questions.

The last question was full of fractions. Many groups seemed fine to keep working with fractions which made me happy. One of the groups kept wanting to change their fractions into decimals and proceed that way. They got a little upset at me for insisting their work be done using fractions (everybody's favourite F-word).

Once they were finished I told them to plot the points and equations for the last two questions in Desmos to see if they got the right answer. Many groups realized that they made a mistake since their line didn't go through the points. They traced back through their algebra to find their errors (often a wrong sign).

Once they were finished I sent groups back to their seats to work on his handout so that they could practice.

I really think that finding the equation of a line that passes through two points is probably the most difficult topic in the course. However, I believe that spiralling the course has really helped. My students have looked at finding equations from tables since the first week of school. We didn't call the parts of the equation the slope and the y-intercept at the beginning of the semester. We had an entire table rather than just two points.  But, I really feel like my students have a good understanding of these parts of equations and are now able to hang the proper terminology on their understanding. Students who are still struggling with this concept will have an opportunity to revisit it was we move forward.

MPM1D1 - Day 1

This year I decided to change things up for the first day. I decided to skip all the regular first day stuff and dive right into the math. We can do the first day stuff some other day (I guess that doesn't make it first day stuff anymore though). I wanted my grade nine students to be doing math and enjoying themselves rather than being bored of listening to me.

We started with some Estimation 180. I had students guess a number that was too low, another that was too high and, finally, an actual guess. I like starting with this because everyone can pick a number. It's very low risk. I was pleasantly surprised at the too low and too high guesses. Nobody gave number that were crazy low or high. I gave students time to come up with their guesses. I took a bunch and wrote them on the board, which was a great way to get students participating. Once the list was on the board I went to move on when a student asked what the answer was. We had a look, then figured out what their percent errors were. They were all quite close.

After the estimating we moved onto a number talk. I asked students to figure out what 25*8 was without using a calculator. As I said it to the class it occurred to me that this was an easy one to relate to money so perhaps it would be too easy. Oh well. Next time I'll refer to my notes rather than working from memory. I had originally intended to ask 25*12. In any case, we had a few different methods that were shared. Nobody used an area model so I went over it and a couple of other methods. This was another fairly simple task that helped students build confidence.

Once we finished the number talk we moved onto Skyscrapers.

The idea is that you must have a tower of each height (1,2,3 and 4) in each row and each column and the numbers along the outside indicate the number of tower you can see from that location. It's very Sudoku like. I've seen a lot of people use this activity in the past, but I wasn't sure about it. It wasn't until I was at a session where teachers tried the activity that I realized what a great first day activity this could be. It involved problem solving, collaboration, attempting and failing then reattempting and lots of communication.

I was hoping to get to some integer addition and subtraction today as well, but I guess that will have to wait until tomorrow.

I had a great day and I hope my students did as well. I hope they had fun, felt comfortable and enjoyed themselves. We covered a fair bit of ground: estimation, percent, multiplication and problem solving.

I need to remind my self to take more pictures!