After a two week Winter break and a cold-shortened first week back, this past week offered the first full, five-day week since December 16-20. The week started with us graphing using a table and finished with writing the equation of a line in slope-intercept form, given two points. In prior years of teaching, this would have taken weeks to get through. So, what is different this year?
First, we began the week by graphing a line using a table, something students should already know how to do. I put a problem up and allowed the students to work in their cooperative learning groups to see who remembered what to do. Some students knew what to do right away and, with a little refresher, most students caught on after showing how to find one or two points. My goal with this question was for students to not only remember how to do this, but to give myself the opportunity to sell the fact that you can graph a line much more efficiently using the slope and y-intercept. I used the same equation to show students the relationship between the slope, y-intercept, and graph. With the next question, students were asked to identify the slope and y-intercept and graph without writing the two down, if they were able. In just minutes, students were graphing lines within seconds using the slope and y-intercept. The only problem a few students were having was switching the slope and y-intercept, otherwise, things were going great.
Tuesday brought us a second day of graphing using slope and y-intercept along with students being introduced in the equations of horizontal and vertical lines. By Wednesday, students began writing the equation of a line, given a graph. Students did great with this, again with a few students in each class confusing which value was slope and y-intercept in the equation y=mx+b.
During the second half of Wednesday’s class, students began finding the slope of the line between two points. They started off graphing the points, then I forced them to find another way to find slope when we can’t fit the points on our graph. Once students were shown how to find slope, they preferred not graphing. I did not teach students the slope formula. Instead, we talked about rate of change/slope as the relationship of how the y-values are changing compared to how the x-values are changing. This seemed to work better and students didn’t get confused about what the first and second point are and what the subscripts mean in the formula. Yet again, the students did great.
The only lesson I didn’t really like this week was Thursday’s in which students were asked to compare slopes using graphs, tables and equations. Some classes did great with this, and some were completely lost. I think that next year I need to be more specific with my learning targets and more explicit with students as to what my expectations are for the lesson. However, there was one class that did great and really progressed through this lesson and topic. At the end of the lesson, I had students try to write the equation of a line, given two points, to see what information they could apply from this unit so far and what they retained from Unit 4. Some students came up with the equation, but some could only find the slope. I felt comfortable with where students were at the end of the day.
Friday brought one of those lessons that you want the principal to walk in during. If everyday were like my class was this past Friday, my classroom would be a pretty intense place. Our warm up had us finding slope and then progressing to using slope to find the y-intercept. Instead of having students input a point and the slope into the slope-intercept formula, I had students think about what the intercept would have to be to get the y-value in their point. For example, if students get a slope of 2 and their point is (2, 3), I have them multiply their slope times the x-value, 2, and see what they would have to do to get 3. In this case, students would have to subtract 1 from (2*2) which means their equation would be y=2x-1. Throughout this lesson, students were given the option of making a table and graphing in order to find the slope and y-intercept. Although many didn’t do it, I still liked the fact that students were given options and still found the answer, even if it were in a less efficient way.
Throughout this week, there were two things that came to my attention. The first is that, the more I use learning targets and write them on my board, the more comfortable with them I become. A colleague and I were discussing how much they helped us shape our lesson and formative assessment at the end of each class. By being forced to determine how I would assess whether or not a student knows a skill, I get a better idea of how I am going to get students to that point. If you are not familiar with learning targets, this website has some great information about them.
The second thing that is becoming apparent to me as this year goes on is the fact that most students will meet whatever expectations you set for them. I spent the first years of teaching feeling as if I was lowering my expectations to try to get all students to meet expectations. This year, the expectations are much higher and almost all are meeting them. If they aren’t, I am getting them into my Enrichment class to help them meet those expectations.
This coming week will be me giving an interim assessment with a performance task. I’ll report back next week with how that goes and what students thought of it. We’ll also continue to learn material that would have normally been taught in a freshman algebra class. I love the fact that Common Core has forced me to teach these things a year later, and forced me to rethink my teaching. So far, this has been the best year of teaching for me in my short, eight-year career. Have a great week!