Day 4 – An Introduction to Slope and y-intercept

What does y = Mx + B mean? I didn’t want my students to just memorize what M and B meant, I wanted them to understand it. So, instead of just telling (or showing) them what M and B stood for, this year I let them discover it for themselves! And since seeing is believing, I decided to use an online graphing calculator.

First, I taught them how to use a basic graphing calculator that I found online. Then, they graphed a series of graphs on the online calculator. I had them answer questions for each graph on a Discovering M and B worksheet. I had shown them the equation y=Mx+B the day before. I did this very briefly, just to show them how to pick out the M and the B from an equation. I did not tell them what M and B meant.

After graphing a series of graphs, they had to answer questions at the bottom of their worksheet. Side one focused on slope, and side two focused on the y-intercept. I taught this lesson two classes in a row. In the first class, I had never used this lesson before and wasn’t sure how easy it would be since they had not used the online graphing calculator before. Plus, I was being observed so I was a little nervous. However, I realized in the first class that my students were trying to “zip” through the questions in order to get to the other side. They weren’t thinking enough about the questions. And, when I told them that their answers weren’t correct, they wanted me to tell them the answer right away without further thought. So, in the next class, I decided to try to get the students to really focus on the questions at the bottom of each page by making it kind of a “challenge”.

*** Note: As the teacher, you MUST make your students focus on the questions at the bottom of each page. Do NOT give them the answers until they try to figure it out themselves. This is the key to this entire lesson. ***

I told the students that in order to answer the questions, they would have to look through their worksheet to try to figure out the pattern. To make it more dramatic, I called the pattern a “puzzle” and made a huge deal about “figuring out” what B meant. I was tough on them, looking for great descriptions for slope and insisting on an accurate description for B. I told kids when they were close! But, I wouldn’t say, “You GOT it!” until I saw the word intersection. A few kids got it early, and after my, “Yes!!” I put my finger to my lips in a shhhh, don’t tell the secret! It drove the other kids crazy! I told them, I am looking for one special word! After a few failed attempts, some students were even googling, “linear equations and B” to try to find out what word I was looking for! It was so much fun for me, and you could feel the excitement in the room!

All of my students were able to figure out that M indicated the steepness of the line and which way the line went (positive or negative). Most of them were also able to figure out that B was the point where the line intersected the y-axis. Quite a few of them even came up with the word intersection. It was a great day! Worksheet included.

I hope you also accepted other correct answers that did not use the word “intersection”. Descriptions like “the y value where the line crosses the y axis” should have been just as good.

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I’m sorry that I wasn’t more clear in my original post. I would not tell students that an answer such as yours was incorrect, as it is obviously not incorrect. However, I encouraged them to continue thinking about what one word could best describe what was happening. I would say, “YES! That is what is happening! Now can you think of one word that could describe that?”.

I have often found that students know what they are doing, but are lacking the mathematical terminology. By making a “big deal” out of the word intersection, and by having them think very hard about it, I was hoping to impress the word upon them. From intersection it is a short walk to intercept. Hopefully then, the term y-intercept would not only mean something, but also make sense to them because it was something that THEY came up with.

Your lesson looks great but I am not able to see the video- the one posted is on menopause.

What?!?! Lol! Ah, the joys of YouTube! Lol