Deriving y = mx + b
Lesson 6 of 7
Objective: SWBAT derive the equation of a line in slope-intercept form.
For today's Warm Up problems, I've included in two that build on the previous days' lessons. First, I want to give students additional experience applying the slope formula. I intentionally include points that will yield a negative slope. I do this to check for student understanding about integer operations so that I can make note of students who continue to struggle and may need additional interventions.
The second questions asks students to identify which of the three slope triangles would fall on the line from the first question. This allows an opportunity for exploration of slope from right triangles. This question will also likely reveal students who struggle understanding slope as rise-over-run or change in y-values over change in x-value.
Once the students have complete the two warm up problems and come to consensus about the answers, I launch today's lesson by introducing the learning objective: SWBAT derive the equation y = mx + b for a line.
Deriving y = mx + b Foldable
Derivation in mathematics often poses a challenge for students, especially when dealing with variables, so I have designed a lesson that gives students an opportunity to see the steps for deriving the slope-intercept equation from the slope formula. As I display and explain each step on the board, I ask students to take notes on the front of their Deriving y = mx + b foldable. Once we have completed the steps, I distribute the Cut-and-order steps, which the students will cut out and then order and glue on the inside of their foldable during work time.
The Work Time slide provides the students directions for the work time activity which involves cutting out the six steps of the derivation process and correctly ordering them as they explain what is occurring mathematically at each step. Students work with a partner to explain and verify their work. During work time, I circulate through the room to check for understanding and answer any questions students may have.
When the work time timer sounds, I encourage students who have not finished to continue working while the students who have completed the assignment help me order the steps of the derivation process on the smartboard in the Wrap Up. I begin by asking students to discuss at their table groups which of the listed steps should come first. Once we have class consensus, I then select students randomly from their name sticks and ask them to come to the board and drag and drop the next appropriate step into the sequence. This gives a third opportunity for students to make sense of the process and consolidate their understanding.
Ticket Out the Door
Now that students have had three exposures to deriving the y= mx + b equation, I ask students to now consider the y = mx equation through the origin. I ask them to look at their graph inside their foldable that models the line from today's lesson. I then ask a student volunteer to come the board to draw a line parallel to that line but passes through the origin, which students can then draw in their own foldable. I then distribute blank note cards to the students and ask them to now derive the equation of the line through the origin, reminding them that the y-value of the origin has now changed as I write (0,0) under the origin. As students work, I circulate throughout the room offering guiding questions to students who may be struggling to get started or to understand the task. These exit tickets serve as a great formative assessment and the student's responses will help guide my lessons for subsequent days.