Applying Similar Triangles to Finding the Slope of a LInear Equation Concluded
Lesson 16 of 23
Objective: Structure the same lesson in three ways so that each student group learns a different connection between similar triangles and the slope of a linear equation.
Clarify the intentions of the lesson again. Tell students that in 10 minutes each group will be called to the board to present at least two connections they have made between similar triangles and the slope of a linear equation. If groups are struggling to understand possible connections, I encourage them to look at question 3 to get ideas as this is individualized for each group. I allow 10 minutes to complete the group work and I move about the room assessing learning, providing feedback, and discussing with each group which ideas they will present to ensure I get variety and I know in which order to pull groups to the board.
The bulk of the class period is spent allowing student groups to present their learning. I called groups to the board in a particular order beginning with group one students, then group 2 students, and lastly group 3 students. I asked questions as the groups presented to ensure the big ideas were presented if groups began to forget what they planned to discuss (stage freight sometimes).
I recorded my student presentations and the video is somewhat lengthy but very informative. Click on Students Share Ideas from Similar Triangles Activity to watch my students present their thinking during one class period.
This activity applies similar triangles to finding the slope of a linear equation using any two points along the line. Different groups are meant to make different connections to this main idea but the overall math standard addressed is 8.EE.B.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
The math practice standards used throughout this activity arise from students working in cooperative groups to determine how similar triangles apply to slope of a linear equation and then decide which two connections to present to the rest of the class. Working throughout the activity to make difficult connections addresses practice standard MP1 Make sense of problems and persevere in solving them. Group discussion addresses standard MP3 Construct viable arguments and critique the reasoning of others. Working with similar triangles to see slope and make connections brings in standard MP7 Look for and make use of structure. Using coordinates to graph and find distance to the nearest hundredth bring in accuracy and address standard MP6 Attend to precision. One goal of this activity is that every group will understand why students who graph linear equations fluently use the concept rise/run to graph additional points past the y-intercept. By looking at this structure of similar triangles, the pattern of consistent rise/run should become obvious and this structure is really applying practice standard MP8 Look for and express regularity in repeated reasoning.