Equations of Parallel and Perpendicular Line
Lesson 1: Our lesson plan was a type of guided discovery lesson that tries to pull real life examples. The students are going to take pictures of parallel and perpendicular lines around campus. Students need flip cameras and laptops equipped with GSP. The lesson is set up to use a document camera, but this can be adjusted based on the technology available to you. Students should also have graphing calculators available.

Lesson 2: Our lesson plan was more of a guided-discovery and focused on the manipulation of triangles in order to discover the slopes of parallel and perpendicular lines. The students worked individually for the majority of the time with the exception of working in pairs during the brief Check for Understanding. Very little technology involved--the lesson is guided with a PowerPoint (but this can be changed/printed) and the only other materials required are scissors and graph paper.

Lesson 3: Our lesson plan uses Geometer's Sketch Pad (GSP) to have students investigate shapes with parallel and perpendicular sides. Through finding the slope and then the equation of the line which contains the line segment of the different sides, students are directed to pay close attention to the relationships between the slopes. Ultimately, they should be able to make conjectures based on the relationship of the slopes of parallel and perpendicular lines.

Lesson 4: Blurb Please

Lesson 5: Our lesson was a bit of a guided discovery for the slopes of parallel and perpendicular lines. Students will use the applet to explore the slopes of parallel and perpendicular lines. The applet allows students to manipulate two lines and announces to the student when the lines are parallel or perpendicular and states their slopes. They will be given a worksheet with questions on it designed to guide their investigation.

Lesson 6: Our lesson uses GSP to allow students to discover the real world applications of perpendicular and parallel lines by letting them create roadways and intersections. Students learn how to write equations of parallel and perpendicular lines in relation to another line, through a given point. They then apply what they learn in this lesson to help with their road planning on GSP.

Lesson 7: This lesson uses a warm-up to transition from analyzing a single line to analyzing the relationships between two or more lines. The students will find the equation which represent the given lines. They will then be lead in an investigation of whether the lines are parallel or perpendicular. Using their assumptions, the class then examines how slope is used to determine those relationships. It relies upon the misconceptions that students may use because of their preconceived and instilled ideas. After analyzing those lines given in the warm-up, the students are shown a single graph with five lines. Again, they will make assumptions which will be confirmed or disproved during discussions. Finally, the students will investigate parallel and perpendicular lines using slope in the worksheet below. They are asked to determine if there is a relationship between two functions and to also find an equation which satisfies certain criteria.

Lesson 8: In this lesson, students use an online applet to create parallel and perpendicular lines in the coordinate plane. The applet announces to the students when the lines are parallel or perpendicular, shows the coordinate points, and shows the slopes of both lines. Students have instructions and guided questions on a Google Form which help the students develop the relationships between the slopes of parallel and perpendicular lines and apply that knowledge in other situations.

Lesson 9: The lesson is a hands-on (potentially out of seat) guided discovery type activity that guides students towards discovering how to determine if two lines are parallel or perpendicular given their equations, graphs, or both. If you have a smaller class (~20 or less) and room to spread out, this lesson requires a roll of masking tape and some string or yarn. But if you have a larger class, you can just use poster-board and some string.