Graphing Parallel and Perpendicular Lines (Day 1 of 2)

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Objective

SWBAT graph parallel and perpendicular lines by discovering the relationship between the slope of a pair of lines.

Big Idea

Through graphing students will deduce that the slopes of parallel lines are the same and the slopes of perpendicular lines are opposite reciprocals.

Do-Now

10 minutes

Leading up to today's lesson, students have learned three new concepts (graphing, intercepts, and standard form). Today's Do Now is an opportunity for students to review those idea before moving on a new objective.  Students will complete the Do-Now in 5 minutes. Next three students will come up to the front of the classroom to throughly explain their responses to the class. 

Next, a student will read the objective: "SWBAT graph parallel and perpendicular lines by discovering the relationship between the slope of a pair of lines".

The terms parallel and perpendicular will be familiar to my students from middle school, but many mixed-up their definitions. To help students remember the correct representation of each word, I will ask the class to hold their arms in the air to model the following terms: parallel, intersecting, perpendicular, coinciding. I will ask a volunteer to give a verbal description of each term. I will also call on a student to describe the difference between intersecting and perpendicular.

Guided Notes + Practice

35 minutes

Students will explore today's objective using the graphic organizer from the parallel perpendicular lines packet.

 

Page One: To begin the lesson I will ask students to graph the following three lines:

  • Line A: y = 2x - 3
  • Line B: y = 2x + 1
  • Line C: y = 2x

I will ask students to describe the appearance of the lines on the graph. Then I will ask students to examine the equation of each line for any commonalities. Next, I will guide students with the following verbal prompts:

  •  "Lines A,B, and C all have a slope of 2 and ended up as parallel lines."
  •  "Let’s run with this idea, and graph two more lines with that have a slope of two."
  • "Create two lines of your own (Line D and Line E) that have a slope of 2." 
  • "Graph them on your paper. What happened?"

I will tell students to use their own words to write one sentence about the conclusion we made about parallel lines on the empty scroll on their notes.

 

 

Page Two: Next I will ask students to graph the following two lines:

  • Line F: y = 3/2x + 1
  • Line G: y = -2/3x + 5

I will ask students to describe the appearance of the two lines. I will then ask students to graph two additional lines:

  • Line H: y = 2x - 6
  • Line J: y = -1/2x + 3

Students should see another set of perpendicular lines. I will guide students to a conclusion about perpendicular lines by asking the following questions:

  • How can they be certain that the lines that they have are perpendicular and not just intersecting?
  • "What are perpendicular lines? Think back to what you learned about perpendicular lines in middle school." (4 right angles are formed)
  • "What tool do you need to measure angles?" (Using a protractor, I will measure the 4 angles formed where the two lines intersect to prove that they are perpendicular.)
  • "Examine the slopes of the 2 pairs of lines? Are they the same?"
  • "Are they different?"
  • "How are they different?"
  • "What’s another word we can use in math to say 'upside down'. You learned this word when you learned about fractions in elementary school."

 

With guidance, the class will come to the conclusion that perpendicular lines have slopes that are opposite reciprocal numbers. Students will write their conclusion inside of the scroll on the bottom of page two.

Guided Practice

25 minutes

Students will practice today's objective using the parallel perpendicular lines packet.

Page One: Students will complete the You-Try! section with a partner for 10 minutes while I circulate around the room working with individual pairs. We will then review the answers as a class. I will place special emphasis on number 3, 4, and  7 since the equations of those lines are in standard form and students will have to solve for y  in order to identify its slope. 

Page Three: The class will practice finding the opposite reciprocal of a number on the top of page three. Students will complete the You-Try 2! section with a partner for 10 minutes while I circulate around the room working with individual pairs. We will then review the answers as a class. I will place special emphasis on number 11, 12, and  15 since the equations of those lines are in standard form and students will have to solve for y  in order to identify its slope. 

Pages Five and Six: Students will complete the practice section during the remainder of class. I will encourage students to refer to the properties of parallel and perpendicular lines while they complete the assignment. We will review the answers to all questions during the last 5 minutes of class as a whole group.

Exit Card

10 minutes

Two volunteers will give a short summary about what we learned in class today. I will then ask students to describe how they can use a coordinate plane to check their answers when graphing equations of a line that are parallel and perpendicular. Students will then complete an exit card. The exit cards should be graded directly after class, and the students should then be grouped by the percentage of correct questions for our next class.