Finding Equations of Parallel and Perpendicular Lines

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Students will be able to determine whether find lines are parallel, perpendicular or neither and use their understanding of parallel and perpendicular linear equations to context of a rectangle.

Big Idea

Using slope properties to write linear equations for parallel and perpendicular lines.

Warm up and Homework Review

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations.  The Video Narrative explains this lesson’s Warm Up- Finding Equations of Parallel and Perpendicular Lines which asks students  to determine if two given equations are parallel (Math Practice 4 and 7).

I also use this time to correct and record the previous day's Homework.    

Today's question of may students to ask their new partners is: If you could plan your ultimate vacation, where would you go?

Introduction to Parallel and Perpendicular Lines

10 minutes

In this lesson, students will compare the properties of lines in different forms to determine whether they are parallel or perpendicular.  This lesson is from the Math Assessment Project which I have found contains very high quality material which I try to use whenever I can.  These lessons are complete by themselves.  So rather than writing out the lesson again, I will provide perspective on how I will implement it in my classroom.  

The introduction is done with personal white boards.  Often, I will ask one person in each row to get boards for their entire row.  I will mix this up so it isn't the same person each time.  

This Introduction reviews some the features of lines as well as parallel and perpendicular slopes. 

Matching Activity

17 minutes

The MAP lesson plan (link is in the introduction section) suggests groups of three, however since my students are already partnered (pairs) this is an easy modification .  For each pair of students you will need a set of cards and a glue stick.  As the students work through the matching activity, be sure to circulate around the classroom providing support.  The lesson plan gives some great ideas such as asking questions or making comments like:

How can you determine the slope for any equation?

Is there a form of the equation that makes this easier?

How do you find the x-intercept from a written equation?

If you cannot place all the cards, you may need to rethink some of your categorizations.

One major focus is to encourage student vocalization of their thinking (Math Practice 3).  I will model this for the class before they begin the activity. You may need to remind students as you walk around as well. 

Once the cards are sorted students switch groups and share their findings.  My pairs sit next to each other so I simply have them work with the person right in front of or behind them for this portion.  

Class Discussion

15 minutes

This culminating activity begins with a short period of time to share findings as a class.  You will want to monitor and keep the sharing conversations relatively short as the final activity is really important.  The Final Activity starts with a rectangle and the equation for one of the four sides.  Each pair of students then find possible equations for the other three sides.  These will all be different as there is no indication of the lengths of the sides.  

Exit Ticket

2 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

This Exit Ticket asks students to identify a parallel and a perpendicular slope to a given equation.