Authentic Lessons for 21st Century Learning

Airplanes and Airstrips, Part 1

Writing Linear Equations: Graphs

K20 Center, Michell Eike, Sherry Franklin, Dy'Nelle Todman | Published: May 20th, 2022 by K20 Center

Summary

This lesson addresses writing linear equations in slope-intercept form when given a graph. Students will use their knowledge of slope and y-intercept to analyze linear graphs and represent what they see graphically in an equation. Prerequisites for this lesson include identifying slope and y-intercept when given an equation, graphing linear equations, and finding the slope of a line. This lesson also offers an opportunity to reiterate the meaning of slope and y-intercept, while placing emphasis on linear relationships being represented and modeled in multiple ways. This lesson includes optional modifications for distance learning. Resources for use in Google Classroom are included.

Essential Question(s)

How can linear relationships be represented/modeled in multiple ways?

Snapshot

Engage

Students activate prior knowledge and show what they know about identifying slope and y-intercepts from graphs and equations.

Explore

Students are introduced to writing linear equations through a Desmos classroom activity, by acting as pilots and attempting to safely land airplanes on an airstrip.

Explain

Students reassess the equations they wrote during the Explore activity.

Extend

Students create their own airstrips using linear equations as the center.

Evaluate

Students write linear equations for other students' airstrips.

Materials

  • Chromebooks (or other similar student technology with Internet access, e.g., tablets, computer lab)

  • Writing utensils

  • Matching Equations and Graphs Card Sort (print and cut out sets equal half the number of students, who will work in pairs)

  • Lesson Slides (attached)

  • Student Notes/Planes Landed handout (attached; print double-sided, one for each student)

  • Airstrip handout (attached; one per student)

  • Smart Board (or other technology to show the plane video and the project model graph in the Explain section)

Engage

Introduce the lesson using the attached teacher slides and begin by pairing students and introducing the Card Sort activity on slide two. Have students work in pairs to match the linear graphs with their corresponding equations.

Once students have successfully matched their graphs and equations, have pairs group with another pair (to form a group of four) and justify how they matched their cards.

Transition to slide three. Bring the class back together and have pairs share out with the whole group how they matched their graphs and equations.

After (or while) students are sharing, ask some of the following questions:

  • "What methods did you use to match the graphs and equations?"

  • "How did you know which graph went with each equation?"

  • "What characteristics did you look for in the graph that helped you pick its matching equation?"

  • "What characteristics did you look for in the equation that helped you pick its matching graph?"

  • "Were all the equations in slope-intercept form? If not, how did you find the matching graph for that equation?"

  • "What is slope-intercept form?"

  • "What is slope?"

  • "What is y-intercept?"

Move to slide 4 and begin transitioning to the Explore section by asking students if they have ever been on an airplane. Would they like to ride on a plane? What do they think are the best and worst parts? Is it the takeoff or the landing? Who would like to be a pilot?

Explore

Before getting started, have students watch this video on airplane landings. Ask students to imagine they are pilots. Do they think they could do a better job than the pilots in the video?

Pilots are tasked with landing airplanes in the center of a landing strip to ensure the safest landing possible. However, as students saw in the video, it doesn't always happen that way. What if pilots had a better concept of linear functions to help them have more successful landings and/or safer landings? Explain to students that they all have a pretty good knowledge of linear functions, and they will explore, as pilots, how this knowledge can help them land some airplanes.

Transition to slide 5 and introduce the Desmos "Land the Plane" activity, in which "students practice finding equations of lines in order to land a plane on a runway" (Desmos, 2017). Follow these steps to facilitate the activity:

  • Display the class code that you created earlier.

  • Provide students with the "Student Notes/Planes Landed" handout. (Make sure they do not write on the "planes landed" side. They will need that later.)

  • Have students retrieve a Chromebook (or other technology that can connect to the Internet).

  • Once logged on to the Chromebook, have students visit Desmos at student.desmos.com and enter the class code. It is recommended that students log in with their district-provided Google accounts and passwords. Personal Google accounts can be used if they do not have one provided by the district. If students do not have Google logins at all, they should create a Desmos account manually. This gives students the opportunity to return and view their work again anytime after the lesson.

  • Ask students to complete screens one and two. Be sure to control the pacing. It should take no more than five minutes to complete each screen. Have students take notes about things they feel are important, things they need to know, and/or things that can help them complete the other screens.

  • To assist students with their note taking, have them use either of the following instructional strategies: Stop and Jot or Question Generator (see further details in Teacher's Note below).

  • Students may work individually or in pairs to complete screens three through five.

Slide 6 contains some guidance for the Stop and Jot strategy. When students finish the activity, ask them to write down an equation to challenge their fellow students and which models the questions in the Desmos activity. Make sure they solve your equation so they can check their peers' work later. Have them save this equation for now. They will use it later in the lesson.

Explain

Provide each student with a sticky note. Display slide seven and present the question to students: What determined if the plane would go through the center of the landing strip?

Allow students time (one to two minutes) to write their thoughts on their sticky notes. Write the question on a poster at the front of the class and present it to the students.

Ask for a few student volunteers to read their thoughts out loud. Prompt all students to come forward and place their sticky notes on the poster.

Using one of the graphs from their Explore activity (such as the one below), model how to write a linear equation in slope-intercept form. Prompt students to take notes in the "student notes" section of their handout.

Reflect 1—Slide 6

Guide students by asking the following questions, shown on slide 8:

  • "What is the first thing you need to know to write an equation in slope-intercept form?"

  • "What is slope-intercept form? "

  • "What do the variables in slope-intercept form represent?"

  • "What "parts" of the slope-intercept form equation can you find on the graphs?"

Remember the questions students wrote down? Now is time for students to bring those out to test their peers' knowledge. Ask students to trade papers with someone and answer their question to determine if they can write an equation for the challenge question.

Extend

Provide students with the "Airstrip Handout," found in the attachments and display slide 11.

Ask students to draw a landing strip graph with a line (linear equation) that passes through the center of the landing strip. The goal is for students to create an equation that they think their classmates won't be able to find.

Have students give their landing strip a name.

Have students write their equations on a separate sheet of paper (not on the graph). Keep a list of all the equations. Post the graphs around the classroom on desks, tables, and walls.

Evaluate

Prompt students to flip over their Student Notes/Planes Landed handout to the side titled, "Planes Landed."

Introduce a Gallery Walk strategy and have students participate by visiting each of the landing strips graphs created by their classmates that have been posted around the room. Ask them to attempt to successfully "land" a plane on each one.

Landing a plane on the landing strip means finding the linear equation that passes through the center of the landing strip.

Through this activity, students will obtain more practice writing linear equations given a graph in slope-intercept form.

Each student will turn in a "Planes Landed" handout at the end of the class. This will be the student's Exit Ticket.

Resources