Summary
This lesson addresses writing linear equations given a table of values. Students will use their knowledge of slope and y-intercept to analyze linear data tables and represent the linear relationship in the data as an equation. Students also will watch a video of a former air traffic controller speaking about his career. Prerequisites for this lesson include identifying slope and y-intercept given an equation, graphing linear equations, writing linear equations given a graph, and calculating the slope of a line given two points. This lesson places emphasis on linear relationships being represented and modeled in multiple ways.
Essential Question(s)
How can linear relationships be represented in multiple ways?
Snapshot
Engage
Students watch a video of a former air traffic controller speaking about his career and then use prior knowledge to represent linear relationships as graphs, equations, and tables.
Explore
Students explore writing linear equations from tables while acting as a flight crew and create a poster illustrating the steps.
Explain
Students reflect on their peers’ posters and find the similarities and differences and eliminate earlier misconceptions of how to represent a table of values as a linear equation.
Extend
Students create their own problem by creating a table of data with a linear relationship.
Evaluate
Students demonstrate their understanding by writing a linear equation from their peer’s table.
Materials
Lesson Slides (attached)
Flight Data handout (attached; one page per group of 3; printed front only)
Landing Changes handout (attached; one per class; printed front only)
Poster Planning handout (optional; attached; one per group; printed front only)
Note Catcher handout (attached; one per student; printed front only)
Paper
Pencils
Poster paper
Sticky notes (optional)
Markers (3 colors per group)
Engage
20 Minute(s)
Introduce the lesson using the attached Lesson Slides. Slide 3 displays the lesson's Essential Question: “How can linear relationships be represented in multiple ways?” Slide 4 identifies the lesson's learning objective. Review each of these with your class to the extent you feel necessary.
Go to slide 5. Distribute one strip of paper from the attached Flight Data handout to each student.
Students with a given graph are also given the job title of flight captains. Instruct the flight captains to individually work to write an equation and create a table of values, containing five ordered pairs, for their given graph.
Students with a given equation are also given the job title of first officers. Instruct the first officers to individually work to create a graph and a table of values, containing five ordered pairs, for their given equation.
Students with a given table of values are also given the job title of flight engineer. Instruct the flight engineers to individually work to write an equation and create a graph for their given table.
Once their individual exercise is complete, display slide 6 and have students find and sit with their flight crew — the two other people in the room that have the same equation, graph, and table of values as them. Direct students to discuss with their flight crew how they found their missing information from their given information.
Move to slide 7. Introduce the “Airplanes and Airstrips, Part 2” video, which features a former air traffic controller talking about his career and how he uses linear equations. Play the video for students.
Have each group discuss the following question: When he mentioned “rate of change” and “speed,” how does that relate to what we know about linear equations?
After giving groups a couple of minutes to discuss, ask for a few volunteers to share out. If needed, facilitate a discussion that pushes the class to see that “speed” is a “rate of change” and that “rate of change” is the “slope.”
Explore
30 Minute(s)
Go to slide 8 and give students the following scenario:
Sometimes pilots need to make in-flight decisions when landing a plane. Luckily, they do not have to make those decisions alone. Due to inclement weather, the air traffic controller sent each flight crew alternate landing data. Using the new data, each crew must write an equation for the airstrip they now need to land their aircraft on.
Transition to slide 9 and distribute one Flight Crew strip from the attached Landing Changes handout to each Flight Crew (group of three students). Explain to students that they have each been given new data and need to complete the challenge of writing a linear equation without graphing or plotting any of the given points. Ask the questions on the screen and give them approximately 5 minutes to discuss as a group.
What information would you need?
How do you get that information?
What steps would you take?
As students discuss, move to slide 10 and give each group a copy of the attached Poster Planning handout or ask them to create a plan on notebook paper before giving out poster paper. This is a space for students to plan out their ideas before using markers on poster paper.
After 5–8 minutes, students should be finished with planning their poster. Show slide 11. When students show you their poster plan, give them (or indicate the location of supplies) a poster and two markers. Direct their attention to slide 11 and explain that they should use one color to make their table, show their work, and write their equation. Their second color is for numbering and labeling steps. For example, “Step 1: Make a Table” should be a different color than the table of values on their poster.
Explain
30 Minute(s)
Go to slide 12 and have students hang their posters around the room. Give each student a copy of the attached Note Catcher handout. Explain the Expert Stay and Stray strategy: one student will stay at the poster and explain to the flight crew how to take data and write a linear equation. Those who are listening need to pay careful attention because each round a new person stays and becomes the new expert/presenter. Continue previewing the activity by explaining that there will be three rounds, and that everyone will have a turn as the expert. There will be 5 minutes per round where learners need to visit half of the other posters during that time. The expert will also use a third color marker to add important information to the poster as they answer clarifying questions. Alternatively, sticky notes can be an option to add information instead of writing directly on the poster.
Show slide 13 and begin round 1. Direct all flight captains to stay at their posters, ready to present. Direct all first officers and flight engineers to visit the other posters and take notes and ask questions. Remind them that they are preparing to be the next expert.
Start the 5-minute timer on slide 13.
When the timer expires, direct students to “freeze,” and show slide 14. Direct all flight engineers to move to the nearest poster. If there are multiple flight engineers at a poster, direct them to move to a different poster without a flight engineer such that all flight engineers are at a poster that they have visited, ready to be the new expert for that poster.
Show slide 15 and begin Round 2 by starting the 5-minute timer.
When the timer expires, use slides 16-17 to repeat the activity once more, now with first officers as the new experts.
When the timer expires the final time, direct students to find their original flight crews (original group).
Display slide 18 and have the students answer the questions on the slide and write their responses on the back of their Note Catcher handout.
What did you notice that all the posters had in common?
Why were all the posters not the same?
Once you discuss the questions above as a whole class, consider the misunderstandings that you heard and take time to correct students. Ask the class if there are any questions. Use this time to make sure students understand how to write a linear equation from a table of data.
Extend
5 Minute(s)
Go to slide 19. Prompt students to create a table of values with five ordered pairs that model a linear relationship on a piece of notebook paper. Once they have completed their table and believe they have modeled a linear relationship, have the students fold their paper into a paper airplane.
Preview the activity by explaining to students that they are going to gently throw their paper airplane across the room. Then they are going to pick up one paper airplane.
Instruct the class to throw their paper airplanes. Then direct them to pick up one paper airplane.
Evaluate
10 Minute(s)
Display slide 20 and instruct students to unfold the paper airplane they picked up. Ask students to trade if they picked up their own original paper airplane.
Now direct students to write the linear equation represented by the table. Remind students to use their steps from their poster. Allow students time to reflect on the process. Prompt them by asking them if the steps they used give them the correct answer? If not, what should they do to edit them?
Collect the paper airplanes to assess student understanding of the lesson.
Resources
Fillieul, T. (2015, September 10). Douglas Dakota [Photograph]. Wikimedia Commons. https://commons.wikimedia.org/wiki/File:Douglas_Dakota_ZA947_at_Jersey-1046493.jpeg
K20 Center. (n.d.). Expert Stay and Stray. Strategies. https://learn.k20center.ou.edu/strategy/2650
