Summary
In this lesson, students use graphs with linear and nonlinear relationships to connect the idea of a constant rate of change with a graph being linear. Then, students identify or calculate the rate of change from a given scenario and use it—along with the y-intercept—to write a linear equation in slope-intercept form.
Essential Question(s)
How do we know when a relation is linear?
Snapshot
Engage
Students compare graphs and consider what must be true about graphs with straight lines.
Explore
Students graph given scenarios then describe the graph.
Explain
Students connect academic language to their exploration of linear and nonlinear relations.
Extend
Students construct their own scenarios with corresponding graphs, tables, and equations.
Evaluate
Students match peers’ scenarios through a Card Matching activity.
Materials
Lesson Slides (attached)
Reading the Situation handout (attached; one per student; print two-sided)
Reading the Situation (Sample Responses) document (attached)
Create Your Own handout (attached; one per student; print one-sided)
Scissors (one per student)
Engage
5 Minute(s)
Display slide 3 from the attached Lesson Slides. As they walk into class, ask students to think about what the graph on the slide tells them. Here students are shown a graph of how delicious different foods are depending on their temperature.
If it is a classroom norm, have students get out their math notebooks once class begins. If not, have them get out a piece of paper. Direct students to write everything they think the graph is telling them.
After a couple of minutes, facilitate a brief discussion, asking for volunteers to each share one thing they wrote.
Move to slide 4 and introduce the Think-Pair-Share strategy. Ask students what the straight lines mean compared to the curved lines. Instruct students to write what they think on their paper. Have students find a partner and share what they wrote. As time allows, ask for volunteers to share what they or their partner wrote.
Share the lesson’s essential question on slide 5 and the learning objectives on slide 6. Review each of these with your class to the extent you feel necessary.
Explore
20 Minute(s)
Display slide 7 and give each student a copy of the attached Reading the Situation handout. Explain to students that they are to read each scenario (situation), graph the scenario, and then determine if the graph is a line (or not) and identify the y-intercept.
As students work, circulate the room to monitor progress and answer questions.
Explain
15 Minute(s)
Once students complete their Reading the Situation handouts, display slide 8 and walk students through the first two scenarios, asking if each could be graphed as a straight line or not. Facilitate a discussion on each situation, have students “vote” either way, and have them share their processes on how they graphed that scenario.
After reviewing the situations, share with students that there is academic language for these graphs with straight lines and their characteristics. Transition through slides 9–10 and have students write these vocabulary words (with definitions) in their math notebooks: linear relationship, nonlinear relationship, rate, slope, and y-intercept.
Point to the word rate on slide 10. Explain that this is probably how they figured out how to correctly graph the scenarios.
Display slide 11 and introduce slope-intercept form to students. Walk students through how to calculate the rate of the first linear scenario (Situation 1) then have them go back through and find rates of the other linear scenarios (Situations 3 and 4).
Show slide 12 and ask the class why they think they were not asked to write a rate of change for the nonlinear scenario. If students are unsure, ask guiding questions about the scenarios having a constant change or about the scenarios describing an always increasing or always decreasing situation. Before moving on, make sure that students understand that the rate of change being constant is what makes the graph linear.
Extend
15 Minute(s)
Display slide 13 and ask students if there is a situation in their life that could have a constant rate. Give each student a copy of the Create Your Own handout. This includes a section for students to represent their situation in different ways:
Verbally: write their situation like a narrative
Numerically: record their data points in a table
Visually: graph their situation
Algebraically: identify their rate of change and y-intercept then write their equation in slope-intercept form
Evaluate
15 Minute(s)
Show slide 14 and give each student a pair of scissors. Have students cut their Create Your Own handout along the dashed lines separating all the components of their scenario, creating four cards.
Have students form groups of 4–5 or assign groups and display slide 15. Introduce the Card Matching instructional strategy, then have groups gently shuffle all of their cards.
Have groups trade card decks and collaborate to match cards, creating sets of four.
As students work, circulate the room and listen to conversations. Use what you hear as a formative assessment to determine if students are ready to move to the next topic or need further practice. If they do need further practice, consider creating a few additional scenarios for students to use.
Resources
K20 Center. (n.d.) Card matching. Strategies. https://learn.k20center.ou.edu/strategy/1837
K20 Center. (n.d.) Think-pair-share. Strategies. https://learn.k20center.ou.edu/strategy/139
