Summary
This lesson focuses on how to analyze and solve systems of linear equations by using the graphing method. The goal is for students to use prior knowledge to expand their understanding of equations and how they connect to real-world scenarios. Students will be able to identify, solve, and write systems of equations using graphing as their tool. This is the first lesson of three in the "Two Worlds Collide" lesson series.
Essential Question(s)
How can systems of equations be used to represent situations and solve problems?
Snapshot
Engage
Students evaluate a statement by using the Always, Sometimes, or Never True strategy.
Explore
Students discover intersection points through a Desmos activity.
Explain
Students formalize their understanding of different types of systems of equations: consistent and independent, consistent and dependent, and inconsistent.
Extend
Students solve a problem based on a real-world scenario.
Evaluate
Students reflect on their understanding of the lesson.
Materials
Lesson Slides (attached)
Note Catcher handout (attached; one per student; print one-sided)
Skate Park handout (attached; one per student; print one-sided)
Paper
Pencil
Student device with internet access
Engage
5 Minute(s)
Introduce the lesson using the attached Lesson Slides. Display slide 3 to share the lesson’s essential question. Go to slide 4 to share the lesson’s learning objectives. Review these slides with students to the extent you feel necessary.
Have students find a partner or assign partners and show slide 5. Have pairs use the Always, Sometimes, or Never True strategy to discuss the prompt on the slide, “Two lines cross at only one point.”
Give pairs a couple minutes to analyze the statement and choose their claim, and then conduct a whole-class discussion by asking different pairs to share their viewpoints on the statement.
Explore
15 Minute(s)
Display slide 6 and provide students with your session code. Then, have students go to student.amplify.com/join and enter the session code.
Pass out the attached Note Catcher handout to each student. Invite students to take notes on the top portion of the handout as they work through the activity.
Explain
20 Minute(s)
Have students find a new partner or assign them. Display slide 7 and give pairs time to read the definitions for consistent, inconsistent, dependent, and independent. Remind students these definitions are also on the Note Catcher handout for later reference.
Move to slide 8 and have pairs use the definitions to match each graph on the slide with what they think is the best description: consistent and independent, consistent and dependent, or inconsistent. Ask students to draw, in pencil, a rough sketch of each graph in the corresponding columns on the Note Catcher handout.
As students finish sketching the graphs, go to slide 9. On the handout, ask pairs to use their own words to describe each type of system of equations. The goal is for each student to have both visual and verbal representations of the different types of systems of equations on their handout.
As students finish writing their descriptions, bring the class together to go through slides 10–12. Have students use these slides to confirm that they put the graphs in the right columns. Encourage students to write down any information from the slides that they may be missing on their handouts.
Ask for volunteers to share anything they wrote that was not on the slides. Use students’ responses to check for misunderstandings. Then, use this time to correct any of those misunderstandings.
Extend
15 Minute(s)
Display slide 13. To expand students’ knowledge of using graphs and equations to solve real-world problems, read aloud the following scenario: You and your friend want to go to a skate park this weekend. There are two parks in the area, Scissortail and Silverstone. Scissortail costs $3 to enter and $1 for every hour you stay. Silverstone costs $5 to enter and 50 cents for every hour you stay. Which skate park will you and your friend attend? Explain your reasoning.
Pass out the attached Skate Park handout to each student. Have students work individually to create and graph their own equations based on the given scenario. Using their findings, have students determine which skate park they want to attend and explain why on their handouts.
After providing time for students to work through the problem, show slide 14. Ask students to share with the class which park they decided to attend and why.
Emphasize that the solution to this system of equations is the point where the two parks cost the same dollar amount for the same amount of time—in other words, the point where they have the same y-value for the same x-value.
If time allows, consider asking the class to come up with a skate park example where there would not be a solution to that system of equations. This would occur when both parks would need to have the same rate (price per hour) while having different entrance fees.
For an extra challenge, ask the class if they can think of a skate park example where there would be infinitely many solutions. An example of this would be if Silverstone kept its $5 entry fee and a rate of 50 cents per hour, but Scissortail had a $5 entry fee and a rate of $1 per 2 hours, then the cost at the two parks would always be the same.
Evaluate
5 Minute(s)
To wrap up the lesson, have students use the How Am I Feeling? What Am I Thinking? strategy to reflect on their learning. Display slide 15 and ask students to recreate the table on the slide on the back of their Skate Park handouts.
Show slide 16. In the "How Am I Feeling?" column of the table, ask students to draw or write a description of how they feel about the content they have explored. In the "What Am I Thinking?" column, have students write a sentence that explains what they understand or think about the content they have explored. This could be a question or a comment about their learning or a description of the experience itself.
Use students’ responses to give you an understanding of how well they comprehend the material and what you might have to tweak moving forward. Make sure students have a clear understanding of the visual representation of how a system of equations works before the next lesson: Two Worlds Collide, Part 2.
Resources
K20 Center. (n.d.). Always, sometimes, or never true. Strategies. https://learn.k20center.ou.edu/strategy/145
K20 Center. (n.d.). How am I feeling? What am I thinking? Strategies. https://learn.k20center.ou.edu/strategy/187
K20 Center. (n.d.). Desmos Classroom. Tech tools. https://learn.k20center.ou.edu/tech-tool/1081
Zimmermann, M. (n.d.). Solutions to Systems of Linear Equations [Interactive activity]. Amplify Classroom. https://classroom.amplify.com/activity/564a325345d9115d06270607?collections=5da6485a83c0877d4b5708dd