Relating Graphs to Events
Common Core State Standards:
N-Q.1, N-Q.2, N-Q.3
Paper, pencil, big graph paper, markers, rulers
General Outline of Lesson:
Students will interpret, sketch, and analyze graphs from situations that their classmates have created. Students will define (in their own words) and think critically about domain, range, x- and y-intercepts, etc.
Each student will write a "journey" involving different speeds and distances from a starting point, then graph that journey. Next they trade their journeys with another student and graph the new journey. Have students compare/discuss answers and reach a consensus. Lastly, each student graphs his/her equation on a big piece of graph paper and presents the results to the class. After the lesson we'll hang the graphs in the classroom.
How Students Will Work:
Students will work independently to create their journeys, then in pairs or small groups to compare/discuss their results.
How Students Will Record/Report Their Work:
Each journey writeup will be on a separate piece of paper. Graphs will be on big graph paper with clearly-defined axes, labeled sections, titles, etc. in marker.
Questions to Help Them Get Started/Make Progress:
What do the axes represent? What units should we measure them in? What does the slope represent? When should it be steep? When should it be gradual? What do the x- and y-intercepts represent?
Questions to Encourage Students to Share Their Thinking:
Do you agree with your partner's graph of your journey? Does he/she agree with your graph of his/hers? Were there any parts that you're not sure about? Which ones?
How to Orchestrate the Discussion:
If needed, review the concepts of slopes, intercepts, rates of change, etc. Make sure all students understands every concept and can restate them in their own words.
Questions so Students Will Make Sense of Math Ideas:
What is slope? How do we measure it? What are x- and y-intercepts? What do they represent for this specific journey?
Questions to Expand the Debate:
When comparing with your partner, where did you differ? Why do you think that is? Can there be more than one "right answer"? Explain.
Could part of the graph be perfectly horizontal? What would its slope be? What would that represent? Could part of the graph be perfectly vertical? What would its slope be? What would that represent?
Have Each Student Share His/Her Thinking:
Peer-sharing is built into the lesson, both when comparing graphs with a partner (or multiple partners, if desired) and when presenting the journey/final graph to the class.