Summary
This lesson is intended to introduce and reinforce how proportional relationships are displayed in graphs and tables. Students will need a basic understanding of graphing and will apply that knowledge to calculating rates based on scenarios.
Essential Question(s)
How are graphs, tables, and rates connected?
Snapshot
Engage
Students look at two social media posts and observe the different graphs in each.
Explore
Students interpret scenarios and determine if their graphical properties.
Explain
Students connect academic language about linear proportionality to scenarios, graphs, and justifications.
Extend
Students construct their own scenarios and answer keys.
Evaluate
Students switch scenarios and try to solve a classmate’s scenario.
Materials
Lesson Slides (attached)
Linear Proportions Scenarios (attached)
Make Your Own Scenario (attached)
Engage
Ask students what kind of stuff they like to follow on social media. Let them just informally share out.
Display the first graph on the slide, and say that this is an Instagram account that makes funny graphs (so a cool, yet nerdy, social media account).
Ask students:
What is this graph telling you? Write down in your notebook EVERYTHING you think the graph is telling you.
What does the straight line mean compared to the curved lines? Write down your thoughts in your notebook.
Allow students to share their thoughts with their neighbors after each question, but don’t make a production out of it.
If you have time, show the next graph on the next slide. (If you don’t have time, just move on.)
Explore
Pass out the worksheet with a variety of scenarios written out. Tell students their job is to see if the scenario could be graphed as a straight line, and what characteristics the line would have, and how they would figure out how to graph that line.
While students work through the scenarios, walk around and help as needed.
Explain
Once students are done, walk through each scenario and ask if it could be graphed as a straight line or not. Have students “vote” either way, and for the first few, have them talk out their process on how to graph out the scenario.
Tell students that there is academic math language for what we just did, and they’re going to write the following words down.
Display slide 12 with the following words and definitions:
Point to rate; explain that this is probably how they figured out how to correctly graph the scenarios. Walk them through how to write out the rate of the first linear scenario, and then have them go back through and write out the rates of the other linear scenario.
Wrap up this section by asking “Why did we not write a rate for the non-linear scenarios?” If students struggle with this, point out that we can’t write one rate for non-linear (or even piecewise linear scenarios) to help them get to the idea that a simple rate will always be a line, and nonlinear has a lot of different rates in one graph.
Extend
Ask students if there is a situation in their life that could have a constant rate to it. Pass out the handout that will help them map out and graph their personal scenario. This includes a section to write out the scenario like a narrative, a table to put their data points in, a blank for the rate (with units!), and a graph for them to chart it out.
Evaluate
Have students cut up their handout along the dotted lines separating all the components of their scenario. Group students in groups of four or five, and mix all of their pieces together in the center.
Then, have the groups try to match all pieces together successfully.
