Comparing Rates in Various Forms

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SWBAT to compare two different proportional relationships represented in different ways.

Big Idea

Once students are proficient at determining unit rates from graphs, it's now time for them to compare those rates to ones in different forms: tables and equations.

Warm Up

5 minutes

Today's Warm Up builds on the previous lesson on determining unit rates from graphs. Because my students often have difficulty with graphs that lack numerated labels on axes, I provide additional practice to begin today's lesson. The warmup also gives students practice with writing equations that describe a graph. 

Learning Objective/Launch

6 minutes

After reviewing today's learning objective with students, I plan to reveal an example to help them understand today's work time task (see Comparing Unit Rates In Various Forms). I want to make sure that students understand that they will be comparing rates of change (slope) in different forms and what those forms might take including tables, graphs, and equations.

Work Time

12 minutes

For Work Time, students will work with a table partner (already preassigned, like-performance peers) to identify rates in given forms for two different cartoon characters in 12 scenario cards.  As they work, I have instructed them to record their answers, as well as evidence, in their math journals so they are ready to share when the timer sounds.

As students work, I will eavesdrop on conversations and provide support, as needed, to partner pairs. I make note of particular points that are well made by students and ask them to share with the class during Consensus Building time.

Consensus Building

10 minutes

Once the Work Time timer sounds, I bring groups' focus to the front where I reveal each scenario for Consensus Building. While the majority of the scenarios bring instant consensus because of the obviousness of the given rates, others pose a greater challenge and result in differing answers.  In particular, Scenarios I and K pose issues due to the scaling on the graphs. These bring additional opportunity for students to apply their knowledge from previous lessons on unit rates.

After the class reaches consensus on the answers to each of the scenarios, I introduce our Wrap Up activity for the day.

Wrap Up

12 minutes

For today's lesson Wrap Up, I ask my students to write in their journals. I ask them to come up with scenarios involving two characters of their own choice. In their scenarios they should represent a rate for each the characters in two different ways.

After they have written their scenarios, I will have my students exchange their creations with someone at their table. Their table partner should try to represent the scenario and solve problems that are posed.

As my students complete this task, I will circulate and challenge them to choose three characters and represent those rates using a table, a graph, and an equation.