Determining Unit Rates From Graphs

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SWBAT to calculate a unit rate given a graph.

Big Idea

Today's Work Time activity provides students additional practice calculating unit rate (and slope) from graphs, many of which include fractional rates.

Warm Up

5 minutes

For today's Warm Up, I selected a problem from IllustrativeMathematics that challenges students to use their previous knowledge of slope to determine the best equation for one of two given lines. This problem is particularly useful to me as a pre-assessment for today's lesson, as students will need to have a strong understanding of slope. If students struggles with this Warm Up more than I expect them to, I may need to make adjustments to my pre-selected groups so that stronger students can anchor each group and assist struggling peers.

Objective & Launch

9 minutes

After previewing the day's learning objective, I launch directly into practice problems. I display each task using Determining Rates From Graphs Launch. I will then ask my students to work with their groups to determine the answer.  We will discuss the students' responses to each task before moving on. As discrepancies arise in the answers that groups share with the class, I will ask groups to explain their answers for the class. We'll continue to discuss each task until there is a consensus about how to interpret the graph. My goal is to build my students confidence in reading information from graphs, and, using it in an explanation of a solution. 

Work Time- Graph Carousel

16 minutes

Before class, I have taped 8 different Carousel Activity Posters around the room for the Work Time Activity about interpreting rates from Graphs.

For a Carousel Activity, my students travel in their table groups of 3 or 4 from poster to poster and record their answers in their math journals. In this case their answers will be interpretations of the graph. I use a SmartBoard timer to keep the groups moving at a reasonable pace, but adjust the time up or down as needed. Once all the teams have visited each of the posters, students return to their tables for consensus building. Consensus building is a time to discuss each of the answers further, either because there was disagreement as they traveled, or, they have changed their minds about one or more answers based on their work during the activity. 

Solution Consensus

10 minutes

To bring the Carousel Activity to closure, I display each of the eight graphs on the SmartBoard and ask for student groups to volunteer their solutions, which I record. If discrepancies occur, I will once again ask students to justify their thinking. Once all answers have been recorded, I will reveal the answers and we will discuss the answers as needed. The need for discussion varies considerably from year to year. 

Wrap Up- Snow Ball Fight

5 minutes

Because I need individual feedback to determine if students are ready for the next lessons in this unit, for today's Wrap Up, I use a Learning Objective Self-Assessment.  The self-assessment includes a problem to solve independently, and a learning scale that students can mark to let me know privately where s/he stands with the content of the day's lesson.

Rather than just distributing these to students and asking them to respond, I add a little fun by asking students to wad the papers into a ball and have a fifteen-second Snowball Fight by throwing the papers at one another. Before we start, I explain to students that once the timer sounds at the end of the fight, they have five seconds to pick up a paper near them and respond.

I always keep several extra papers on hand as invariably, a few get lost during the barrage! These papers serve as today's Ticket out the Door. I will collect them as students leave the classroom.