## Reflection: Perseverance Graphs ----> Tables ----> Rules - Section 2: Investigation

My students definitely struggled to find a rate of change that was both negative and not a whole number.  As I wrote about in the lesson plan, we looked at changes over set periods of time that were easy to find on the graph. For example, we drew a step to show that over 40 days, 10 gallons of water was consumed.  Students did NOT struggle with the idea that the amount of water was changing at a constant rate.  This worked in our favor!  Once we drew in the step and asked the question, "If they drank 10 gallons over 40 days, how can we find how much they drank in 1 day?" students were able to figure out that they needed to divide in order to determine the rate of consumption.

Students also struggled to write an equation to the second problem. I think this was due to the negative rate of change. Once we determined that they drank .25 gallons of water a day, I kept asking them questions like, "Well how would you figure out how much water was left after 5 days?" After performing some calculations together I would ask for a few more days. For example, "How much water is left after 10 days?, 20 days?" each time queuing students to calculate, rather than refer to their graphs.  Finally, I asked, "So how much water would be left after "x" days?"  From there, students were quickly able to figure out the equation.

Once we had the equation we talked a lot about where things show up in the graph. We compared how the equation and graph in this problem were different than the cafeteria table problem that we worked on first.

Perseverance: Writing an equation for a negative rate of change

# Graphs ----> Tables ----> Rules

Unit 2: Multiple Representations: Situations, Tables, Graphs, and Equations
Lesson 6 of 17

## Big Idea: How can we write rules to represent graphs? Students practice moving from graphs to tables and, ultimately, to rules.

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60 minutes

### Amanda Hathaway

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