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# Rate of Change

Lesson 9 of 19

## Objective: SWBAT determine the rate of change between two variables by examining tables of values.

## Big Idea: Students will develop their understanding of rate of change by exploring real world contexts.

*40 minutes*

#### Open

*3 min*

In this opening activity we are asking students to reason quantitatively (MP2) about the meaning of a car traveling at 60 miles per hour. Have students work on writing down an explanation by themselves at first and then share with a partner (Think-Pair-Share). When students share out, guide the conversation towards an understanding that "60 miles per hour" is a comparison of miles and hours (rise and run). This in turn is also connected to the concept of slope.

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#### Investigation

*20 min*

In this investigation, students will be working in pairs to determine the rate of change between pairs of variables set into a context. Students will need to examine the structure of each table to determine the rate of change (MP7). The context of the problem will help students understand and visualize rate of change in a way that may be more familiar to them (not so abstract). For example, students will be investigating scenarios involving "dollars per hour", or "meters per second."

I will structure this investigation as follows. First I will print off 2 copies of the slides in the accompanying powerpoint rate_of_change_day1_launch.pptx (1 on each page). I hang the 12 slides around the room (there will be two of each slide). I then number each slide 1-1, 1-2, 1-3, 1-4, 1-5 and 1-6. For the other identical slides I label them 2-1, 2-2, 2-3, 2-4, 2-5, and 2-6. I make index cards with the same numbering system on them. For this activity, I will allow students to choose their own partner. Once they choose a partner they come to see me and get an index card. This tells the pair of students which slide to start at. I give students about 3-4 minutes per slide to answer the questions in the rate_of_change_day 1_graphic organizer. Students move to the next slide when given the signal.

**Instructional Note**: If you want students to travel in groups of 3-4 then you would only have to print one copy of each slide and they could be more spaced out around the room.

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#### Debrief

*12 min*

For this portion of the lesson, I project each slide on the screen at the front of the room. Two pairs of students will come together to share their solution for the table that they started with. For example, the pair of students that had 1-1 and the pair that had 2-1 will come together (a group of 4) to share their solutions for the "sprinting" table. At this point the rest of the class can critique their reasoning and ask any clarifying questions (MP3). Each groups is given about 2 minutes to present their findings to the class and all students in the group need to share at least one of the solutions from their graphic organizer.

#### Resources

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#### Closure

*5 min*

This Ticket out the Door (rate_of_change_day1_closure.doc) will give students an opportunity to show that they can analyze a table independently. Students will find the rate of change for the table given and find a formula to generalize the values in the table. Students will also have an opportunity to explain (MP3) how they know their formula is correct based on the values in the table. This explanation will give you some insight into how the students are thinking about the connection between the rate of change, the table and the general formula.

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- LESSON 1: Patio Problem: Sequences and Functions
- LESSON 2: Arithmetic Sequences
- LESSON 3: Arithmetic Sequences Day 2 and Quiz
- LESSON 4: Arithmetic Sequences Day 3
- LESSON 5: Arithmetic Sequences: Growing Dots
- LESSON 6: Graphing Linear Functions Using Tables
- LESSON 7: Linear Functions
- LESSON 8: Discrete and Continuous Functions
- LESSON 9: Rate of Change
- LESSON 10: Slope as a Rate of Change - Day 1 of 2
- LESSON 11: Slope as a Rate of Change - Day 2 of 2
- LESSON 12: Graphing Linear Functions Using Intercepts
- LESSON 13: Graphing Linear Functions Using Slope Intercept Form
- LESSON 14: Comparing Graphs of Linear Functions Using Dynamic Algebra
- LESSON 15: Using Linear Functions for Modeling
- LESSON 16: Writing the Equation for a Linear Function (Day 1 of 2)
- LESSON 17: Writing the Equation of A Linear Function (Day 2 of 2)
- LESSON 18: Graph Linear Equations Practice
- LESSON 19: Solving Two Variable Inequalities Part 2