# A Graphing Story

### Using Piecewise Linear Functions

## Subject / Grade / Time Frame

9th Grade

One Block (1 hr 20 min)

## Objectives

1. Students will define appropriate quantities from a situation (a “graphing story”), choose and interpret the scale and the origin of the graph and graph the piecewise linear functions described.

2. Students will describe the relationship between physical measurements and their representation on a graph.## NYS Common Core Standards

**N-Q**

**1. **Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret

units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

**2. **Define appropriate quantities for the purpose of descriptive modeling.

**3. **Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

**A-CED**

**2. **Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales

## Content Covered

- Piecewise functions and the behavior of the domain in each interval
- Determine how to draw the graph using terms such as increasing, decreasing, and remains constant

## Materials

- Internet Access: Prezi, Video
- Student Work Packets
- Overhead Projector / SMARTBoard
- Pencils
- Graph Paper

## Activities

## Activity 1

**Directions:** Follow along in your packets as we work through the notes

Students should be permitted to share their answers aloud to the class, or participate in a Think-Pair-Share.

**Questions to Promote Thinking:**

- What is happening in the story when the graph is increasing/decreasing/staying the same?
- What does it mean for one part of the graph to be steeper than another? [The person is climbing or descending faster than in the other part.]
- Is it reasonable that a person moving up and down a vertical ladder could have produced this elevation versus time graph? [It is not reasonable because the person would be climbing up the later over several minutes. If the same graph had units in seconds then it would be reasonable.]
- Is it possible for someone walking on a hill to produce this elevation versus time graph AND return to her starting point at the 10-minute mark? If it is, describe what the hill might look like. [Yes. The hill could have a long path with a gentle slope that would zigzag back up to the top and then a shorter and slightly steeper path back down to the beginning position

## Activity 2

**Directions:** Use the grid provided in your packet to complete this activity.

You may need to replay parts of the video (0:39 - 1:08) three to seven times in order for students to observe the change in the domain and graph the results.

**Questions to Promote Thinking:**

- Who will share an ideas on describing the motion of the man.

(Some might speak in terms of speed, or distance he traveled over time, or change of elevation. All approaches are valid. Help participants shape their ideas with precise language.) - Is it possible to describe his motion in terms of elevation?
- How high do you think he was at the top of the stairs?
- How did you estimate that elevation?
- Were there intervals of time when his elevation wasn’t changing? Was he still moving?
- Did his elevation ever increase? When?

## Activity 3: Homework

**Directions:**Students will create a piecewise function on the paper provided. They will trade their function with a classmate before the end of class. Students will then write the "graphing story" depicted by the function they received.

## Assessments

Observing the graphs drawn by the students will offer a formative assessment. Drawing a function that resembles what the graph should look like will provide the necessary information to move on with the lesson. Failure to complete the graph successfully will require additional explanation and exploration of piecewise functions.