# "No Slope, or Gentle Slope"?

- Author:
- Arpit Kesharwani

## Drills

What do you notice? What do you wonder?

## Teacher Workshop Activity

Arrange students in groups of 2. Display the graph for all to see. Ask students to consider what the graph might represent.After brief quiet think time, select 1–2 students to share their ideas. (For example, something starts at 12 inches and grows 15 inches for every 5 months that pass.)Remind students that axes labels help us determine what quantities are represented and should always be included. Let them know that in this activity the graphs of three functions have been started, but the labels are missing and part of their work is to figure out what those labels are meant to be.Give students 3–5 minutes of quiet work time and then time to share responses with their partner. Encourage students to compare their explanations for the last three problems and resolve any differences. Follow with a whole-class discussion.

## Raduis, and Circumference Standards

The graphs of three functions are shown.

- Match one of these equations to each of the graphs.
- d=60t, where d is the distance in miles that you would travel in thours if you drove at 60 miles per hour.
- q=50−0.4d, where q is the number of quarters, and d is the number of dimes, in a pile of coins worth $12.50.
- A=πr2, where A is the area in square centimeters of a circle with radius r centimeters.

- Label each of the axes with the independent and dependent variables and the quantities they represent.
- For each function: What is the output when the input is 1? What does this tell you about the situation? Label the corresponding point on the graph.
- Find two more input-output pairs. What do they tell you about the situation? Label the corresponding points on the graph.

## Dude, are you ready for MORE?

"Are you ready for more?"A function inputs fractions ab between 0 and 1 where a and b have no common factors, and outputs the fraction 1b. For example, given the input 34the function outputs 14, and to the input 12 the function outputs 12. These two input-output pairs are shown on the graph.Plot at least 10 more points on the graph of this function. Are most points on the graph above or below a height of 0.3? Of height 0.01?

## Homework/Exit Ticket

- Kiran was running around the track. The graph shows the time, t, he took to run various distances, d. The table shows his time in seconds after every three meters.dt
- How long did it take Kiran to run 6 meters?
- How far had he gone after 6 seconds?
- Estimate when he had run 19.5 meters.
- Estimate how far he ran in 4 seconds.
- Is Kiran's time a function of the distance he has run? Explain how you know.

- Priya is running once around the track. The graph shows her time given how far she is from her starting point.
- What was her farthest distance from her starting point?
- Estimate how long it took her to run around the track.
- Estimate when she was 100 meters from her starting point.
- Estimate how far she was from the starting line after 60 seconds.
- Is Priya's time a function of her distance from her starting point? Explain how you know.