Alg2 Lesson 1.8 Rate of Change

Lesson 1.8: Rate of Change

Obj: I can find the rate of change.

EQ: How do I determine what the rate of change
represents in a given context?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas, vocab,

and prior knowledge

● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

Poll

Talk it over with your team. How do you plan to help your team today?

• Redirect team to write in their journal, be on the correct web pages, and talk about the content.

• Work on Worksheets and explain it to them.

• Ask questions and encourage my team to ask questions.

• Share my journal notes from the slides with my team.

Part 1: Introducing Rate of

Change

Linear Slope is a Constant Rate of Change

The rate of change of a linear function can be
represented as the slope of its associated line.
The units are y unit per x unit.

Draw

Draw the other half of the dragon.

Sort the Cards in Slide 1 of the Desmos Activity

Sort them independently, then compare your matches with your group.
Consider these questions:

Examine the cards with scenarios that have a positive rate of change. In what
ways are they similar? In what ways are they different?

Examine the cards with scenarios that have a negative rate of change. In
what ways are they similar? In what ways are they different?

What is another example of a scenario that has a rate of change of zero over
an interval? What might its graph look like?

Part 2: Interpreting Rate of

Change from a Graph

Complete Desmos Slides 2 through 4

Drag and Drop

According to the scenario in slides 2-4 of the Desmos activity, what can you
conclude about the rate of change? There are ​

Placeholder

rates of change.

Drag these tiles and drop them in the correct blank above

multiple

constant

fluffy

Part 3: Comparing Rates of

Change

Complete Desmos Slides 5 through 8

​While completing the Desmos activity, answer the following:
1. What do you notice about the intervals A, B, D, and F?

2. What do you notice about intervals C and E?

3. During which interval(s) is Karen running at her fastest rate?

4. What is Karen’s fastest rate?

5. Suppose Karen ran at a constant pace for the entire marathon (26.2 mi) but ended at the same time as the original scenario (6.55 hours). What would have been her rate of change?

Drag and Drop

What do you notice about the intervals A, B, D, and F?

The rate of change in distance is ​

Placeholder

and Karen is ​

Placeholder

​ from her starting point.

Drag these tiles and drop them in the correct blank above

positive

moving farther away

negative

moving closer

zero

not moving

Drag and Drop

What do you notice about intervals C and E?

The rate of change in distance is ​

Placeholder

and Karen is ​

Placeholder

during those intervals.

Drag these tiles and drop them in the correct blank above

negative

moving closer

zero

not moving

positive

moving farther away

Multiple Select

During which interval(s) is Karen running at her fastest rate?

• A

• B

• D

• F

Fill in the Blank

What is Karen’s fastest rate in miles per hour?

Multiple Choice

Suppose Karen ran at a constant pace for the entire marathon (26.2 mi) but ended at the same time as the original scenario (6.55 hours). What would have been her rate of change?

• 3.5 mph

• 5.0 mph

• 4.0 mph

• 6.0 mph

Average Rate of Change

Using only the points (0, 0) and (6.55, 26.2), you are
finding the average rate of change of the interval.

Poll

Lessons 1.8 and 1.9 are directly related to your performance task, do you feel ready for it?

• Yes.

• No, I need more practice.

• Maybe after going over lesson 1.9.

● Go to your calendar paper.

● Select a skill to work on.

● Work on Deltamath.

After Finishing These Slides:

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the
wheel as a class and spend a minute or so
discussing our answers.

Open Ended

Answer the essential question: How do I determine what the rate of change
represents in a given context?