Alg2 Lesson 1.9 Average Rate of Change

Lesson 1.9: Average Rate of

Change

Obj: I can find the average rate of change.

EQ: How do I find the average rate of change and
use it to make conclusions?

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.

Word Cloud

How do you plan to contribute to the class today?

● Tasks checked off on Calendar paper.

● 6 or more completed WS attached to Calendar.

● Unit 1 Deltamath.

These should almost be completed:

Part 1: Introducing Average

Rate of Change

Karen’s Marathon Run

After marathons, runners often talk
about their overall speed. What was
Karen’s average rate of change or
average speed for the entire race?

Some runners like to track their pace in
minutes per mile. Use the information
from the graph to determine Karen’s
pace in minutes per mile.

Fill in the Blank

What was Karen’s average rate of change or average speed in miles per hour for the entire race?

Fill in the Blank

How many minutes is 6.55 hours?

Multiple Choice

Use the information from the graph to determine Karen’s pace in minutes per mile.

• 8 minutes per mile
• 12 minutes per mile
• 15 minutes per mile
• 10 minutes per mile

During a snowstorm, Tomas measured the height of the
snow, in inches, in his yard several times over a 12-hour
period. He made the following graph with his data set:

1. What was the height of the snow at 4 p.m.? How do you know?
2. What was the average rate of change between 6pm and midnight? What does this mean about the snow?
3. Over what two-hour interval on the graph was the height of the snow increasing at the fastest rate? Justify
your answer.
4. At about what time did the snow stop falling? How do you know?
5. Write a description of how the height of the snow in Tomas’s yard changes between noon and midnight.

Write in
your
journal

Hotspot

Click the point where the graph is at 4pm.

Multiple Choice

What was the height of the snow at 4 p.m.?

• 6 inches
• 3 inches
• 2 inches
• 4 inches

Multiple Choice

What was the average rate of change between 6pm and midnight?

• -1.000 in/hr

• -0.583 in/hr

• -0.251 in/hr

• -0.750 in/hr

Categorize

Options (3)

noon to 2pm

4pm to 6pm

6pm to midnight

Sort each time interval.

Snowing

Melting Snow

Constant Snow

Multiple Choice

What was the average rate of change of the height of the snow between 1pm and 6pm?

• 1.0 in/hr
• 0.4 in/hr
• 0.6 in/hr
• 0.8 in/hr

Multiple Choice

What was the average rate of change of the height of the snow between noon and
midnight?

• 0.042 in/hr
• 0.050 in/hr
• 0.025 in/hr
• 0.030 in/hr

Key Points

A function that is increasing over an interval has a positive average rate of
change over that interval.

A function that is decreasing over an interval has a negative average rate of
change over that interval.

The average rate of change over an interval can be interpreted as the slope
of the line through the endpoints of that interval.

Unlike the slope of a line, average rate of change is not an absolute quantity.

Part 2: Defining Average

Rate of Change

The graph shows the number of people who watched the Super Bowl on TV from
1990 to 2019. Your task is to create a headline for an online news article about the
data set shown in the graph using a specific interval and the rate of change over
that interval.

Intervals to Focus on:

●1990-1995

●1995-2000

●2000-2005

●2005-2010

●2010-2015

●2015-2020

How does the
choice of interval
affect the story told
about a scenario?

How can changing
the interval have
an impact on the
reader?

Multiple Choice

What was the average rate of change in Super Bowl viewership from 1990 to
2019?

• 1.52 million people

• 0.839 million people
• 2.178 million people

• 0.53 million people

Drag and Drop

Over what one-year interval did the viewership appear to have the greatest positive change? ​

Placeholder

with ​

Placeholder

more viewers.
Over what one-year interval did the viewership appear to have the greatest negative change? ​

Placeholder

with ​

Placeholder

less viewers.

Drag these tiles and drop them in the correct blank above

1995 to 1996

10 million

2017 to 2018

8 million

Drag and Drop

Over what five-year interval did the viewership appear to have the greatest positive change? ​

Placeholder

with ​

Placeholder

more viewers.
Over what five year interval did the viewership appear to have the greatest negative change? ​

Placeholder

with ​

Placeholder

less viewers.

Drag these tiles and drop them in the correct blank above

2005 to 2010

20 million

2000 to 2005

2 million

[a, b] a ≤ x ≤ b

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.

Part 3: Making Predictions with

Average Rate of Change

The table shows the federal minimum hourly wage in the
United States in dollars for several years from 1980
through 2009.

1. What was the average rate of change of the
federal minimum wage from 1980 to 1981?
If the minimum wage increased at that rate every
year from 1981 through 1990, what
would the minimum wage have been in 1990?
2. Use the average rate of change from 1991 to
1997 to estimate the minimum wage in 1996.
3. The minimum wage experienced a substantial
increase from 2007 to 2009. Suppose
that the average rate of change from 2007 to
2009 was used to determine the federal
minimum wage in 2025. What would you expect
the minimum wage to be in 2025?

In this Scenario…

The average rate of change provides the change in the dependent variable over

each unit of the independent variable over an interval. In this example, the

average rate of change from 1980 to 2000 tells us the change in dollars per hour

per year over that interval.

Multiple Choice

The minimum wage increased 25 cents per hour from 1980 to 1981. If the same
change applied from 1981 to 1982, what would the minimum wage have been in
1982? (The minimum wage in 1981 was $3.35).

• $3.50
• $3.25
• $3.75
• $3.60

Multiple Choice

The minimum wage increased 25 cents per hour from 1980 to 1981. If the same
change applied from 1981 to 1990, what would the minimum wage have been in
1990? (The minimum wage in 1981 was $3.35).

• $4.25

• $5.60
• $3.80

• $4.85

Multiple Choice

Use the average rate of change from 1991 to 1997 to estimate the minimum wage in 1996.

• $4.75
• $6.67

• $4.70

• $5.00

Multiple Choice

The actual minimum wage in 1996 was $4.75. How does this compare to your
solution ($5) from the previous question?

• Your solution was an overestimate by $0.25.

• Your solution was an underestimate by $0.25.

• Your solution was the same as the actual amount.

Multiple Choice

What is the average rate of change from 2007 through 2009?

• $0.70 increase per year

• $6.55 increase per year

• $3.28 increase per year

• $2.18 increase per year

• $0.08 increase per year

Multiple Choice

Using the average rate of change from 2007 through 2009 ($0.70 increase per year), predict the minimum wage in 2025.

• $7.25 per hour

• $15.86 per hour

• $18.45 per hour
• $19.23 per hour

Poll

Do you think that the federal minimum wage in 2025 will be $18.45 per hour?

• No

• Yes

Poll

Are you ready for the Performance Task over average rate of change?

• Yes, and I plan to work with a partner.

• Yes, and I plan to work alone.

• No, I still need more practice.

Open Ended

Share your thoughts on the topics from the lesson here and answer the essential question: How do I find the average rate of change and
use it to make conclusions?