Alg2 Lesson 1.2: Linear Model Predictions

Lesson 1.2 Making Predictions

with Linear Models

Obj: I can make predictions with linear models.

EQ: How do I make a linear regression model?

Roles:
Facilitator:
Scribe
Resourcer
Includer

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.

• Communicates conflicts or questions to the teacher.

Poll

Which role will you be today?

• Facilitator

• Scribe

• Resourcer

• Includer

Part 1: Determining the Height of a Stack of Cups

Sheng works in a convenience
store and has to record the
inventory of coffee cups that are currently in stock. The store
shelves hold many stacks of cups, so she wants to find a more efficient way to determine the number of cups in the store than counting each cup in every stack. She wonders if she can find a
formula to determine the number of cups in a stack from the height of the stack. Is her method possible? Explain how you know.

Measure the height of 1 cup and 2 cups

Get a ruler and collect data of the height in cm of 1 cup and 2 cups for one of the cup sizes in the picture. Create a table of values to represent this. Be sure to include the cup size.

Multiple Choice

What does Sheng know and what does she want to figure out?

• She knows the height and wants to find the number of cups.

• She knows the number of cups and wants to find the height.

Categorize

Options (4)

Height in cm

Sheng knows this.

Number of Cups

Sheng wants to find this.

Based on what she is trying to determine, which set of values should be the independent variable and which set of values should be the dependent variable? Sort the unit and reasoning.

Independent Variable (x)

Dependent Variable (y)

Multiple Choice

What kind of model could be appropriate for this?

• Linear

• Exponential

• Quadratic

• None of these

In Your Journal...

• What assumptions can we make about this situation?

• Graph this and write an equation for this.

Let’s Look Back at the Original Task

What did it ask us to do?

Have we accomplished this task yet?
Why or why not?

Poll

Which of the following is your favorite drink?

• Coffee

• Juice

• Tea

• Milk

• Soda

Part 2: Determining the Equations of a Line Through More than Two Points

Each partner pair will find another pair that measured the same size cups.

• Compare both groups’ tables of values and equations from Part 1. Are they the same or are they different? If they are different, try to determine why.

• Measure the heights of a stack of 3 cups and a stack of 4 cups. Add that data to your tables and graphs.

Class Discussion

●

Does a linear function model still make sense for this relationship? Why or why not?

●

Does the linear equation you determined in Part 1 still model the relationship between the height of a stack of cups and the number of cups in the stack?

●

The relationship between the height of a stack of cups and the number of cups in a stack seems almost exactly linear. Can you think of another relationship between two quantities that might be close to linear, but not exactly linear?

Linear Regressions using Desmos

+

Table

Input values

Type y1~mx1+b

Use your group’s data to find the linear regression equation for the cups.

Summarizing the Task in your Journal

● Was the equation of your regression line the same or different than the equation you determined in Part 1?

● What is the value of the slope, m, and what does it mean in terms of the height of a stack and the number of cups in the stack?

● What is the value of b and what does it mean in terms of the height of a stack and the number of cups in the stack?

Class Discussion

●

Let’s look back at the original task. What did it ask us to do?

●

Have we accomplished the task yet? Why or why not?

●

What should Sheng do to determine a formula that models the relationship of interest?

●

Suppose that Sheng uses the same type of cup that you used to find her equation. If she discovers that the height of one stack of cups is 119 cm tall, how many cups should she expect to be in the stack? Show how you determine the answer.

Multiple Choice

The wind speed is 20mph. What is the equation of the regression line?

• y=1.291x-21.514

• y=21.514x-1.29

• y=2.361x-32.628

• y=32.628x-2.36

Categorize

Options (6)

Y-Intercept

(0, -21.514)

Slope

1.291

wind chill factor per air temperature

When the air temperature is 0°F at wind speed of 20mph

Identify each characteristic and how it relates to the context of the problem.

Constant Rate of Change

Dependent Variable

Multiple Choice

Use the equation of the regression line to estimate the wind chill factor for a 32°F day with a wind speed of 20mph. Show work in your journal.

• 17.243°F

• 23.179°F

• 19.798°F

• 3.207°F

• 22.316°F

Multiple Choice

The table show several ages and the corresponding target heart rates for moderate-intensity activity. What is the equation of the regression line?

• y = -0.703x+192.097

• y = -0.843x+162.095

• y = 162.095x-0.843

• y = 192.097x-0.703

Categorize

Options (6)

Y-Intercept

Slope

-0.843

162.095

bpm when someone is 0 years old.

beats per minute per year

Identify each characteristic and how it relates to the context of the problem.

Constant Rate of Change

Dependent Variable

Multiple Choice

Use the equation of the regression line to estimate the target pulse rate during moderate-intensity activity for a person who is 21 years old. Show work in your journal.

• 72 bpm

• 60 bpm

• 198 bpm

• 144 bpm

• 125 bpm

Word Cloud

What comes to mind about weather?

Part 3: Determining When Linear Regression is Appropriate

For each of the eight scenarios shown, identify weather a linear function would be an appropriate model for the data set. Explain your reasoning in your journal and share your reasoning to your table group.

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.

● Go to your calendar paper.

● Select a skill to work on independently or with a partner.

● Work on Unit 1 Deltamath.

Self-Acquisition Time