Alg1 Lesson 1.12 Geometric Approach to Point-Slope

Lesson 1.12: A Geometric

Approach to Point-Slope Formula

Obj: 2A, 3C, 6A, 9A, 12A, 12B, 2C, 2B, 3B: I can
formulate linear equations.

EQ: How do I write a linear equation given the slope
and a point?

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

Write a word or phrase on how you plan to contribute today.

● Go to your calendar paper.

● Select a skill to work on.

● Work on Deltamath.

When waiting for other groups to be ready…

Part 1: Slope Triangle

Find (x, y) in Figure 1 and Δx, y, and Δy in Figure 2

Multiple Choice

What is (x, y) in figure 1?

• (3, -2)

• (6, 2)

• (3, 6)

• (3, 2)

Drag and Drop

Δy is ​

Placeholder

, Δx is ​

Placeholder

, and the y-int is ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

6

8

(0, 1)

3

4

(0, 2)

Part 2: Geometry &
Arithmetic of Slope

Pass it On Activity Example

Now you try this using a different
starting point than (1, 2).

Write the name of the person
completing the step
next to each step. Pass it on when
the step is completed. Show the
teacher your completed papers
when done.

Word Cloud

What did you like about the "Pass it On" activity?

Finding Triangle Height Δy (Hint: multiply Δx and m)

Labelling

Label the correct Δy for each. (Hint: multiply Δx and m)

Drag labels to their correct position on the image

3

4

-3

4

-12

5.2

Part 3: Using Crickets as a

Thermometer

The Cricket as a Thermometer

In late 1897, Amos Dolbear published an article called
“The Cricket as a Thermometer.” He had determined that the outside temperature (in Fahrenheit) shared a linear relationship with the number of times the snowy tree cricket would chirp per minute. If you count the number of cricket chirps per minute (while sitting inside your warm house), then you can find the temperature outside. In his research, Dolbear concluded that for every extra cricket chirp per minute, the temperature was 1/4°F higher. Furthermore, he found that when the number of cricket chirps per minute was 120, the temperature outside was 70°F.

Questions & Answers

Match the input and output values.
Input: x, domain, independent, what we know, cricket chirps per minute
Output: y, range, dependent, what we want to know, temperature in
Fahrenheit
What is the slope? ¼
What does the slope represent? 1/4°F increase per cricket chirp
What is the y coordinate y-intercept? 40°F
What does the y-intercept represent? The temperature when there are 0
cricket chirps per minute.
What is the linear equation to represent this where F=temperature and
C=Chirps? F = 1/4C + 40

Categorize

Options (10)

Domain

x

independent

what we know

cricket chirps per minute

y

range

dependent

what we want to know

temperature in Fahrenheit

Match the input and output values.

Input

Output

Multiple Choice

What is the slope?

• 1/4

• 4

• 120

• 70

• 30

Multiple Choice

What does the slope represent?

• The slope represents the temperature decrease per cricket chirp.
• The slope represents the humidity increase per cricket chirp.
• The slope represents the number of crickets per degree.
• The slope represents the temperature increase per cricket chirp.

Drag and Drop

What is the y coordinate y-intercept? ​

Placeholder

What does the y-intercept represent? ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

40°F

The temperature when there are 0 cricket chirps

120°F

70°F

60°F

The cricket chirps when it is snowing

Multiple Choice

What is the linear equation to represent this where F=temperature and
C=Chirps?

• F = 1/4C + 40

• F = 1/4C + 60

• F = 4C - 40

• F = 4C + 60

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 4: Summary & Practice

Steps for Writing a Linear Equation Given the Slope and a Point

Complete Handout 1.12.C with a Partner

Practice writing the point-slope form of a line.

Point-Slope Formula: y - y₁ = m(x − x₁)

Open Ended

Upload pics of your journal for this lesson. Also write something here about your experience with insects.