Lesson 10: Calculating Slope

Calculating Slope

5 min

Teacher Prep

Setup

Display the problems all at once. 1 minute of quiet think time per problem, followed by a whole-class discussion.

Narrative

This Math Talk focuses on operations with integers. It encourages students to think about positive and negative numbers to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students use two points to calculate the slope of a line with a negative slope.

Launch

Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:

Give students quiet think time and ask them to give a signal when they have an answer and a strategy.
Invite students to share their strategies and record and display their responses for all to see.
Use the questions in the activity synthesis to involve more students in the conversation before moving to the next problem.

Keep all previous problems and work displayed throughout the talk.

Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

Mentally find values for $a$ and $b$ that make each equation true.

$a+b=\text-2$
$a-b=\text-2$
$\dfrac{a}{b}=2$
$\dfrac{a}{b}=\text-2$

Sample Response

Sample responses: $a =3$ , $b = \text-5$ ; $a =\text-10$ , $b = 8$
Sample responses: $a =6$ , $b = 8$ ; $a =\text-11$ , $b = \text-9$
Sample responses: $a =4$ , $b = 2$ ; $a =\text-20$ , $b = \text-10$
Sample responses: $a =\text-8$ , $b = 4$ ; $a =100$ , $b = \text-50$

Activity Synthesis (Teacher Notes)

To involve more students in the conversation, consider asking:

“Who can restate $\underline{\hspace{.5in}}$ ’s reasoning in a different way?”
“Did anyone use the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to $\underline{\hspace{.5in}}$ ’s strategy?”
“Do you agree or disagree? Why?”
“What connections to previous problems do you see?”

MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, “First, I

\underline{\hspace{.5in}}

because . . . .” or “I noticed

\underline{\hspace{.5in}}

so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking, Representing

Standards

Building On

7.NS.A·Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
7.NS.A·Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

20 min

10 min

Knowledge Components

All skills for this lesson

No KCs tagged for this lesson

Calculating Slope

5 min

Teacher Prep

Setup

Display the problems all at once. 1 minute of quiet think time per problem, followed by a whole-class discussion.

Narrative

Launch

Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:

Give students quiet think time and ask them to give a signal when they have an answer and a strategy.
Invite students to share their strategies and record and display their responses for all to see.
Use the questions in the activity synthesis to involve more students in the conversation before moving to the next problem.

Keep all previous problems and work displayed throughout the talk.

Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

Mentally find values for $a$ and $b$ that make each equation true.

$a+b=\text-2$
$a-b=\text-2$
$\dfrac{a}{b}=2$
$\dfrac{a}{b}=\text-2$

Sample Response

Sample responses: $a =3$ , $b = \text-5$ ; $a =\text-10$ , $b = 8$
Sample responses: $a =6$ , $b = 8$ ; $a =\text-11$ , $b = \text-9$
Sample responses: $a =4$ , $b = 2$ ; $a =\text-20$ , $b = \text-10$
Sample responses: $a =\text-8$ , $b = 4$ ; $a =100$ , $b = \text-50$

Activity Synthesis (Teacher Notes)

To involve more students in the conversation, consider asking:

“Who can restate $\underline{\hspace{.5in}}$ ’s reasoning in a different way?”
“Did anyone use the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to $\underline{\hspace{.5in}}$ ’s strategy?”
“Do you agree or disagree? Why?”
“What connections to previous problems do you see?”

MLR8 Discussion Supports. Display sentence frames to support students when they explain their strategy. For example, “First, I

\underline{\hspace{.5in}}

because . . . .” or “I noticed

\underline{\hspace{.5in}}

so I . . . .” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking, Representing

Standards

Building On

7.NS.A·Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
7.NS.A·Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Calculating Slope

Warm-upMath Talk: Integer Operations5 minKCs

Setup

Narrative

Launch

Student Task

Sample Response

ActivityToward a More General Slope Formula20 minKCs

ActivityPayback Plan10 minKCs

Knowledge Components

Calculating Slope

Warm-upMath Talk: Integer Operations5 minKCs

Setup

Narrative

Launch

Student Task

Sample Response

ActivityToward a More General Slope Formula20 minKCs

ActivityPayback Plan10 minKCs

5 min

20 min

10 min

5 min

20 min

10 min