Lesson 18: Asking about Solving Systems

Asking about Solving Systems

10 min

Narrative

This Math Talk focuses on finding the slope of a line from a linear equation. It encourages students to think about how to rearrange equations to find slope and to rely on the structure of slope-intercept form to mentally solve problems. The strategy elicited here will be helpful later in the lesson when students determine the number of solutions for a system of equations.

To find the slope, students need to look for and make use of structure (MP7).

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 the slope of each linear equation.

$y = 4 + 2x$
$2y = 6 - 9x$
$9x - 3y = 12$
$\frac{1}{3}y + 5x = \frac{3}{5}$

Sample Response

2. Sample reasoning: The equation is in slope-intercept form in which the $y$ variable is isolated, so the coefficient of $x$ is the slope.
$\frac{-9}{2}$ . Sample reasoning: The equation $y = 3 - \frac{9}{2}x$ is equivalent to the given equation (after dividing each side by 2) and is in slope-intercept form, so the slope is the coefficient of $x$ .
3. Sample reasoning: I rearranged the equation to $3x - 4 = y$ and used the coefficient of $x$ as the slope.
-15. Sample reasoning: An equivalent equation is $y = \text{-}15x + \frac{9}{5}$ , so the slope is -15.

Synthesis

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

Standards

Addressing

A-CED.4·Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
A-CED.4·Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
A-CED.4·Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
A-CED.4·Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
A-CED.4·Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
A-CED.4·Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
HSA-CED.A.4·Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law $V = IR$ to highlight resistance $R$.

Asking about Solving Systems

Warm-upMath Talk: Find the Slope10 min

Narrative

Launch

Student Task

Sample Response

Synthesis

ActivityOne, Zero, Infinitely Many10 min

ActivityInformation Gap: Linear Systems20 min

10 min

10 min

20 min