standard_description: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
problem_activity: Warm-up
The purpose of this algebra talk is to elicit strategies and understandings students have for evaluating an expression for a given value of its variable. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to evaluate expressions.
Launch
Give students a minute to see if they recall that
\(x^2\)
means
\(x \boldcdot x\)
(which they learned about in an earlier unit in this course), but if necessary, remind them what this notation means.
Display one problem at a time. Give students 30 seconds of quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.
Representation: Internalize Comprehension.
To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory; Organization
Student Facing
If
\(x\)
is 6, what is:
\(x + 4\)
\(7 - x\)
\(x^2\)
\(\frac13 x\)
Student Response
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Activity Synthesis
Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:
“Who can restate ___’s reasoning in a different way?”
“Did anyone have the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to _____’s strategy?”
“Do you agree or disagree? Why?”
Speaking: 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 what they will say with a partner before they share with the whole class.
Design Principle(s): Optimize output (for explanation)


aligns: no