standard_description: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
problem_activity: Warm-up
The purpose of this warm-up is to help students recall information about scatter plots, which will be useful when students expand their understanding in a later activity.
While students may notice and wonder many things about these images, the relationship between the number of people and the maximum noise level, interpreting the line of best fit, and a general understanding of a scatter plot are the important discussion points.
Through articulating things they notice and things they wonder about the scatter plot and the linear model, students have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Notice students who use correct terminology in their responses. In particular, the terms scatter plot, linear model, slope, and intercept are important to review during this warm-up.
Launch
Tell students their job is to think of at least one thing they notice and at least one thing they wonder. Display the image for all to see. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice with their partner, followed by a whole-class discussion.
Student Facing
What do you notice? What do you wonder?
\(y = 1.5x+22.7\)
[IMG]
Student Response
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Anticipated Misconceptions
The vertical intercept appears to be approximately 105 decibels, but the origin is not shown on the graph.
Activity Synthesis
Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information. If students do not use these terms in their responses, ensure they recall the vocabulary from grade 8 math:
scatter plot
linear model
slope
intercept


aligns: no