standard_description: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
problem_activity: Warm-up
In a previous lesson, students were exposed to the ideas of center and spread. Here, they begin connecting that idea informally to the word “typical” and a value that could be considered typical or characteristic of a data set by thinking about two good options and reasonings. They continue to interpret a dot plot in the context of a situation (MP2).
During the partner discussion, identify two students—one who agrees with Clare and another who agrees with Tyler—to share during the whole-class discussion (MP3).
Launch
Arrange students in groups of 2. Give students 2 minutes of quiet work time and a minute to share their responses with a partner. Follow with a whole-class discussion.
Student Facing
This dot plot shows the weights of backpacks, in kilograms, of 50 sixth-grade students at a school in New Zealand.
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The dot plot shows several dots at 0 kilograms. What could a value of 0 mean in this context?
Clare and Tyler studied the dot plot.
Clare said, “I think we can use 3 kilograms to describe a typical backpack weight of the group because it represents 20%—or the largest portion—of the data.”
Tyler disagreed and said, “I think 3 kilograms is too low to describe a typical weight. Half of the dots are for backpacks that are heavier than 3 kilograms, so I would use a larger value.”
Do you agree with either of them? Explain your reasoning.
Student Response
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Activity Synthesis
Ask students to share their response to the first question about data points. Record and display their responses for all to see. Ask the selected students—one who agrees with Clare and another who agrees with Tyler—to share their reasoning. Ask if anyone disagrees with both students, and if so, what value they would consider a better description of the center of the data.
Students should have a reasonable explanation for each argument they favor, but it is not necessary to confirm one way or another at this point. Tell students that we will look more closely at different ways to determine a value that is characteristic of a data set in upcoming activities.


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