standard_description: Verify experimentally the properties of dilations given by a center and a scale factor:
- A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
- The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
problem_activity: Warm-up
The mathematical purpose of this activity is for students to compare different distributions using shape, measures of center, and measures of variability. This warm-up prompts students to compare four distributions representing recent bowling scores for potential teammates. It gives students a reason to use language precisely (MP6) and gives you the opportunity to hear how they use terminology and talk about characteristics of the images in comparison to one another.
Launch
Arrange students in groups of 2–4.
Student Facing
Each histogram shows the bowling scores for the last 25 games played by each person. Choose 2 of these people to join your bowling team. Explain your reasoning.
Person A
mean: 118.96
median: 111
standard deviation:​ ​32.96
interquartile range: 44
[IMG]
Person B
mean: 131.08
median: 129
standard deviation: 8.64
interquartile range: 8
[IMG]
Person C
mean: 133.92
median: 145
standard deviation: 45.04
interquartile range: 74
[IMG]
Person D
mean: 116.56
median: 103
standard deviation: 56.22
interquartile range: 31.5
[IMG]
Student Response
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Activity Synthesis
Ask each group to share one bowler they would choose and their reasoning. If none of the groups select a certain player, ask why this player was not chosen or to give reasons why another team may want this player on their team. Since there is no single correct answer to the question of which one does not belong, attend to students’ explanations and ensure the reasons given are correct. During the discussion, ask students to explain how they used the statistics given as well as the histograms.


aligns: no