standard_description: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want (5^(1/3))^(3) = 5(^(1/3))^(3) to hold, so (5^(1/3))^(3) must equal 5.
problem_activity: Activity
In this activity, students analyze data from samples of viewers for different TV shows. The data in this activity is used to begin the analysis as well as to get students thinking about the different shows the sample could represent. The purpose of the activity is to get students thinking about how measures of center from a sample might be used to make decisions about the population of a group.
Launch
Arrange students in groups of 3. Tell students that each person in the group should work on a different sample then share their results with their group. Give students 1 minute quiet work time and then 1 minute to share their work with the group followed by a whole-class discussion.
Representation: Internalize Comprehension.
Activate or supply background knowledge of calculating measures of center. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Speaking, Representing: MLR8 Discussion Supports.
Use this routine to support small-group discussion. Display the following sentence frames for students to respond to their group members’ explanations: “I agree because . . .” or “I disagree because . . . ." If necessary, revoice student ideas to demonstrate mathematical language use by restating a statement as a question in order to clarify, apply appropriate language, and involve more students.
Design Principle(s): Support sense-making
Student Facing
Here are the ages (in years) of a random sample of 10 viewers for 3 different television shows. The shows are titled, “Science Experiments YOU Can Do,” “Learning to Read,” and “Trivia the Game Show.”
sample 1
6
6
5
4
8
5
7
8
6
6
sample 2
15
14
12
13
12
10
12
11
10
8
sample 3
43
60
50
36
58
50
73
59
69
51
Calculate the mean for
one
of the samples. Make sure each person in your group works with a different sample. Record the answers for all three samples.
Which show do you think each sample represents? Explain your reasoning
.
Student Response
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Activity Synthesis
Select students to share how they determined which shows matched with which data set. The purpose of the discussion is for students to notice that the shows are meant to appeal to different age groups.


aligns: no