standard_description: Know and apply the Binomial Theorem for the expansion of (x + y)^(n )in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.)
problem_activity: Warm-up
The purpose of this warm-up is to elicit the idea that calculating the
standard deviation
is very similar to calculating the MAD, which will be useful when students explore standard deviation in a later activity. While students may notice and wonder many things about these dot plots, the similarities and differences between standard deviation and the MAD as measures of variability are the important discussion points.
Launch
Display the dot plots and statistics for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. 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?
mean: 10, MAD: 1.56, standard deviation: 2
[IMG]
mean: 10, MAD: 2.22, standard deviation: 2.58
[IMG]
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mean: 10, MAD: 2.68, standard deviation: 2.92
[IMG]
mean: 10, MAD: 1.12, standard deviation: 1.61
[IMG]
mean: 10, MAD: 2.06, standard deviation: 2.34
[IMG]
mean: 10, MAD: 0, standard deviation: 0
[IMG]
Student Response
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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 images. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information. If the concept of variability does not come up during the conversation, ask students to discuss this idea.


aligns: no