few_shots: 
Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Concept/skill: 
Recognize and represent proportional relationships between quantities.

Answer: 
No. Usually problems that teach recognizing and representing proportional relationships between quantities involve deciding whether two quantities are in a proportional relationship or identifying the constant of proportionality, and then representing proportional relationships by equations or explaining proportional relationship using coordinate graphs.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_000972_neg_0

6
standard_description: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
problem_activity: Warm-up
The purpose of this activity is to focus students' attention on the two parts of a complex number: the real part and the imaginary part. This will be useful in the Information Gap, when students will need to be specific about the information they want and to strategize about how to use it (MP1).
Launch
Display the following for all to see:
\((a+bi)-(\underline{\phantom{00}} + \underline{\phantom{00}}i) = \text?\)
Ask, "In order for the result of this subtraction to be a real number, what has to be true about the missing imaginary part of the complex number subtracted from
\(a+bi\)
?" (It has to match the imaginary part of the other expression so it will sum to 0, which means that
\(b\)
must go in the blank.) After quiet think time, invite students to share their thoughts with a partner. Then invite partners to share with the class.
Student Facing
Here are some complex numbers with an unknown difference:
\((10+4i)-(\underline{\phantom{00}} + \underline{\phantom{00}}i) = \text?\)
If the result of this subtraction is a real number, what could the second complex number be?
If the result of this subtraction is an imaginary number, what could the second complex number be?
Student Response
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Activity Synthesis
Ask students to share the expressions they made by filling in the blanks. Highlight what is common about the responses to each question (all responses to the first question have the same imaginary part, and all responses to the second question have the same real part).
Tell students that in the next activity they will continue to reason about the real and imaginary parts of complex numbers based on what they know about how the numbers are combined.


aligns: no