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 following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_000972_neg_0

6
standard_description: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + Ö3i)^(3) = 8 because (-1 + Ö3i) has modulus 2 and argument 120°.
problem_activity: Warm-up
In this activity, students practice determining the measurement of unknown angles using their relationship to angles with known angle measure and what students already know about the measurement of right angles and straight angles. After they have worked on the activity and shared their solutions, they are introduced to the vocabulary terms complementary and supplementary. Complementary describes angles whose measures sum to 90 degrees and supplementary describes angles whose measures sum to 180 degrees.
Some students may wish to use protractors, either to double check work or to investigate the different angle measures. This is an appropriate use of technology (MP5), but ask these students what other methods they could use instead.
Launch
Provide access to geometry toolkits.
Student Facing
Find the measure of angle
\(JGH\)
. Explain or show your reasoning.
[IMG]
Find and label a second
\(30^\circ\)
angle in the diagram. Find and label an angle congruent to angle
\(JGH\)
.
Angle
\(BAC\)
is a right angle. Find the measure of angle
\(CAD\)
.
[IMG]
​​​​​
Student Response
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Anticipated Misconceptions
If needed, remind students that right angles have a measure of
\(90^\circ\)
and straight angles have a measure of
\(180^\circ\)
.
Activity Synthesis
The goal of this discussion is to introduce students to the terms complementary and supplementary for describing relationships between pairs of angles. Display the images for all to see and select students to briefly share their response to each question, recording any calculations used.
Explain to students that the term
complementary
describes a pair of angles whose measures sum to 90 degrees, and the term
supplementary
describes a pair of angles whose measures sum to 180 degrees. This is true even for pairs of angles that are not adjacent. Conclude the discussion by inviting students to identify pairs of angles that are complementary (
\(CAD\)
and
\(DAB\)
), supplementary (
\(FGJ\)
and
\(JGH\)
,
\(JGH\)
and
\(HGI\)
,
\(HGI\)
and
\(IGF\)
, or
\(IGF\)
and
\(FGJ\)
), or vertical (
\(FGJ\)
and
\(HGI\)
or
\(JGH\)
and
\(IGF\)
) from the activity.


aligns: no