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: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
problem_activity: Warm-up
The purpose of this warm-up is for students to reason about expressions with negative exponents on a number line. Students explore a common misunderstanding about negative exponents that is helpful to address before scientific notation is used to describe very small numbers.
For students’ reference, consider displaying a number line from a previous lesson that shows powers of 10 on a number line.
Launch
Give students 2 minutes of quiet work time, followed by a whole-class discussion.
Student Facing
Kiran drew this number line.
[IMG]
Andre said, “That doesn’t look right to me.”
Explain why Kiran is correct or explain how he can fix the number line.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
The important idea to highlight during the discussion is that the larger the size (or absolute value) of a negative exponent, the closer the value of the expression is to zero. This is because the negative exponent indicates the number of factors that are
\(\frac{1}{10}\)
. For example,
\(10^{\text-5}\)
represents 5 factors that are
\(\frac{1}{10}\)
and
\(10^{\text-6}\)
represents 6 factors that are
\(\frac{1}{10}\)
, so
\(10^{\text-6}\)
is 10 times smaller than
\(10^{\text-5}\)
.
Ask one or more students to explain whether they think the number line is correct and ask for their reasoning. Record and display their reasoning for all to see, preferably on the number line. If possible, show at least two correct ways the number line can be fixed.


aligns: no