few_shots: 
Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

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_001097_pos_0

7
standard_description: Prove the Laws of Sines and Cosines and use them to solve problems.
problem_activity: Narrative
The purpose of this warm-up is to elicit the idea that there are different ways to calculate a product, using the standard algorithm, which will be useful when students find products of a 3-digit number and a 2-digit number in a way that makes sense to them.
Launch
Groups of 2
Display the image.
“What do you notice? What do you wonder?”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
Student Facing
What do you notice? What do you wonder?
[IMG]
[IMG]
Student Response
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Activity Synthesis
“Why do you think the results of the two calculations are the same?” (The factors are the same, just in a different order. The order of the factors does not change the result of multiplication.)
"Which way would you prefer to find the value of
\(417 \times 28\)
?" (I like the one with two partial products as there is less adding up to do.)
"Today you will get to choose how to find products of a 3-digit number and a 2-digit number.


aligns: no