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: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^(2) × 3^(–5) = 3^(–3) = 1/3^(3) = 1/27.
problem_activity: Task
Below are pictures of an equilateral triangle, a square, a regular hexagon, and a circle each having
the same perimeter:
[IMG]
Find the area of the equilateral triangle whose perimeter is $1$ unit.
Find the area of the square whose perimeter is $1$ unit.
Find the area of the regular hexagon whose perimeter is one unit.
Find the area of the circle whose perimeter is $1$ unit.
List the answers to (a), (b), (c) and (d) in increasing size.  How do you think the area of a regular octagon with perimeter $1$ unit would compare to the
triangle, square, hexagon, and circle?


aligns: no