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

shot_info: fl_problem_001097_pos_0

7
standard_description: Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
problem_activity: Problem 1
Expand each expression below as a product of two linear binomials and then multiply to write the product in standard form.
a.
$${(x-5)^2}$$
b.
$${(x+4)^2}$$
c.
$${(x-3)^2}$$
d.
$${(2x+1)^2}$$
e.
$${(3x-2)^2}$$
Describe any patterns you notice between the square of the linear binomial and the resulting quadratic trinomial.
Problem 2
Solve the quadratic equation and then sketch a graph of the parabola.
$${y=(x-4)^2}$$
Problem 3
What is the value of
$$c$$
in the equation below such that the quadratic equation is a perfect square trinomial?
$$y=x^2+12x+c$$


aligns: no