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
$$-\frac{1}{4}$$


Standard options: 
A. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
B. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
C. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


Your response, in json format:
{
  "explanation": "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).",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001097

7
options: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
problem_activity: Problem 1
Jessica gets her favorite shade of purple paint by mixing 2 cups of blue paint with 3 cups of red paint. How many cups of blue and red paint does Jessica need to make 20 cups of her favorite purple paint?
Complete the table of equivalent ratios below to answer the question.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:50%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Blue paint (cups)"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Red paint (cups)"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Purple paint (cups)"}]}]}, {"td": [{}, {}, {}]}, {"td": [{}, {}, {}]}, {"td": [{}, {}, {}]}, {"td": [{}, {}, {}]}]}]}]}
Problem 2
Michaela and Lucas both ran for class treasurer at their middle school. The ratio of votes for Michaela to votes for Lucas was 3:1.
Determine if each statement below is true or false.
a.    For every 5 votes Lucas got, Michaela got 10 votes.
b.   Michaela got 3 out of every 4 votes.
c.   Lucas got 1 out of every 3 votes.
d.   Lucas got
$$\frac{1}{4}$$
of all the votes.
e.   Out of 32 votes, Michaela got 24.


correct_option_index: 2