few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Your response, in json format:
{
  "explanation": "An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation. Solving this problem does not require use of the Pythagorean identity.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS
options: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Problem 1
Would you rather have
$${{4\over9}}$$
,
$${{2\over3}}$$
,
$${{5\over7}}$$
, or
$${{3\over4}}$$
of your favorite pie? Show or explain your reasoning.
Problem 2
Play the following game with a partner using a set of
Fraction Cards
. The goal is to compare the two fractions appearing on each card, determining if they are equivalent and, if not, which is larger. The rules for the game are as follows:
Deal out the cards evenly so that each player has half of the deck. Each player should place their stack face down in front of them.
Each player turns up a card at the same time.
The player with the greater fraction takes both cards and puts them on the bottom of their stack of cards. Students can use any method to compare them. If they disagree, they should discuss until reaching a consensus, drawing a model if necessary.
If the fractions are equivalent, then each player deals three cards facedown and turns the fourth one face up to compare. The player with the larger second fraction takes all of the cards that have been dealt out. If the fractions are again equivalent, then another three are dealt facedown and the fourth face up to be compared. (This can continue as long as it needs to.)
The game is over when one player has all of the cards.


correct_option_index: 0

1