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:
Thought: 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: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
problem_activity: Task
Some of the problems below can be solved by multiplying $\frac18\times\frac25$, while others need a different operation.  Select the ones that can be solved by multiplying these two numbers.  For the remaining, tell what operation is appropriate.  In all cases, solve the problem (if possible) and include appropriate units in the answer.
Two-fifths of the students in Anya’s fifth grade class are girls.  One-eighth of the girls wear glasses.  What fraction of Anya’s class consists of girls who wear glasses?
A farm is in the shape of a rectangle $\frac18$ of a mile long and $\frac25$ of a mile wide.  What is the area of the farm?
There is $\frac25$ of a pizza left.  If Jamie eats another  $\frac18$ of the original whole pizza, what fraction of the original pizza is left over?
In Sam’s fifth grade class, $\frac18$ of the students are boys.  Of those boys, $\frac25$ have red hair.  What fraction of the class is red-haired boys?
Only $\frac{1}{20}$ of the guests at the party wore both red and green.  If $\frac18$ of the guests wore red, what fraction of the guests who wore red also wore green?
Alex was planting a garden. He planted $\frac25$ of the garden with potatoes and $\frac18$ of the garden with lettuce. What fraction of the garden is planted with potatoes or lettuce?
At the start of the trip, the gas tank on the car was $\frac25$ full.  If the trip used $\frac18$ of the remaining gas, what fraction of a tank of gas is left at the end of the trip?
On Monday, $\frac18$ of the students in Mr. Brown’s class were absent from school.  The nurse told Mr. Brown that $\frac25$ of those students who were absent had the flu.  What fraction of the absent students had the flu?
Of the children at Molly’s daycare, $\frac18$ are boys and $\frac25$ of the boys are under 1 year old.  How many boys at the daycare are under one year old?
The track at school is $\frac25$ of a mile long.  If Jason has run $\frac18$ of the way around the track, what fraction of a mile has he run?


correct_option_index: 0

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