few_shots: Example 1:
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:
{
  "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"
}

Example 2:
Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Standard options: 
A. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
B. Solve quadratic equations in one variable.


Your response:
{
  "explanation": "This task shows one quadratic equation with one variable, x.",
  "answer": "B"
}

Example 3:
Problem/activity:
Task
Suppose $A$ is an angle with vertex $P$, as pictured below:
[IMG]
Draw a circle with center $P$ and with  radius $r \gt 0$.  Explain why the circle
meets each ray of angle $A$ in a single point.  Label these points $Q$ and $R$ respectively.
Draw circles with centers $Q$ and $R$ respectively and radius $r$.  These circles meet at $P$ and a second point to be labelled $B$.
Show that ray $\overrightarrow{PB}$  bisects angle $P$.


Standard options: 
A. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
B. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.


Your response:
{
  "explanation": "This task asks students to draw a ray that bisects an angle. The act of drawing circles and rays may involve compass and straightedge or dynamic geometric software.",
  "answer": "A"
}

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

HS_0

im_task_000870

HS_1

im_task_001160

HS_2
options: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = �� ÷ 3, 6 × 6 = ?.

Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
problem_activity: Task
Your teacher was just awarded \$1,000 to spend on materials for your classroom.  She asked all 20 of her students in the class to help her decide how to spend the money.  Think about which supplies will benefit the class the most.
{"table": [{"_attributes": {"class": ["regular", "centered"]}, "tbody": [{"tr": [{"th": [{"_value": "Supplies"}, {"_value": "Cost"}]}, {"td": [{"_value": "A box of 20 markers"}, {"_value": "\\$5"}]}, {"td": [{"_value": "A box of 100 crayons"}, {"_value": "\\$8"}]}, {"td": [{"_value": "A box of 60 pencils"}, {"_value": "\\$5"}]}, {"td": [{"_value": "A box of 5,000 pieces of printer paper"}, {"_value": "\\$40"}]}, {"td": [{"_value": "A package of 10 pads of lined paper"}, {"_value": "\\$15"}]}, {"td": [{"_value": "A box of 50 pieces of construction paper"}, {"_value": "\\$32"}]}, {"th": [{"_value": "Books and maps"}, {}]}, {"td": [{"_value": "A set of 20 books about science"}, {"_value": "\\$250"}]}, {"td": [{"_value": "A set of books about the 50 states"}, {"_value": "\\$400"}]}, {"td": [{"_value": "A story book (there are 80 to choose from)"}, {"_value": "\\$8"}]}, {"td": [{"_value": "A map: there is one of your city, one for every state, one of the country, and one of the world to choose from"}, {"_value": "\\$45"}]}, {"th": [{"_value": "Puzzles and games"}, {}]}, {"td": [{"_value": "Puzzles (there are 30 to choose from)"}, {"_value": "\\$12"}]}, {"td": [{"_value": "Board games (there are 40 to choose from)"}, {"_value": "\\$15"}]}, {"td": [{"_value": "Interactive computer games (math and reading)"}, {"_value": "\\$75"}]}, {"th": [{"_value": "Special Items"}, {}]}, {"td": [{"_value": "A bean bag chair for the reading corner"}, {"_value": "\\$65"}]}, {"td": [{"_value": "A class pet"}, {"_value": "\\$150"}]}, {"td": [{"_value": "Three month's supply of food for a class pet"}, {"_value": "\\$55"}]}, {"td": [{"_value": "A field trip to the zoo"}, {"_value": "\\$350"}]}]}]}]}
Write down the different items and how many of each you would choose. Find the total for each category.
Supplies
Books and maps
Puzzles and games
Special items
Create a bar graph to represent how you would spend the money.  Scale the vertical axis by \$100.  Write all of the labels.
What was the total cost of all your choices?  Did you have any money left over?  If so, how much?
Compare your choices with a partner. How much more or less did you choose to spend on each category than your partner? How much more or less did you choose to spend in total than your partner?


correct_option_index: 0