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.


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

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.


Thought: 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.


Thought: 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: 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.

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.
problem_activity: Problem 1
Look at the title and image of the Newsweek article,
More Than Half of Medical Advice on 'Dr. Oz' Lacks Proof or Contradicts Best Available Science: Study
.
According to this article, a research team looked at 80 pieces of medical advice from
The Dr. Oz Show
and found no evidence to support 43 of these recommendations.
a.   Do you agree or disagree with the claim in the headline based on this information? Why or why not?
b.   Determine whether the following fractions are greater or less than
$$\frac12$$
.
$$\frac{5}{12}$$
$$\frac35$$
Problem 2
a.   Ishmael says that he knows
$$\frac{5}{12}$$
is less than
$$\frac35$$
because
$$\frac{5}{12}$$
is less than
$$\frac12 $$
and
$$\frac35$$
is more than
$$\frac12$$
, so
$$\frac{5}{12}$$
must be less than
$$\frac35$$
. Explain why Ishmael’s reasoning is correct using words or pictures.
b.   Use Ishmael’s strategy to compare the following pairs of fractions. Record your answer with
$$\lt$$
,
$$\gt$$
, or
$$=$$
.
$${{4\over10}}$$
and
$${{5\over8}}$$
$${{7\over12}}$$
and
$${{4\over9}}$$
$${{1\over3}}$$
and
$${{4\over7}}$$
Problem 3
a.   Now Joslyn is comparing
$$\frac46$$
and
$$\frac58$$
. She says that she knows
$$\frac46$$
is more than
$$\frac58$$
because
$$\frac46$$
is
$$\frac16$$
more than
$$\frac12$$
and
$$\frac58$$
is
$$\frac18$$
more than
$$\frac12$$
and
$$\frac16$$
is more than
$$\frac18$$
. Explain why Jocelyn’s reasoning is correct using words or pictures.
b.   Use any strategy to compare the following pairs of fractions. Record your answer with
$$\lt$$
,
$$\gt$$
, or
$$=$$
.
$$\frac{5}{12}$$
and
$${{4\over10}}$$
$${{3\over5}}$$
and
$${{5\over9}}$$
$${{1\over3}}$$
and
$${{3\over7}}$$


correct_option_index: 0