few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


Answer: 
Yes. 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.

Example 2:
Concept/skill: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

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


Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

Example 3:
Concept/skill: 
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.

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 $P$.


Answer: 
Yes. 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.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: 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.)
problem_activity: Problem 1
Evaluate the following numerical expressions.
a.
$${-2(5+(3)(-2)+4)}$$
b.
$${-2((5+3)(-2+4))}$$
c.
$${-2(5+3(-2+4))}$$
d.   Can the parentheses in any of these expressions be removed without changing the value of the expression?
Problem 2
An expression is shown below with three expressions that are
not
equivalent to it. Explain the error(s) that were made in writing each expression.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
a.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
$$\neq \frac{3(-4)}{2(3)^2}$$
b.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
$$\neq \frac{6-3(-4)}{(6)^2}$$
c.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
$$\neq \frac{6-12}{(2+4)^2}$$
d.   Evaluate the expression.
Problem 3
Evaluate:
$${\frac{1}{2}(-3-1)^2-\left ( 10 \div \frac{5}{6} \right )}$$


aligns: yes