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: 
Solve quadratic equations in one variable.

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


Answer: 
Yes. This task shows one quadratic equation with one variable, x.

Example 3:
Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

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: 
No. This task does not involve drawing lines that are tangent to circles. The only line that may be drawn is the ray between points P and B.

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_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
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
For the class party, Robin and Shawn each made a loaf of banana bread. Their loaf pans were exactly the same size. Robin sliced her banana bread into 6 equal slices. Shawn also sliced his into 6 equal slices. After the party, Robin had more slices of banana bread left to take home than Shawn did. What fraction of the whole loaf pan might each person take home?
Problem 2
a.   Choose each statement that is true.
i.
$$\frac{3}{4}$$
is greater than
$$\frac{5}{4}$$
.
ii.
$$\frac{5}{4}$$
is greater than
$$\frac{3}{4}$$
.
iii.
$$\frac{3}{4}>\frac{5}{4}.$$
iv.
$$\frac{3}{4}<\frac{5}{4}.$$
v.
$$\frac{5}{4}>\frac{3}{4}.$$
vi.
$$\frac{5}{4}<\frac{3}{4}.$$
vii.  None of these.
b.
$$\frac{3}{4}$$
and
$$\frac{5}{4}$$
are shown on the number line. Which is correct?
i.
[IMG]
ii.
[IMG]
iii. Neither of these.


aligns: no