few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


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

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


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).

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

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 $P$.


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

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, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
problem_activity: Problem 1
Randomly select a digit 0–9 (by using a ten-sided die, a spinner, or a random number generator). Whatever number it lands on, enter the digit in one of the eight spots below. After eight turns, the board becomes an addition problem with two 4-digit numbers to add together. The goal is to place the numbers in strategic places to get the highest sum without going over 10,000.
[IMG]
Problem 2
Estimate. Then solve.
a.
$$\begin{align} 207,426 \\ {+ \ 128,744}& \\ \hline \end{align}$$
b.   252, 393 =
$$\square$$
− 747,607
c.
$$k$$
= 94,989 + 619,732 + 4,506
Problem 3
Tom Brady has 66,159 career passing yards. Peyton Manning, the all-time leading quarterback with the most career passing yards, has 5,781 more passing yards than Tom Brady does. How many passing yards does Peyton Manning have?


aligns: no