few_shots: 
Example 1:
Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

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


Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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: 
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, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: fl_problem_001894_neg_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?
problem_activity: Task
Arianna has been saving her chore money all summer. Her mother has allowed her to
spend the money on school supplies of Arianna’s choosing. Here are some of her favorite
items and the price for each:
[IMG]
{"table": [{"tbody": [{"tr": [{"td": [{"_value": "Lunchbox"}, {"_value": "Art Supplies"}, {"_value": "Pencil Box"}, {"_value": "Mechanical Pencil"}]}, {"td": [{"_value": "\\$2 and 50\u00a2"}, {"_value": "75\u00a2"}, {"_value": "$1 and 25\u00a2"}, {"_value": "45\u00a2"}]}]}]}]}
Arianna has four dollars and twenty-five cents to spend.
Select two items she might choose to purchase. What is the total cost of these two items?
Select three items she might choose to purchase. What is the total cost of these three items? How much money will Arianna have left over if she buys these three items
How many pencil boxes can Arianna buy without going over the $4 and 25¢ she has saved?
Explain your thinking for part (c) in words.


aligns: yes