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


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.

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


Concept/skill: 
Solve quadratic equations in one variable.

Answer: 
Yes. This task shows one quadratic equation with 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_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
problem_activity: Problem 1
Quiana measures the width of her doorway entrance using a measuring tape. She measures the width as 33 inches. She later finds a better tape measure that measures to the nearest half of an inch. After re-measuring, she determines that the actual measure of the doorway is 32 ½ inches.
a.   What is the amount of error from using the first measuring tape?
b.   What is the error as a percentage of the actual width?
Problem 2
Paul and Kimberly both estimate the weight of their dogs before bringing them to the vet. The table below shows each of their estimates along with the actual weights of the dogs from the vet’s office.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "width:60%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align:center"}}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Estimate (lbs.)"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Actual (lbs.)"}]}]}, {"td": [{"_value": "Paul's dog"}, {"_attributes": {"style": "text-align:center"}, "_value": "10"}, {"_attributes": {"style": "text-align:center"}, "_value": "11.5"}]}, {"td": [{"_value": "Kimberly's dog"}, {"_attributes": {"style": "text-align:center"}, "_value": "84"}, {"_attributes": {"style": "text-align:center"}, "_value": "82.5"}]}]}]}]}
Paul notices that both his and Kimberly’s estimates were only 1.5 pounds off from the actual weights. Paul says that means his estimate was as good as Kimberly’s estimate.
Do you agree with Paul? Find the percent error for each person’s guess of their dog’s weight, and use it in your answer.
Problem 3
In science class, Justine measured a rock sample and found it to be 15 grams. Her teacher told her that the scale is off and the actual weight is 0.3 grams more than her measurement.
What is the percent error? Give your answer to the nearest percent.


aligns: no