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: 
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_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
problem_activity: Task
Hand span is a measure of distance from the tip of the thumb to the tip of the little finger with the hand fully extended.
Each student places his or her dominant hand on the edge of a piece of paper with the hand fully extended.
The student should make a mark at the tip of the thumb and the tip of the little finger. The distance between marks is the length of the hand span.
The student should measure his or her hand span with a centimeter ruler and round the measurement to the nearest whole centimeter.
Each student should record his or her measurement on a piece of paper.
The teacher can ask each student for his or her measurement and record the data using a line plot with a horizontal scale marked off in whole centimeters. Alternatively, the teacher can set up the line plot and ask each student to come record his or her own hand span, showing the students how by recording the teacher's hand span.
Students should comment about patterns they observe the line plot and write or discuss the answers to these two questions:
What are the largest and smallest spans?  What is the difference between the largest and smallest spans?
Use words to describe the shape of the data set.  Does it appear taller in the center like a mountain?  Are there peaks in more than one place?  Is the shape of the data flat like a table top?  Are there gaps?  Are some hand spans much bigger or smaller than the others?


aligns: yes