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: 
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Answer: 
Yes. This task asks students to draw a ray that bisects an angle. The act of drawing circles and rays may involve compass and straightedge or dynamic geometric software.

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_pos_0

HS_2
standard_description: Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), 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: Narrative
The purpose of this activity is for students to learn stage 2 of the Check It Off center. Students take turns picking two number cards that are multiples of 10 (0–90) and choose whether to make an addition or subtraction expression. Students check off the value of the sum or difference (0–90) and then write the addition or subtraction expression on the recording sheet.
Required Materials
Materials to Gather
Connecting cubes in towers of 10 and singles
Materials to Copy
Number Cards, Multiples of 10 (0-90)
Check It Off Stage 3 Recording Sheet
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2
Give each group a set of cards, two recording sheets, and access to connecting cubes in towers of 10.
“We are going to learn a new way to do the Check It Off center. It is called Check It Off, Add or Subtract Tens.”
“Choose two cards and decide whether you want to add or subtract. After you find the sum or difference, check it off on the recording sheet and write the expression. Take turns with your partner. At the end of the game the partner who checks off the most numbers wins.”
Activity
10 minutes: partner work time
Activity Synthesis
Display a recording sheet with 90 checked off and 10 not checked off.
Display cards 40 and 50.
“Should we add or subtract these numbers? Why?” (We should subtract because
\(50 - 40 =10\)
and we haven’t checked off 10 yet, but
\(40 + 50 = 90\)
and 90 is already checked off.)


aligns: yes