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: 
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_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_pos_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: Narrative
The purpose of this activity is for students to learn stage 1 of the Jump the Line center. In this stage, students take turns making strategic choices about numbers to add or subtract to reach target numbers. Students choose 3 target numbers and mark them on the number line. Both players start at the beginning of the number line. They spin all 3 spinners and decide which of the moves they want to use on their turn. Students take turns spinning and moving, trying to land exactly on the target numbers. The first player to land on 2 target numbers wins.
Required Materials
Materials to Gather
Dry erase markers
Paper clips
Sheet protectors
Materials to Copy
Jump the Line Stage 1 Gameboard
Jump the Line Stage 1 Spinners
Launch
Groups of 2
Give each group a spinner, paper clip, dry erase marker and gameboard.
Display spinners and gameboard.
“You and your partner will choose 3 target numbers and mark them on your number line.”
“Then you will take turns spinning all 3 spinners. On your turn you can decide which spin to use. Your goal is to jump to one of the numbers you and your partner marked.”
“The first player to land exactly on 2 of the target numbers wins.”
Play a round with the class, if needed.
Activity
15 minutes: partner work time
Activity Synthesis
Display a gameboard with 3 target numbers. Spin the three spinners.
“This is my gameboard and my spins. Which spin would you use? Why?”


aligns: no