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: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
problem_activity: Narrative
The purpose of this activity is for students to compare a Put Together, Total Unknown story problem and a Put Together/Take Apart, Both Addends Unknown story problem with a similar context. This is the first time that students have worked with a Put Together/Take Apart, Both Addends Unknown story problem.
Representation: Access for Perception.
Synthesis: Create a visual display to represent each story. For Mai, draw 7 circles and ask, “how many should I color in yellow?” and “how many should I color in red?” (5 yellow and 2 red). For Lin, draw 8 unshaded circles, and ask, “do we know which colors to use for Lin’s apples?” (no, we do not know how many of each color she picked).
Supports accessibility for: Visual-Spatial Processing, Organization
Launch
Groups of 2
Read both stories.
“What do you notice? What do you wonder?” (There are 2 stories. They are both about picking apples. There are red apples and yellow apples in both. I wonder how many red apples Lin picked.)
Activity
Read the first story problem.
“What do you know about Mai’s apples in this story? What do you not know?” (We know that she picked red and yellow apples. We know that she picked 5 yellow apples and 2 red apples. We do not know how many apples she picked altogether.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Read the second story problem.
“What do you know about Lin’s apples in this story? What do you not know?” (We know that she picked 8 apples. We know that some of them were red and some of them were yellow. We don’t know how many red ones or how many yellow ones she picked.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Student Facing
Mai was picking apples at the orchard.
Mai picked 5 yellow apples and 2 red apples.
Lin picked 8 apples at the orchard.
Some of the apples were yellow.
The rest of the apples were red.
[IMG]
[IMG]
Activity Synthesis
“What is the same about these stories?” (They are both about picking apples. They both have red and yellow apples.)
“What is different about the stories?” (The first story is about Mai and the next story is about Lin. In the first story we knew how many yellow apples and how many red apples. In the second story we know that there are 8 apples altogether.)
“In the next activity, we will work on showing what happened in the second story.”


aligns: no