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: 
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.

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: 
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, 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_pos_0

HS_2
standard_description: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
In the second round of analysis and design, students use their knowledge of operations and expressions to complete a Which One Doesn’t Belong set with two missing items. Students first study the attributes of the given items. They articulate why the items all belong to a set and why each one has a reason not to belong. Next, they propose a new item that shares a feature with others in the set but also has a unique feature that excludes it from the set.
Launch
Groups of 2
5 minutes: independent work time
Activity
“Work with your partner to make sure each new item added to the set has a reason to belong and not to belong.”
5 minutes: partner work time
Student Facing
Here is an incomplete Which One Doesn’t Belong set. It has two missing items.
[IMG]
Find at least one reason that the first two items, A and B, belong in the set.
Add two items to complete the set. Make sure there is at least one reason that each new item belongs and at least one reason it doesn’t belong.
C and D both belong because . . .
C doesn't belong because . . .
D doesn't belong because . . .
After you’ve completed the set, check items A and B. Does each one still have a reason not to belong? If not, adjust your new items so that A and B are each still unique in some way.
Student Response
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Activity Synthesis
Invite students to share their analyses and new items.
“Why do both A and B belong to the set?”
“What were some features of the expressions that you looked at or experimented with to complete your set?” (The kind of numbers used, how many numbers are used, the order of the numbers, the symbols, the value of the expression.)
If no students considered the value of the expression, ask them about it.
“After adding C and D, did A and B still have a reason not to belong in your set? Did you have to revise your items?”


aligns: yes