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: Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
problem_activity: Narrative
The purpose of this activity is for students to use their knowledge of the number sequence to find the number that matches clues with one more and one less. Numbers 1–20 are displayed around the room. The numbers may be displayed in order, or the sequence of numbers can be mixed up for more of a challenge. The cards with number clues are included as a blackline master; one example is included in the student-facing task statement. Consider developing a signal, such as ringing a bell, so that students know when to move around the classroom. In the activity synthesis, students consider why there can be different clues that match a given number.
Engagement: Internalize Self-Regulation.
Provide students an opportunity to self-assess and reflect on the number clue and if that number clue matches the number they will stand by. For example, students can choral count together to check that the number 9 is 1 less than 10.
Supports accessibility for: Memory, Conceptual Processing
Required Materials
Materials to Copy
Number Clues
Required Preparation
Each group of 2 needs one card from the blackline master.
Display large numbers 1 to 20 around the room. The numbers may be displayed in order, or the sequence of numbers can be mixed up for more of a challenge.
Launch
Groups of 2
Display number cards 0–20 around the room, in order or mixed up.
Give each group of students a card.
“On your card there are some clues. Each clue says ‘1 more than _____’ or ‘1 less than _____.’”
“Look at your first clue. Decide with your partner which number matches the clue. Then look around the room and find that number. When I give the signal, walk over to that number.”
Activity
2 minutes: partner work time
“Discuss with the other people at your number. Did you have the same clue? Are you all at the correct number? How do you know?”
2 minutes: small-group work time
Repeat the steps with the rest of the clues.
During the final round, monitor for a group that notices there are 2 different clues that match the number and discuss why they both match.
Student Response
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Activity Synthesis
Invite previously identified students to share what they noticed during the last round of number clues.
“‘1 more than 15’ and ‘1 less than 17’ are both clues to 16.”
“What are two different clues that could match the number 12?”


aligns: no