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: 
Construct a tangent line from a point outside a given circle to the circle.

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: 
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, 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_neg_0

HS_2
standard_description: Count within 1000; skip-count by 5s, 10s, and 100s.
problem_activity: Narrative
The purpose of this activity is to count an organized arrangement of images and write a number to represent the quantity. The arrangement is designed to encourage kids to count by 10 as each row, except the last, has ten cats. Students may determine the number of tens and ones (10 tens 8 ones is 108) or they may skip count the groups and count on by ones (10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108).
MLR7 Compare and Connect.
Synthesis: After all strategies have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask: “How are the strategies similar? How are the strategies different? What connections can you make between the strategies?”
Advances: Representing, Conversing
Launch
Groups of 2
Activity
Read the task statement.
3 minutes: independent work time
“Explain how you counted to your partner. If you got different answers, work together to figure out how many cats there are.”
3 minutes: partner work time
Monitor for students who count by:
circling groups of cats and then skip counting or adding them
recognizing that first ten rows each have 10 cats
Student Facing
How many cats are there?
[IMG]
There are ____________ cats.
Show your thinking using drawings, numbers, or words.
Student Response
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Activity Synthesis
Display student work that shows grouping in different ways.
“How did they group the cats? How did it help them figure out how many there were?” (They circled 5 rows for 50 and another 5 rows, and knew that
\(50 + 50 = 100\)
. Then there are 8 more, which is 108.)


aligns: no