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: 
Solve quadratic equations in one variable.

Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Answer: 
Yes. This task shows one quadratic equation with 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_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
problem_activity: Narrative
The purpose of this activity is for students to add and subtract within 1,000. Students begin the activity by analyzing different expressions without adding or subtracting to determine which values they think would be the least and most challenging to find. In the synthesis, students share different reasons why sums and differences were chosen to be “least” and “most challenging” and different methods for finding the values of the expressions.
Although students may have many different reasons for why they think expressions are more or less challenging to find, the synthesis focuses on reasons based on composing or decomposing units. Discussing whether students will compose or decompose units will support students in fluently finding sums and differences within 100 in the next activity.
This activity uses
MLR8 Discussion Supports. Advances: speaking
Launch
Groups of 2
Activity
“Without finding the value of any of the sums or differences, read each expression and circle the two you think would be the most challenging to find the value of.”
3 minutes: independent work time
“Choose one of the expressions you circled and find the value. Then choose 2 other expressions and find their value.”
4 minutes: independent work time
“Share your work with your partner. Explain why you picked your expressions and the method you used to find the values.”
MLR8 Discussion Supports
Display sentence frames to support students when they explain their strategy:
“I picked _____ because . . . .“
“First, I _____ because . . . .”
“I noticed _____ so I . . . .”
4 minutes: partner discussion
Student Facing
A
\(102 + 341\)
G
\(64 + 37\)
B
\(385 - 124\)
H
\(302 - 198\)
C
\(611 - 45\)
I
\(73 - 27\)
D
\(87 + 38\)
J
\(685 + 279\)
E
\(571 - 268\)
K
\(320 + 509\)
F
\(885 - 142\)
L
\(53 + 52\)
Circle 2 sums or differences you think would be the most challenging to find. Find the value of one of these expressions. Show your thinking.
Choose 2 other expressions and find the values. Show your thinking.
Student Response
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Activity Synthesis
Poll the class. For each expression, ask students to “Show one finger if the expression was not challenging, two fingers if it was a little challenging, or three fingers if it was the most challenging to find.”
Consider displaying:
A, D, E, F, H, J
Stop for any expressions where there is a mix of ratings.
Consider asking:
“Why did you feel this expression is more challenging?”
“Who can share why this expression was less challenging?”
For expressions where most or all students felt the expression was most challenging, select students to share different methods for finding the value.
“All the expressions you felt were most challenging can become less challenging with practice and using what you know about place value.”


aligns: yes