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: Fluently add and subtract within 20 using mental strategies. (See standard 1.OA.6 for a list of mental strategies.) By end of Grade 2, know from memory all sums of two one-digit numbers.
problem_activity: Narrative
This Number Talk encourages students to think about how to use the addition and subtraction facts they know and their understanding of place value to mentally find values of expressions. The strategies elicited here will be helpful as students use the facts they know to develop fluency with addition and subtraction within 100.
Students may notice that calculating
\(6 - 3\)
is repeated in each expression and use this to mentally find the values (MP8). Students must also attend to precision in how they describe how they use known facts or other methods (MP6), especially when they describe subtracting by place. Encourage students to tell more about their strategy if they use unclear language to describe their method and to reflect on how their description could be interpreted differently without more precise language. For example, if students say they knew
\(66-30=36\)
because they know
\(6-3\)
, ask students to explain how that fact helped them subtract.
Launch
Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
1 minute: quiet think time
Activity
Record answers and strategy.
Keep expressions and work displayed.
Repeat with each expression.
Student Facing
Find the value of each expression mentally.
\(6 - 3\)
\(66 - 3\)
\(66 - 30\)
\(66 - 33\)
Student Response
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Activity Synthesis
“How is each expression like
\(6 - 3\)
? How are the expressions different?” (Each expression has the digits 6 and 3. In each expression you could use what you know about
\(6 - 3\)
. Some expressions you are finding 6 ones
\(-\)
3 ones. In some expressions you are finding 6 tens
\(-\)
3 tens.)


aligns: no