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: 
Solve quadratic equations in one variable.

Answer: 
Yes. This task shows one quadratic equation with 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: 
Construct a tangent line from a point outside a given circle to the circle.

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, 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_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
problem_activity: Narrative
The purpose of this Number Talk is for students to interpret a fraction as division of the numerator by the denominator. The strategies elicited here will be helpful later in the lesson when students match division situations, expressions, and diagrams. In this activity, students have an opportunity to notice and make use of structure (MP7) because the divisor stays the same.
Launch
Display one problem.
“Give me a signal when you have an answer and can explain how you got it.”
Activity
1 minute: quiet think time
Record answers and strategy.
Keep problems and work displayed.
Repeat with each problem.
Student Facing
Find the value of each expression mentally.
\(35 \div 7\)
\(1 \div 7\)
\(36 \div 7\)
\(37 \div 7\)
Student Response
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Activity Synthesis
“What patterns do you notice?” (The solutions for
\(35 \div 7\)
,
\(36 \div 7\)
,
\(37 \div 7\)
increase by
\(\frac {1}{7}\)
)
“If we kept increasing the dividend by 1, what would be the next whole number quotient?” (6)


aligns: yes