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: 
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 following problem or activity 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_neg_0

HS_2
standard_description: Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Narrative
This Number Talk encourages students to think about equivalent forms of whole numbers and decomposing fractions in order to subtract. When students consider equivalent fractions, look for ways to decompose fractions, or use the structure of mixed numbers to find the value of each difference, they look for and make use of structure (MP7).
Launch
Display one expression.
“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 expressions and work displayed.
Repeat with each expression.
Student Facing
Find the value of each expression mentally.
\(1 - \frac{8}{10}\)
\(1\frac{4}{10} - \frac{8}{10}\)
\(2\frac{4}{10} - \frac{8}{10}\)
\(10\frac{5}{10} - \frac{8}{10}\)
Student Response
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Activity Synthesis
“How are these expressions alike?” (They all involve subtracting
\(\frac{8}{10}\)
from a number that is at least 1. To subtract, it’s helpful or necessary to decompose a 1 or to write an equivalent fraction.)
“How did you use earlier expressions to help you find the value of later expressions?”


aligns: yes