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, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

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: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
problem_activity: Problem 1
Two different students solved the problem
$$1\frac9{10}+5\frac4{10}$$
below. Study their work and determine whether the strategy they used works.
{"table": [{"_attributes": {"class": ["table"], "style": "width: 100%; layout: fixed"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align: center; width: 50%;"}, "strong": [{"_value": "Student A"}]}, {"_attributes": {"style": "text-align: center; width: 50%;"}, "strong": [{"_value": "Student B"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/uploads/2022/03/24/g4mathu5l14_at1a.png", "style": "width: 200px; height: 108px;"}}]}, {"_attributes": {"style": "text-align: center;"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/uploads/2022/03/24/g4mathu5l14_at1b.png", "style": "width: 125px; height: 140px;"}}]}]}]}]}]}
Problem 2
Two different students solved the problem
$$4\frac38-3\frac68$$
below. Study their work and determine whether the strategy they used works.
{"table": [{"_attributes": {"class": ["table"], "style": "width: 100%;"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align: center; width: 50%;"}, "strong": [{"_value": "Student C"}]}, {"_attributes": {"style": "text-align: center; width: 50%;"}, "strong": [{"_value": "Student D"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/uploads/2022/03/24/g4mathu5l14_at2a.png", "style": "width: 175px; height: 169px;"}}]}, {"_attributes": {"style": "text-align: center;"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/uploads/2022/03/24/g4mathu5l14_at2b.png", "style": "width: 100px; height: 206px;"}}]}]}]}]}]}
Problem 3
Solve.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width: 100%;"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align: center;"}, "p": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$1+\\frac{5}{12}$$"}]}, {"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{11}{12} + \\frac5{12}$$"}]}]}, {"_attributes": {"style": "text-align: center;"}, "p": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$8+4\\frac36$$"}]}, {"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$7\\frac56+4\\frac36$$"}]}]}, {"_attributes": {"style": "text-align: center;"}, "p": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$1\\frac1{10}-\\frac1{10}$$"}]}, {"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$1\\frac1{10}-\\frac2{10}$$"}]}, {"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$1\\frac1{10}-\\frac4{10}$$"}]}]}, {"_attributes": {"style": "text-align: center;"}, "p": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$6\\frac15-5$$"}]}, {"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$6\\frac15-4\\frac45$$"}]}, {"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$6\\frac15-4\\frac25$$"}]}]}]}]}]}]}


aligns: no