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: 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: Problem 1
Mrs. Fowler knew that the perimeter of the soccer field was
$${{1\over6}}$$
mile. She walked
$$2{{{1\over6}}}$$
miles in total. How many times did she walk around the field? Show or explain your work.
Problem 2
Convert the following mixed numbers to fractions greater than 1. Show or explain your work.
a.
$${3{1\over2}}$$
b.
$${4{1\over4}}$$
c.
$${5{3\over5}}$$
Problem 3
Ben wrote the mixed number
$$7\frac{1}{3}$$
as a fraction. Here is his work:
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "width:40%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$7\\frac{1}{3}= 7 + \\frac{1}{3}$$"}]}, {"_value": "(Step 1)"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$=\\frac{7}{1}+\\frac{1}{3}$$"}]}, {"_value": "(Step 2)"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$=\\frac{21}{3}+\\frac{1}{3}$$"}]}, {"_value": "(Step 3)"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${={22\\over3}}$$"}]}, {"_value": "(Step 4)"}]}]}]}]}
Explain what Ben did in each step.


aligns: yes