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: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
problem_activity: Problem 1
The table below shows the distance that Ms. Smith's fourth graders ran before stopping for a rest.
{"table": [{"_attributes": {"align": "Center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:50%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "_value": "Student"}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "_value": "Distance (in miles)"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Joe"}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${2{1\\over2}}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Arianna"}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${1{3\\over4}}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Bobbi"}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${2{1\\over8}}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Morgan"}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${1{{5\\over8}}}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Jack"}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${2{{5\\over8}}}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Sasha"}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${2{1\\over4}}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Tyler"}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${2{2\\over4}}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Jenny"}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${{5\\over8}}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Anson"}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${2{2\\over8}}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "Chandra"}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${2{4\\over8}}$$"}]}]}]}]}]}
Using the information in the table, answer the following questions:
a.   What was the longest distance a student ran?
b.   What was the shortest distance a student ran?
c.   What was the most common distance that students ran?
Problem 2
Use the data from Anchor Task #1 to create a line plot.
Problem 3
a.   With a partner or group, gather a handful of round buttons from a diverse collection and use a ruler to measure the diameter of each button to the nearest eighth inch.
b.   Make a dot plot of button diameters, marking your scale in eighth-inch increments.
c.   What is the most common diameter in your collection? How does that compare with the collection from another group?
d.   Now measure the diameters of these same buttons to the nearest quarter inch.
e.   Make a dot plot of button diameters, marking your scale in quarter-inch increments.
f.   Describe the differences between the two dot plots you created. Which one gives you more information? Which one is easier to read?


aligns: yes