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: 
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Answer: 
Yes. This task asks students to draw a ray that bisects an angle. The act of drawing circles and rays may involve compass and straightedge or dynamic geometric software.

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_pos_0

HS_2
standard_description: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
problem_activity: Problem 1
Josie makes 1.7 liters of lemonade. Josie’s mom tells her to split it evenly with her brother. How much lemonade, in liters, will Josie and her brother each get?
Problem 2
Here is how Mai used base-ten diagrams to calculate 0.62 ÷ 5. She started by representing 0.62.
[IMG]
She then made 5 groups, each with 1 tenth. There was 1 tenth left. She unbundled it into 10 hundredths and distributed the hundredths into 5 groups. Here is her diagram for 0.62 ÷ 5.
[IMG]
Mai should have a total of 12 hundredths, but her diagram shows only 10. Why?
She did not originally have thousandths, but in her diagrams each group has 4 thousandths. Why?
What value has Mai found for 0.62 ÷ 5?
Problem 3
Here is how Lin calculated 0.62 ÷ 5.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "table-layout:Fixed; width:100%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center; vertical-align:top"}, "p": [{"_attributes": {"style": "text-align: left;"}, "_value": "Lin wrote the dividend, 0.62, and the divisor, 5."}]}, {"_attributes": {"style": "text-align:center; vertical-align:top"}, "p": [{"_attributes": {"style": "text-align: left;"}, "_value": "She subtracted 5 groups of different amounts from 0.62, starting with 5 groups of 0.10, then 5 groups of 0.02."}]}, {"_attributes": {"style": "text-align:center; vertical-align:top"}, "p": [{"_attributes": {"style": "text-align: left;"}, "_value": "Lin wrote 0 to the right of the 2, which made 0.020."}]}, {"_attributes": {"style": "text-align:center; vertical-align:top"}, "p": [{"_attributes": {"style": "text-align: left;"}, "_value": "Lastly, she subtracted 5 times 0.004 from 0.020, which left no remainder."}, {"_attributes": {"style": "text-align: left;"}, "_value": "Then she added 0.100 + 0.020 + 0.004, which gave a quotient of 0.124."}]}]}, {"td": [{"_attributes": {"style": "text-align:center; vertical-align:top"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/9FyZXfKqijxVpRgv2Bc6qf_CDWBZL.png"}}]}, {"_attributes": {"style": "text-align:center; vertical-align:top"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/nxKMGc5DKRKgY6x2FVmo07_YDGM41.png"}}]}, {"_attributes": {"style": "text-align:center; vertical-align:top"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/O3iHOw3zlpAkiFdwXHFNPB_NVXARD.png"}}]}, {"_attributes": {"style": "text-align:center; vertical-align:top"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/91UkRicG3K9xdXGPqEsgOT_06NZSH.png"}}]}]}]}]}]}
Lin put a 0 after the remainder of 0.02. Why? Why does this 0 not change the value of the quotient?
What value did Lin find for 0.62 ÷ 5?
Problem 4
Solve. Show or explain your work.
27 ÷ 6
0.84 ÷ 8
18.03 ÷ 6
3 ÷ 4


aligns: no