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: 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