few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
problem_activity: Problem 1
Shade in the grids to represent the following fractions:
{"table": [{"_attributes": {"class": ["table"], "style": "width:100%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "a.", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${30\\over 100}$$"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "b.", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${3 \\over100}$$"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "c.", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${{1\\over3}\\over 100}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2017/12/18/screen-shot-2017-12-18-at-40254-pm.png", "style": "height:207px; width:184px"}}]}, {"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2017/12/18/screen-shot-2017-12-18-at-40254-pm.png", "style": "height:207px; width:184px"}}]}, {"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2017/12/18/screen-shot-2017-12-18-at-40254-pm.png", "style": "height:207px; width:184px"}}]}]}]}]}]}
Problem 2
Fill in the chart below to represent equivalent fractions, decimals, and percentages.
{"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"}, "strong": [{"_value": "Fraction"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Decimal"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Percent"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{4}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "0.5"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "20%"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{3}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "0.05"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{3}{8}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "1.3"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{2}$$"}], "_value": "%"}]}]}]}]}
Problem 3
Use mental math to answer the questions below.
a.
What is 50% of 20?
What is 25% of 48?
What is 10% of 125?
What is 5% of 50?
b.
6 is 50% of what number?
10 is 25% of what number?
9 is 10% of what number?
c.
21 is what percent of 210?
450 is what percent of 900?
20 is what percent of 80?
30 is what percent of 20?


aligns: no