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: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
problem_activity: Problem 1
Mark and label a point for each fraction below on the number line to its right.
a.
{"table": [{"_attributes": {"class": ["table"], "style": "width:100%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "vertical-align:middle"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{3}$$"}]}, {"_attributes": {"style": "vertical-align:middle"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2019/03/29/math3_u6_l10_tt1.png", "style": "width: 344px; height: 40px;"}}]}]}]}]}]}
b.
{"table": [{"_attributes": {"class": ["table"], "style": "width:100%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "vertical-align:middle"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{5}{6}$$"}]}, {"_attributes": {"style": "vertical-align:middle"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2019/03/29/math3_u6_l10_tt1.png", "style": "height:40px; width:344px"}}]}]}]}]}]}
c.
{"table": [{"_attributes": {"class": ["table"], "style": "width:100%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "vertical-align:middle"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{3}{8}$$"}]}, {"_attributes": {"style": "vertical-align:middle"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2019/03/29/math3_u6_l11_at1b.png", "style": "height:40px; width:344px"}}]}]}]}]}]}
Problem 2
Determine the location of each of the following points.
a.
[IMG]
b.
[IMG]
Problem 3
Erin walked 1 mile from her house to the library. Along the way, she passed several places shown on the number line below.
[IMG]
a.   Which place is
$$\frac{4}{8} $$
mile from Erin’s house?
b.   Erin also passed the fire station, which is
$$\frac{1}{8} $$
mile from Erin’s house. Plot the location of the fire station on the number line above.
c.   What is the distance, in miles, between the park and the market?


aligns: no