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: 
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_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Task
The fifth grade teachers are in charge of planning the annual Davis Elementary Fun Run.  The teachers decide that each adult should run $\frac{6}{4}$ as far as each student in grade 5 and each student in grade 1 should run $\frac{3}{4}$ as far as each student in grade 5.
Who has to run the longest distance?  Who has to run the shortest distance?  Explain your reasoning.
The fifth grade students decide that they should each run four laps around the track.  How many laps should each adult and each first grade student run?
Peyton, a fifth grader calculates that he will run a$\frac{1}{2}$ mile.  Write two multiplication equations involving $\frac{1}{2}$, one that shows how many miles each adult will run and one that shows how many miles each first grade student will run.
When Peyton showed the adults his calculations, some of them were confused. Some of the adults thought multiplication always makes a number larger, for example $2\times5$ is bigger than 5. When calculating the distance the first graders ran, Peyton used multiplication but got a smaller number. Explain why the product of 5 and another number is not always greater than 5, and write an example to help the adults understand.
Presley, another fifth grade student, wanted to write the distance she ran in eighths.  She noticed that you could write this equation: $\frac{4}{4}\times\frac{1}{2}$miles = $\frac{4}{8}$ miles.  Explain why in this case multiplying by $\frac{1}{2}$ results in a product that is neither larger nor smaller than $\frac{1}{2}$.


aligns: no