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 parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
problem_activity: Narrative
The purpose of this activity is for students to use a method of their choice, likely multiplication or division, to solve a contextual problem about equal sharing of the longest noodle ever made. The numbers in this activity are larger than the numbers students have worked with in previous lessons on division. Students estimate the number of feet of noodle each person ate at the record breaking event. The numbers and context were chosen to encourage students to consider what they know about the meaning of division, to make a reasonable estimate, and to reason about the meaning of the quotient in the context of the situation presented (MP2).
Monitor and select students with the following strategies to share in the synthesis:
Students use multiplication or division to estimate that each person will get about 25 feet of noodle.
Students can explain why 25 feet of noodle for each person is a low estimate.
Launch
“What kind of noodles do you like to eat?” (ramen, spaghetti, fettucini, chicken noodle soup)
30 seconds: partner discussion
“About how long is one of the noodles you like to eat?” (about 1 foot long)
Groups of 2
Activity
5 minutes: independent work time
5 minutes: partner discussion
As students work, consider asking “What do the numbers in your calculations mean, in terms of the situation?”
Student Facing
A Chinese food company cooked a single noodle measuring about 10,119 ft. It served 400 people.
If the noodle was shared equally, estimate how many feet of noodle each person was served.
Is your estimate lower or higher than the actual length of noodle each person ate? Explain your reasoning without calculating the actual length.
Student Response
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Activity Synthesis
Ask selected students to share in the given order (or use the provided student solutions if needed).
“How are the methods for estimating the amount of noodle each person gets the same?”(They both start by giving each person 10 feet of noodle. Then they give more until they have both given 25 feet to each person. They both find multiples of 400.)
“How are they different?” (One thinks of the process as division and one uses just multiplication.)
“How do you know the estimate of 25 feet is too low?” (Because there was still some of the noodle left. There are 119 feet left over.)


aligns: no