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 place value understanding to round whole numbers to the nearest 10 or 100.
problem_activity: Narrative
The purpose of this activity is for students to practice rounding to the nearest ten and hundred in context. Students work with numbers from a previous lesson to estimate the total number of students in a school. They learn that how you round (to the nearest ten or hundred) can give different estimates for the same situation.
Launch
Groups of 2
“Let’s revisit the number of students in different areas in a school. We’re going to use rounding to help Andre and Lin make an estimate of the number of people in the whole school. Andre plans to round the numbers to the nearest hundred. Lin plans to round them to the nearest ten.”
“Make a prediction: Whose estimate is going to be greater? Be prepared to explain your reasoning.”
30 seconds: quiet think time
Share responses.
Activity
“Work with your partner to complete the table and the last problem.”
7–10 minutes: partner work time
Student Facing
The table shows the numbers of people in different parts of a school at noon during a school day.
Andre and Lin are trying to estimate the number of people in the whole school. Andre plans to round the numbers to the nearest hundred. Lin plans to round them to the nearest ten.
Make a prediction: Whose estimate is going to be greater? Explain your reasoning.
Work with a partner to find Andre and Lin’s estimates. Record them in the table. Then find the totals.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center"}, "_value": "location"}, {"_attributes": {"scope": "col", "style": "text-align:center"}, "_value": "number"}, {"_attributes": {"scope": "col", "style": "text-align:center"}, "br": [{}], "_values": ["Andre's estimate", "(nearest hundred)"]}, {"_attributes": {"scope": "col", "style": "text-align:center"}, "br": [{}], "_values": ["Lin's estimate", "(nearest ten)"]}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "playground"}, {"_attributes": {"style": "text-align:center"}, "_value": "94"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "cafeteria"}, {"_attributes": {"style": "text-align:center"}, "_value": "163"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "art room"}, {"_attributes": {"style": "text-align:center"}, "_value": "36"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "library"}, {"_attributes": {"style": "text-align:center"}, "_value": "13"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "classrooms"}, {"_attributes": {"style": "text-align:center"}, "_value": "216"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "gymnasium"}, {"_attributes": {"style": "text-align:center"}, "_value": "109"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "music room"}, {"_attributes": {"style": "text-align:center"}, "_value": "52"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "total"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}]}]}]}
Make two observations about the completed table. Was your prediction correct?
Student Response
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Activity Synthesis
Invite students to share their observations about the completed table, including whether it matched their predictions.
“When we are estimating a total, rounding to the nearest ten or the nearest hundred can give us different results. If you were rounding to estimate a total, would you round to the nearest ten or nearest hundred?” (The nearest ten because you get an estimate that’s closer to the total. The nearest hundred because multiples of 100 are easier to work with.)
“Keep these ideas in mind as you use rounding to estimate in future lessons.”


aligns: yes