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


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Your response, in json format:
{
  "explanation": "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. Solving this problem does not require use of the Pythagorean identity.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS
options: Use place value understanding to round whole numbers to the nearest 10 or 100.

Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
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
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
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.”


correct_option_index: 0