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: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) ^( )Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
problem_activity: Narrative
The purpose of this optional activity is for students to practice evaluating division expressions in order to make comparisons. Compare is a center that focuses on the procedural skills needed to solve single- and multi-step word problems. In this stage, students will use division to evaluate and compare quotients within 100.
This stage of the Compare center is used in grades 3, 4, and 5. When used in grade 3, remove the cards with two-digit divisors.
Required Materials
Materials to Copy
Compare Stage 4 Division Cards
Required Preparation
Create a set of cards from the blackline master for each group of 2. Remove the cards with two-digit divisors.
Launch
Groups of 2
Give each group of students a set of cards from the blackline master.
“Now let’s play Compare to practice what you learned about dividing numbers.”
“Take a minute to read the directions with your partner.”
1 minute: quiet think time
Answer any questions about the directions. If needed, play a turn with the class.
Activity
5–7 minutes: partner work time
If time permits, provide extra time to play Compare.
Student Facing
Play Compare with 2 players.
Shuffle the cards and
split the deck between the players.
Each player turns over a card.
Compare the values. The player with the greater value keeps both cards.
Play until you run out of cards. The player with the most cards at the end of the game wins.
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
Display:
\(92 \div 4\)
and
\(72 \div 3\)
.
“Suppose these are the two cards you draw. How would you decide which expression has the greatest value?”


correct_option_index: 0