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: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

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: Narrative
This optional activity allows students to practice adding tenths and hundredths (and to reinforce their ability to compare fractions) through a game. Students use fraction cards to play a game in groups of 2, 3, or 4. To win the game is to draw pairs of cards with the greater (or greatest) sum, as many times as possible.
Consider arranging students in groups of 2 for the first game or two (so that students would need to compare only 2 sums at a time), and arranging groups of 3 or 4 for subsequent games. Before students begin playing, ask them to keep track of and record pairs of fractions that they find challenging to add.
Required Materials
Materials to Copy
Fraction Action: Tenths, Hundredths
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2 for the first game or two, then groups of 3–4 for subsequent games, if time permits
Give each group one set of fraction cards from the blackline master.
Tell students that they will play one or more games of Fraction Action.
Demonstrate how to play the game. Invite a student to be your opponent in the demonstration game.
Read the rules as a class and clarify any questions students might have.
Activity
“Play one game with your partner.”
“As you play, you may come across one or more pairs of fractions whose sums are hard to find. Record those fractions. Be prepared to explain how you eventually figured out which sum is greater.”
“If you finish before time is up, play another game with the same partner, or play a game with the players from another group.”
15 minutes: group play time
Student Facing
Play Fraction Action with 2 players:
Shuffle the cards from your teacher. Place the cards in a stack, face down.
Each player turns 2 cards over and adds the fractions on the cards.
Compare the sums. The player with the greater sum wins that round and keeps all four cards.
If the sums are equivalent, each player turns one more card over and adds the value to their sum. The player with the greater new sum keeps all cards.
The player with the most cards wins the game.
Play Fraction Action with 3 or 4 players:
The player with the greatest sum of fractions wins the round.
If 2 or more players have the greatest sum, those players turn two more cards over and find their sum. The player with the greatest sum keeps all the cards.
Record any pair of fractions whose sum is challenging to find here.
________ and ________
________ and ________
________ and ________
________ and ________
Student Response
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for free access to Student Response.
Activity Synthesis
Invite groups to share some of the challenging expressions they recorded and how they eventually determined the sums.
As one group shares, ask others if they have other ideas about how the fractions could be added.


correct_option_index: 1