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:
Thought: 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 two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
- The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
- The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
- 10 can be thought of as a bundle of ten ones — called a “ten.”
problem_activity: Narrative
The purpose of this activity is for students to write the symbol or number that makes a comparison statement true. Students then read the comparison statement. This activity has two parts. In the first part, students are given two numbers with a blank space in which to write a comparison symbol that makes the statement true. After students write the symbol, they read the comparison statement. Reading the statement encourages students to relate the language of comparison to the symbols (MP6). In the second part of the activity, students are given a comparison symbol and either one number or neither number. Students determine a number or numbers that will make the comparison true.
MLR8 Discussion Supports.
Before pairs begin working together, remind students to use phrases such as greater than and less than. Model how to use these phrases when comparing two numbers. Invite students to chorally repeat the phrases in context.
Advances: Speaking, Conversing
Required Materials
Materials to Gather
Connecting cubes in towers of 10 and singles
Launch
Groups of 2
Give students access to connecting cubes in towers of 10 and singles.
Activity
Read the task statement.
8 minutes: partner work time
Student Facing
Compare the numbers.
Write <, >, or = in each blank.
Then read the comparison statement.
\(56 \underline{\hspace{1 cm}} 26\)
\(72 \underline{\hspace{1 cm}} 78\)
\(6 \underline{\hspace{1 cm}} 55\)
\(92 \underline{\hspace{1 cm}} 29\)
\(23 \underline{\hspace{1 cm}} 23\)
[IMG]
Fill in each box with a number to make each statement true.
\(\boxed{\phantom{\frac{aaai}{aaai}}} > 78\)
\(39 < \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(13 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(\boxed{\phantom{\frac{aaai}{aaai}}} < \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(\boxed{\phantom{\frac{aaai}{aaai}}} > \boxed{\phantom{\frac{aaai}{aaai}}}\)
Student Response
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Advancing Student Thinking
If students create statements that are not true, consider asking:
“Read your statement. How could you prove that it is a true statement?”
“What other numbers could you use to make this a true statement? Explain how you know.”
Activity Synthesis
Display
\(\boxed{\phantom{3}} > 78\)
.
“How did you know what number would make the statement true?” (I knew it had to be greater than 78 because I read the statement ‘blank is greater than 78’. I put in a number and read the statement out loud to see if it was true. I chose a number with more than 7 tens so I knew it would be greater than 78.)
Display
\(39 < \boxed{\phantom{3}}\)
.
“How did you know what number would make the statement true?” (I knew it had to be greater than 39 because I read the statement ‘39 is less than blank’. I put in a number and read the statement out loud to see if it was true. I chose a number with more than 3 tens so I knew that it would be greater than 39.)
Invite students to share comparisons they made for
\(\boxed{\phantom{3}}< \boxed{\phantom{3}}\)
and
\(\boxed{\phantom{3}} >\boxed{\phantom{3}}\)
.
\(\)
For each comparison shared, have the class decide if it is true or not.


correct_option_index: 0