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: Fluently multiply multi-digit whole numbers using the standard algorithm.

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
problem_activity: Narrative
The purpose of this activity is for students to practice multiplying multi-digit numbers that have one or more digits of 0 at the end. Monitor for students who:
use the standard algorithm to evaluate
\(6,\!700 \times 89\)
.
multiply the product
\(67 \times 89\)
by 10 to find the value of the product
\(670 \times 89\)
.
multiply the product of
\(670 \times 89\)
by 10 to find the value of the product
\(6,\!700 \times 89\)
.
Students who observe that
\(670 = 10 \times 67\)
and
\(6,\!700 = 10 \times 670\)
and use these relationships to find the values of the products are observing regularity in repeated reasoning and using their knowledge of how to multiply a whole number by 10 (MP7, MP8).
Representation: Internalize Comprehension.
Synthesis: Invite students to identify which details were important to find products of multi-digit numbers that have zero digits. Display the sentence frame, “The next time I multiply a number that contains zero digits, I will pay attention to . . . .“
Supports accessibility for: Conceptual Processing, Memory
Launch
Groups of 2
Activity
5–7 minutes: independent work time
5–7 minutes: partner discussion
Student Facing
Find the value of each product.
1.
[IMG]
2.
[IMG]
3.
[IMG]
4.
[IMG]
Student Response
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Activity Synthesis
Display the product
\(6,\!700 \times 89\)
:
Ask previously identified students to share their solutions.
Display student work or the image from the sample response:
[IMG]
“What is the relationship between
\(670\times89\)
and
\(6,\!700\times89\)
?” (The product
\(6,\!700\times89\)
is ten times larger because one of the factors is ten times greater.)
“What is the relationship between
\(67 \times 89\)
and
\(6,\!700 \times 89\)
?” (The product
\(6,\!700 \times 89\)
is 100 times as large as
\(67 \times 89\)
since 6,700 is
\(100 \times 67\)
.)


correct_option_index: 0