few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Standard options: 
A. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
B. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
C. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


Your response:
Thought: This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001097

7
options: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Use place value understanding to round multi-digit whole numbers to any place.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
This optional activity gives students another opportunity to practice identifying multiples of some powers of 10 that border a given number and identify the nearest ones. As before, students may use number lines to support their reasoning, but here the number lines are unlabeled.
Launch
Groups of 2
Activity
“Work independently for a few minutes. Then, discuss your responses with your partner.”
5 minutes: independent work time
2 minutes: partner discussion
Student Facing
Answer each question. Label and use the number lines if they are helpful.
Is 425,193 closer to 400,000 or 500,000?
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Is 425,193 closer to 420,000 or 430,000?
[IMG]
Is 425,193 closer to 425,000 or 426,000?
[IMG]
Is 425,193 closer to 425,100 or to 425,200?
[IMG]
Is 425,193 closer to 425,190 or to 425,200?
[IMG]
For the number 425,193:
The nearest multiple of 100,000 is _______________.
The nearest multiple of 10,000 is _______________.
The nearest multiple of 1,000 is _______________.
The nearest multiple of 100 is _______________.
The nearest multiple of 10 is _______________.
Student Response
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Activity Synthesis
Invite students to share their responses and reasoning.
“Which nearest multiples were you able to identify fairly easily?”
“Which were a bit more challenging, if any? Why might that be?”


correct_option_index: 2