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: Distinguish between situations that can be modeled with linear functions and with exponential functions.

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
problem_activity: Problem 1
Four sequences are shown below. Which one does not belong and why?
|  $${4, 8, 12, 16, 20 ...}$$  |    $${50, 46, 42, 38, 34, ...}$$    |
|------------------------------|-------------------------------------|
| $${1, 4, 16, 64, 216, ...}$$ | $${1600, 400, 100, 25, 12.5, ...}$$ |
Problem 2
Complete each sequence by filling in the missing terms. Then identify each sequence as arithmetic or geometric and name the common difference or common ratio.
a.
$${-2}$$
,
$$4$$
, ___, ___, ___,
$${28}$$
, ...
b.
$${{1\over2}}$$
, ___, ___,
$$4$$
,
$$8$$
, ___, …
c.
$$5$$
, ___, ___, ___,
$${2{1\over3}}$$
,
$${1{2\over3}}$$
, ...
d.   ___,
$$3$$
,
$${-9}$$
, ___,
$$-81$$
, ___, …
Problem 3
Write a recursive formula for each sequence.
a.
$${11, \space14,\space 17,\space 20,\space 23, …}$$
b.
$${{1\over9},\space {1\over3},\space1,\space 3,\space 9,\space …}$$
c.
$${32,\space 16,\space 8,\space 4,\space 2,\space …}$$


correct_option_index: 3