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
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Your response:
Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Represent and solve problems involving addition and subtraction.

Understand properties of multiplication and the relationship between multiplication and division.

Solve equations and inequalities in one variable.

Gain familiarity with factors and multiples.

Use the four operations with whole numbers to solve problems.

Generate and analyze patterns.

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Perform arithmetic operations on polynomials.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Work with addition and subtraction equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Multiply and divide within 100.

Interpret the structure of expressions.

Analyze patterns and relationships.

Add and subtract within 20.

Understand and apply properties of operations and the relationship between addition and subtraction.

Solve systems of equations.

Use polynomial identities to solve problems.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Represent and solve problems involving multiplication and division.

Write and interpret numerical expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Create equations that describe numbers or relationships

Work with radicals and integer exponents.

Write expressions in equivalent forms to solve problems.

Understand the connections between proportional relationships, lines, and linear equations.

Reason about and solve one-variable equations and inequalities.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Rewrite rational expressions.

Understand solving equations as a process of reasoning and explain the reasoning.

Represent and solve equations and inequalities graphically.

Use properties of operations to generate equivalent expressions.

Work with equal groups of objects to gain foundations for multiplication.
problem_activity: Task
A penny is about $\frac{1}{16}$ of an inch thick.
In 2011 there were approximately 5 billion pennies minted. If all of these pennies were placed in a single stack, how many miles high would that stack be?
In the past 100 years, nearly 500 billion pennies have been minted. If all of these pennies were placed in a single stack, how many miles high would that stack be?
The distance from the moon to the earth is about 239,000 miles. How many pennies would need to be in a stack in order to reach the moon?


correct_option_index: 24

27