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: Reason about and solve one-variable equations and inequalities.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving multiplication and division.

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

Perform arithmetic operations on polynomials.

Understand the relationship between zeros and factors of polynomials.

Work with radicals and integer exponents.

Write and interpret numerical expressions.

Interpret the structure of expressions.

Use properties of operations to generate equivalent expressions.

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

Use polynomial identities to solve problems.

Multiply and divide within 100.

Solve equations and inequalities in one variable.

Work with addition and subtraction equations.

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

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

Write expressions in equivalent forms to solve problems.

Represent and solve equations and inequalities graphically.

Solve systems of equations.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Generate and analyze patterns.

Rewrite rational expressions.

Create equations that describe numbers or relationships

Work with equal groups of objects to gain foundations for multiplication.

Represent and solve problems involving addition and subtraction.

Gain familiarity with factors and multiples.

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

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

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

Analyze patterns and relationships.

Add and subtract within 20.
problem_activity: Problem 1
Graph the system of equations in the coordinate plane and identify the solution.
| $${y=4}$$                        $${y=-x+2}$$ | .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/09/23/slice-1-2022-09-23t102423420.png |
|-----------------------------------------------|------------------------------------------------------------------------------------------------------|
Problem 2
Graph the system of equations in the coordinate plane. Identify the solution to the system and verify it algebraically.
| $${2x-3y=18}$$                          $${2x+y=2}$$ | |https://d21royfkw9g4l6.cloudfront.net/uploads/2022/09/23/slice-1-2022-09-23t103817981.png|  |https://d21royfkw9g4l6.cloudfront.net/uploads/2022/09/23/slice-1-2022-09-23t103817981.png| image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/09/23/slice-1-2022-09-23t103817981.png |
|------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
Problem 3
Line
$$a$$
is shown on the coordinate grid. Construct line
$$b$$
on the coordinate grid so that
Line
$$a$$
and line
$$b$$
represent a system of linear equations with a solution of (
$$6$$
,
$$-2$$
).
The slope of line
$$b$$
is greater than
$$-1$$
and less than
$$0$$
.
The
$$y$$
-intercept of line
$$b$$
is positive.
[IMG]


correct_option_index: 30