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: Solve systems of equations.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Add and subtract within 20.

Work with addition and subtraction equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Reason about and solve one-variable equations and inequalities.

Write and interpret numerical expressions.

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

Write expressions in equivalent forms to solve problems.

Perform arithmetic operations on polynomials.

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

Use the four operations with whole numbers to solve problems.

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

Analyze patterns and relationships.

Create equations that describe numbers or relationships

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

Understand the relationship between zeros and factors of polynomials.

Represent and solve equations and inequalities graphically.

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

Represent and solve problems involving addition and subtraction.

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

Work with radicals and integer exponents.

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

Solve equations and inequalities in one variable.

Generate and analyze patterns.

Multiply and divide within 100.

Represent and solve problems involving multiplication and division.

Interpret the structure of expressions.

Use polynomial identities to solve problems.

Use properties of operations to generate equivalent expressions.

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

Gain familiarity with factors and multiples.

Rewrite rational expressions.
problem_activity: Problem 1
Evaluate the following numerical expressions.
a.
$${-2(5+(3)(-2)+4)}$$
b.
$${-2((5+3)(-2+4))}$$
c.
$${-2(5+3(-2+4))}$$
d.   Can the parentheses in any of these expressions be removed without changing the value of the expression?
Problem 2
An expression is shown below with three expressions that are
not
equivalent to it. Explain the error(s) that were made in writing each expression.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
a.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
$$\neq \frac{3(-4)}{2(3)^2}$$
b.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
$$\neq \frac{6-3(-4)}{(6)^2}$$
c.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
$$\neq \frac{6-12}{(2+4)^2}$$
d.   Evaluate the expression.
Problem 3
Evaluate:
$${\frac{1}{2}(-3-1)^2-\left ( 10 \div \frac{5}{6} \right )}$$


correct_option_index: 30