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:
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 equations and inequalities in one variable.

Understand the relationship between zeros and factors of polynomials.

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

Rewrite rational expressions.

Add and subtract within 20.

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

Represent and solve problems involving multiplication and division.

Reason about and solve one-variable equations and inequalities.

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

Interpret the structure of expressions.

Solve systems of equations.

Perform arithmetic operations on polynomials.

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

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

Represent and analyze quantitative relationships between dependent and independent variables.

Gain familiarity with factors and multiples.

Use the four operations with whole numbers to solve problems.

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

Multiply and divide within 100.

Use polynomial identities to solve problems.

Write and interpret numerical expressions.

Work with addition and subtraction equations.

Represent and solve problems involving addition and subtraction.

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

Represent and solve equations and inequalities graphically.

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

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

Analyze patterns and relationships.

Use properties of operations to generate equivalent expressions.

Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with radicals and integer exponents.

Write expressions in equivalent forms to solve problems.

Generate and analyze patterns.
problem_activity: Problem 1
How many?
[IMG]
Problem 2
Determine the value of the unknown in each equation below.
a.
$$a = 7 \times 8$$
b.
$$42 \div b =7$$
c.
$$49 = 7 \times c$$
d.
$$d\div 7 = 9$$
Problem 3
Here is the partially filled-in multiplication table from Lessons 1 and 6.
| **           x          **  | **           1          ** | **           2          ** | **           3          ** | **           4          ** | **           5          ** | **           6          ** | **           7          ** | **           8          ** | **           9          ** | **           10          ** |
|-----------------------------|----------------------------|----------------------------|----------------------------|----------------------------|----------------------------|----------------------------|----------------------------|----------------------------|----------------------------|-----------------------------|
| **           1          **  |             1              |             2              |             3              |             4              |             5              |             6              |             7              |             8              |             9              |             10              |
| **           2          **  |             2              |             4              |             6              |             8              |             10             |             12             |             14             |             16             |             18             |             20              |
| **           3          **  |             3              |             6              |             9              |             12             |             15             |             18             |             21             |             24             |             27             |             30              |
| **           4          **  |             4              |             8              |             12             |             16             |             20             |             24             |             28             |             32             |             36             |             40              |
| **           5          **  |             5              |             10             |             15             |             20             |             25             |             30             |             35             |             40             |             45             |             50              |
| **           6          **  |             6              |             12             |             18             |             24             |             30             |             36             |             42             |             48             |             54             |             60              |
| **           7          **  |             7              |             14             |             21             |             28             |             35             |             42             |                            |                            |                            |             70              |
| **           8          **  |             8              |             16             |             24             |             32             |             40             |             48             |                            |                            |                            |             80              |
| **           9          **  |             9              |             18             |             27             |             36             |             45             |             54             |                            |                            |                            |             90              |
| **           10          ** |             10             |             20             |             30             |             40             |             50             |             60             |             70             |             80             |             90             |             100             |
Add the new facts you encountered in this lesson to your multiplication table.


correct_option_index: 6

18