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, in json format:
{
  "explanation": "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: Perform arithmetic operations on polynomials.

Use polynomial identities to solve problems.

Work with addition and subtraction equations.

Write and interpret numerical expressions.

Reason about and solve one-variable equations and inequalities.

Rewrite rational expressions.

Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand the relationship between zeros and factors of polynomials.

Solve equations and inequalities in one variable.

Represent and solve problems involving multiplication and division.

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

Represent and solve problems involving addition and subtraction.

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

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

Represent and analyze quantitative relationships between dependent and independent variables.

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

Use the four operations with whole numbers to solve problems.

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

Use properties of operations to generate equivalent expressions.

Write expressions in equivalent forms to solve problems.

Solve systems of equations.

Analyze patterns and relationships.

Interpret the structure of expressions.

Multiply and divide within 100.

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

Generate and analyze patterns.

Create equations that describe numbers or relationships

Represent and solve equations and inequalities graphically.

Work with radicals and integer exponents.

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

Add and subtract within 20.

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

Understand the connections between proportional relationships, lines, and linear equations.
problem_activity: Task
Materials
Number cards labeled 1-10 (attached as a PDF)
[IMG]
Actions
Begin by playing the game as a whole class to demonstrate the rules and for students to illustrate the range of possible strategies.
Have a student pick 5 number cards from the cards labeled 1 through 10. Then, have another student pick a “Target Number” between 10 through 20.  Students must add and/or subtract 2 or more of the 5 number cards to arrive at the “target” number.
As students present the different number combinations for the “target” number, write their expressions on the board and have them explain how they were able to mentally come up with the solution.
As students explain their reasoning, name the strategies they used. For example, look for students making fives (e.g. 6 + 8 = 5 + 1 + 5 +3= 10 + 4 = 14) and tens (9 + 8 = 10 + 7), and using known facts (e.g. 8 + 8 is 16 so 8 + 7 is one less than 16) to encourage flexible thinking about the relationship among the facts.
When students understand how the game works, they can play in pairs, checking each other's solutions.


correct_option_index: 31