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

Work with radicals and integer exponents.

Use the four operations with whole numbers to solve problems.

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

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

Solve equations and inequalities in one variable.

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

Write expressions in equivalent forms to solve problems.

Perform arithmetic operations on polynomials.

Solve systems of equations.

Write and interpret numerical expressions.

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

Work with addition and subtraction equations.

Gain familiarity with factors and multiples.

Add and subtract within 20.

Multiply and divide within 100.

Use polynomial identities to solve problems.

Rewrite rational expressions.

Create equations that describe numbers or relationships

Interpret the structure of expressions.

Analyze patterns and relationships.

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

Generate and analyze patterns.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Reason about and solve one-variable equations and inequalities.

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

Represent and solve equations and inequalities graphically.

Represent and solve problems involving addition and subtraction.

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving multiplication and division.

Understand the relationship between zeros and factors of polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
problem_activity: Optional activity
This activity gives students an opportunity to interpret the graph of a line in context, including the meaning of a negative slope and the meaning of the horizontal and vertical intercepts.
Launch
3 minutes of quiet work time, followed by 2 minutes to confer in small groups to verify answers.
Reading: MLR6 Three Reads.
Use this routine for Elena’s situation to support reading comprehension for students. In the first read, students read the problem with the goal of comprehending the situation (e.g., Elena is paying back her brother every week.). In the second read, ask students to look for quantities represented in the graph (e.g., at week 0, Elena owes him
$
18; at 6 weeks, she has paid him back completely). In the third read, ask students to brainstorm possible strategies to answer the question: “What is the slope of the line and what does it represent?” This will help students reflect on the situation and interpret the slope in the given context.
Design Principle(s): Support sense-making; Maximize meta-awareness
Student Facing
Elena borrowed some money from her brother. She pays him back by giving him the same amount every week. The graph shows how much she owes after each week.
[IMG]
Answer and explain your reasoning for each question.
What is the slope of the line?
Explain how you know whether the slope is positive or negative.
What does the slope represent in this situation?
How much did Elena borrow?
How much time will it take for Elena to pay back all the money she borrowed?
Student Response
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Anticipated Misconceptions
Students may interpret money owed as negative. In this setup, the axis is labeled so that money owed is treated as positive.
Activity Synthesis
Ask students to share answers to each question and indicate how to use the graph to find the answers. For example, draw a slope triangle for the first question: the slope is -3 rather than 3, because the number of dollars owed is decreasing over time. Label the vertical intercept for the amount Elena borrowed and the horizontal intercept for the time it took her to pay back the loan.


correct_option_index: 26