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: Perform arithmetic operations on polynomials.

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

Use properties of operations to generate equivalent expressions.

Use polynomial identities to solve problems.

Gain familiarity with factors and multiples.

Represent and solve problems involving addition and subtraction.

Represent and solve equations and inequalities graphically.

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

Use the four operations with whole numbers to solve problems.

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

Multiply and divide within 100.

Analyze patterns and relationships.

Rewrite rational expressions.

Generate and analyze patterns.

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

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

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

Work with addition and subtraction equations.

Interpret the structure of expressions.

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

Solve systems of equations.

Solve equations and inequalities in one variable.

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

Work with radicals and integer exponents.

Create equations that describe numbers or relationships

Represent and solve problems involving multiplication and division.

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

Write and interpret numerical expressions.

Understand the relationship between zeros and factors of polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Add and subtract within 20.

Represent and analyze quantitative relationships between dependent and independent variables.

Understand properties of multiplication and the relationship between multiplication and division.
problem_activity: Narrative
Students begin the activity by looking at the problem displayed, rather than in their books. At the end of the launch, students work on the problem. This activity prompts students to use what they know about multiplication, division, factors, and multiples to solve problems. The problem does not have a question, so students will need to make sense of the context and generate potential questions that might be answered (MP2). Students are encouraged in the task to attend to the details of the situation and to engage in genuine curiosity about the mathematics that is embedded within it.
This activity uses MLR5 Co-craft Questions. Advances: writing, reading, representing
Representation: Develop Language and Symbols.
Represent the problem in multiple ways to support understanding. For example, invite students to represent the situation as a comic strip or a collage. Offer relevant images such as a movie theater, a sign showing admissions prices, a cash register, and a calendar. Alternatively, invite students to act out the situation. Consider using play money, signs with two days of the week written on them, and the action of “fast forwarding” through days and a night. Consider asking, “How might you represent the situation in a mathematical diagram?”
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing, Attention
Launch
Groups of 2
MLR5 Co-Craft Questions
Read only the first two paragraphs without revealing the question(s).
“Write a list of mathematical questions that could be asked about this situation.”
2 minutes: independent work time
2–3 minutes: partner discussion
Invite several students to share one question with the class. Record responses for use later in the task.
“What information from the situation can be used to answer this question?” (The number of days tickets were purchased, the total number of money earned by the theater, the price of movie tickets)
Reveal the task (students open books), and invite additional connections.
Activity
“Choose a question from the list to answer.”
“Work with a partner to complete the activity.”
Remind students of the list of questions generated during the launch as a reference during the activity.
Student Facing
Movie tickets are \$9 each. The theater sold the same number of tickets two days in a row.
The theater made \$3,132 from ticket sales on the first day.
[IMG]
Record and answer one question of your choice from the list the class generated. Discuss your strategy with your partner.
Use the given information about movie tickets to complete the following statement:
__________ tickets were sold on the first and second days.
A medium drink is \$7 and small popcorn is \$5. If each ticket holder purchases popcorn and a drink, how much money will the theater collect from the sales of popcorn and drink?
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Advancing Student Thinking
Students may think of questions that cannot be answered using the information provided. Consider asking: “What would we need to know to be able to answer this question?” and “How might we find out this information?” The result of these questions may not enable the students to answer the questions, but will support them in making sense of the problem and identifying information necessary to solve the problems.
Activity Synthesis
Select 1–2 students to share their reasoning and responses.
If not clarified in students’ explanations, discuss a possible path for finding out the number of tickets sold over the two days using the given information. (For instance: Each ticket is \$9 and we know the total amount of money earned by selling tickets in one day, \$3,132. If we divide the total amount earned by the price of each ticket, we can find out how many tickets were sold on one day.
\(3,\!132\div 9 = 348\)
. If 348 tickets were sold on one day, then
\(348 \times 2\)
or 696 tickets were sold in the two days. We can also multiply \$3,132 by 2 first then divide by \$9 to get the total number of tickets.)


correct_option_index: 8