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

Analyze patterns and relationships.

Work with addition and subtraction equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Generate and analyze patterns.

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

Solve equations and inequalities in one variable.

Create equations that describe numbers or relationships

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

Represent and solve problems involving addition and subtraction.

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

Write expressions in equivalent forms to solve problems.

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

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

Solve systems of equations.

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

Perform arithmetic operations on polynomials.

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

Represent and solve problems involving multiplication and division.

Write and interpret numerical expressions.

Reason about and solve one-variable equations and inequalities.

Use polynomial identities to solve problems.

Use properties of operations to generate equivalent expressions.

Rewrite rational expressions.

Interpret the structure of expressions.

Use the four operations with whole numbers to solve problems.

Add and subtract within 20.

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

Gain familiarity with factors and multiples.

Represent and analyze quantitative relationships between dependent and independent variables.

Understand the relationship between zeros and factors of polynomials.

Multiply and divide within 100.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
problem_activity: Narrative
The purpose of this activity is to introduce students to the structure of the MLR4 Information Gap routine. This routine facilitates meaningful interactions by positioning some students as holders of information that is needed by other students.
Tell students that first, a demonstration will be conducted with the whole class, in which they are playing the role of the person with the problem card. Explain to students that it is the job of the person with the problem card (in this case, the whole class) to think about what information they need to answer the question.
For each question that is asked, students are expected to explain what they will do with the information, by responding to the question, “Why do you need to know (that piece of information)?” If the problem card person asks for information that is not on the data card (including the answer!), then the data card person must respond with, “I don’t have that information.” In explaining their answers, students need to be precise in their word choice and use of language (MP6).
Once the students have enough information to solve the problem, they solve the problem independently.
The info gap routine requires students to make sense of problems by determining what information is necessary and then ask for information they need to solve them. This may take several rounds of discussion if their first requests do not yield the information they need (MP1).
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Launch
Groups of 2
“The problems in this lesson are about setting up for a special event at a school. What’s your favorite special event at school or in your community?”
Share responses.
Activity
MLR4 Information Gap
Display the Sample Problem Card.
Read the problem aloud.
Listen for and clarify any questions about the context.
“Some of the information you need to solve this problem is missing, and I have it here. What specific information do you need?”
1–2 minutes: quiet think time
“With your partner, decide what information you need to solve the problem, and create a list of questions you can ask to find out.”
2–3 minutes: partner discussion
Invite students to share 1 question at a time.
Record each question on a display, and respond with: “Why do you need to know (restate the information requested)?” Students should provide a justification for how they will use the information before the information is revealed.
Answer questions using only information stated on the Sample Data Card (do not reveal).
Record information that is shared on the display. Give students time to decide whether they have enough information to solve the problem.
Repeat until students decide they have enough information to solve, then ask students to solve.
2–4 minutes: independent work time
Student Facing
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Student Response
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Activity Synthesis
Invite 1–2 students to share how they solved the problem.
“Which questions helped you find out how many chairs were in the room?” (How many chairs were in the corner? How many chairs were in each row? How many rows were there?)
If there were any questions that the data card cannot answer, discuss them here.


correct_option_index: 5