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: Represent and solve equations and inequalities graphically.

Solve systems of equations.

Represent and solve problems involving addition and subtraction.

Write and interpret numerical expressions.

Represent and solve problems involving multiplication and division.

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

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

Solve equations and inequalities in one variable.

Work with radicals and integer exponents.

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

Rewrite rational expressions.

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

Generate and analyze patterns.

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

Create equations that describe numbers or relationships

Interpret the structure of expressions.

Reason about and solve one-variable equations and inequalities.

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

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

Understand the relationship between zeros and factors of polynomials.

Add and subtract within 20.

Write expressions in equivalent forms to solve problems.

Gain familiarity with factors and multiples.

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

Use properties of operations to generate equivalent expressions.

Perform arithmetic operations on polynomials.

Work with addition and subtraction equations.

Analyze patterns and relationships.

Represent and analyze quantitative relationships between dependent and independent variables.

Use the four operations with whole numbers to solve problems.

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.

Use polynomial identities to solve problems.

Multiply and divide within 100.
problem_activity: Narrative
The purpose of this activity is for students to create their own relevant mathematical questions and use their understanding of addition and subtraction to answer questions about their own and their peers' survey data.
Launch
Combine pairs into groups of 4
Activity
“Switch graphs. Use the sentence stems or create your own questions about the other group’s graphs.”
1
–
2 minutes: independent work time
4 minutes: partner work time.
“Take turns to ask each other the questions you came up with and use your own graph to answer.”
“When possible, write down an equation to show your reasoning.”
5 minutes: group discussion.
Monitor for students who write equations to show the categories they combine or compare when answering their peers' questions.
Student Facing
Trade graphs. Create questions about the other group’s graph.
Sentence stems:
How many students picked ___________ and __________ all together?
How many more students picked _______ than _______?
Take turns asking and answering questions.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students rely on counting to find solutions rather than adding or subtracting, consider asking "What equation could you write to represent the categories in the question?"
Activity Synthesis
Invite previously selected students to share.
“Where do we see the equations in their graph? What does the equation mean?”
“What’s the difference between answering the questions from a bar graph and answering them from a picture graph?”


correct_option_index: 2

20