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 radicals and integer exponents.

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

Understand the relationship between zeros and factors of polynomials.

Write expressions in equivalent forms to solve problems.

Generate and analyze patterns.

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

Solve systems of equations.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Work with addition and subtraction equations.

Add and subtract within 20.

Represent and solve problems involving addition and subtraction.

Use polynomial identities to solve problems.

Interpret the structure of expressions.

Rewrite rational expressions.

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

Use properties of operations to generate equivalent expressions.

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

Use the four operations with whole numbers to solve problems.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Multiply and divide within 100.

Represent and solve equations and inequalities graphically.

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

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

Perform arithmetic operations on polynomials.

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

Analyze patterns and relationships.

Write and interpret numerical expressions.

Solve equations and inequalities in one variable.

Reason about and solve one-variable equations and inequalities.

Create equations that describe numbers or relationships

Gain familiarity with factors and multiples.

Represent and solve problems involving multiplication and division.
problem_activity: Narrative
The purpose of this activity is for students to choose from activities focusing on two-digit numbers. Students are introduced to stage 3 of the Target Numbers center. Then students choose between that center or others previously introduced.
Students choose from any stage of previously introduced centers.
Target Numbers
Number Puzzles
Mystery Number
Required Materials
Materials to Gather
Connecting cubes in towers of 10 and singles
Materials from previous centers
Number cubes
Materials to Copy
Target Numbers Stage 3 Recording Sheet
Required Preparation
Gather materials form previous centers:
Target Numbers, Stages 1-2
Number Puzzles, Stages 1-4
Mystery Number, Stage 1
Launch
Groups of 2
“Today you will choose from centers we have already learned. One of the choices is to play Target Numbers in a new way. Just like last time, your target number is 95. You will roll two cubes to get your starting number. Then, on each turn, roll three cubes and choose one of the numbers to represent the tens and another number to represent the ones. Add the new number you made to your starting number and record your equation. Continue playing for six rounds to see who gets closest to 95 without going over.”
Display the center choices in the student book.
“Think about what you would like to do first.”
30 seconds: quiet think time
Activity
8 minutes: center work time
“Choose what you would like to do next.”
8 minutes: center work time
Student Facing
Choose a center.
Target Numbers
[IMG]
Number Puzzles
[IMG]
Mystery Number
[IMG]
Activity Synthesis
“What did you like about the centers you chose?”


correct_option_index: 9