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: Rewrite rational expressions.

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

Perform arithmetic operations on polynomials.

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

Add and subtract within 20.

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

Write and interpret numerical expressions.

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

Represent and solve problems involving addition and subtraction.

Generate and analyze patterns.

Analyze patterns and relationships.

Multiply and divide within 100.

Use polynomial identities to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve problems involving multiplication and division.

Create equations that describe numbers or relationships

Work with radicals and integer exponents.

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

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

Work with addition and subtraction equations.

Gain familiarity with factors and multiples.

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

Represent and solve equations and inequalities graphically.

Use the four operations with whole numbers to solve problems.

Write expressions in equivalent forms to solve problems.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Solve equations and inequalities in one variable.

Use properties of operations to generate equivalent expressions.

Solve systems of equations.

Reason about and solve one-variable equations and inequalities.

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

Interpret the structure of expressions.

Understand the relationship between zeros and factors of polynomials.
problem_activity: Narrative
The purpose of this activity is for students to create stories and relate the action in the stories to the action of adding or taking away counters. While in the first activity, the story was provided, in this activity students create the action in the story, which is an opportunity to hear what language students associate with addition and subtraction (MP6). Mats with pictures of each setting are provided to help students make connections between what they do with their cubes and what is happening in the story. The goal of the activity synthesis is to relate the action in the story to the action with counters and show students expressions that represent these actions (MP2).
MLR8 Discussion Supports.
Synthesis: Provide all students with an opportunity to produce these words and numbers by inviting students to chorally repeat the expression in unison 1-2 times. For example: “7 take away 3” and “
\(7 - 3\)
”.
Advances: Listening, Speaking
Representation: Internalize Comprehension.
Synthesis: First demonstrate, then invite students to name each action they take as they tell their stories. For example, “Four ducks are swimming in a lake. Two ducks fly away. When the ducks fly away, I take away 2 counters.”
Supports accessibility for: Conceptual Processing, Organization
Required Materials
Materials to Gather
Two-color counters
Launch
Groups of 2
“We have heard and acted out some stories about students playing at school. Where else in your community do you see people playing outside? Describe it to your partner.”
30 seconds: quiet think time
1 minute: partner discussion
Share and record responses.
Display images from the student book.
“Some of the places where we play and walk around outside are parks and playgrounds. These stories all take place in different parks and playgrounds. How are these pictures the same as parks and playground that you have been to? How are they different?”
Give each student a bag of 10 two-color counters.
“We’re going to use our counters to show what is happening in our stories, but this time, the stories aren’t finished yet.”
Activity
Display the student workbook page of a field and read the first question. Count out 7 counters and place them on the field.
“I’ve got 7 kids playing tag in the field. What do you think happens next in the story?”
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Choose one student response and demonstrate the action with the counters.
“Now it’s your turn. I’m going to read you the first part of the story. Your job is to think about what happens next in the story. Then tell the story to your partner and show them what happens with your counters.”
Read each question. Give students quiet think time and partner discussion time for each question.
Student Facing
There were 7 kids playing tag on the field.
[IMG]
There were 2 kids eating at the picnic table.
[IMG]
There were 4 ducks swimming in the lake.
[IMG]
There were 5 kids playing hopscotch.
[IMG]
Student Response
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Advancing Student Thinking
If students represent the given sentence with counters but need encouragement to make up the rest of the story, consider asking:
“Can you use your counters to show me what happened first in the story?”
“What do you think happened next? Do you think more kids came to play tag or do you think some kids went home?”
Activity Synthesis
For each question, choose a student to share their story and demonstrate what happens with their counters. Record the action with words and numbers and an expression. For example: “7 take away 3” and “
\(7 - 3\)
”.
As each student shares, ask: “What do the counters represent?”


correct_option_index: 5