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: Solve equations and inequalities in one variable.

Represent and solve equations and inequalities graphically.

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

Represent and solve problems involving addition and subtraction.

Use properties of operations to generate equivalent expressions.

Write and interpret numerical expressions.

Write expressions in equivalent forms to solve problems.

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

Multiply and divide within 100.

Use polynomial identities to solve problems.

Gain familiarity with factors and multiples.

Add and subtract within 20.

Represent and analyze quantitative relationships between dependent and independent variables.

Understand the relationship between zeros and factors of polynomials.

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

Solve systems of equations.

Analyze patterns and relationships.

Create equations that describe numbers or relationships

Reason about and solve one-variable equations and inequalities.

Use the four operations with whole numbers to solve problems.

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

Perform arithmetic operations on polynomials.

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

Work with addition and subtraction equations.

Represent and solve problems involving multiplication and division.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

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

Interpret the structure of expressions.

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

Rewrite rational expressions.

Work with radicals and integer exponents.

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

Generate and analyze patterns.
problem_activity: Narrative
The purpose of this warm-up is to elicit the idea that expressions and equations can be used to represent different compositions and decompositions of 10, which will be useful when students match compositions and decompositions of 10 to equations in a later activity. While students may notice and wonder many things about these images and expressions, the fact that each image and expression represents a total of 10 is the important discussion point. Students have seen equations in previous lessons, but the synthesis is the first time that students are introduced to the term
equation
.
Launch
Groups of 2
Display the image.
“What do you notice? What do you wonder?”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
Student Facing
What do you notice?
What do you wonder?
[IMG]
\(7 + 3\)
[IMG]
\(5 + 5\)
[IMG]
\(8 + 2\)
Student Response
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Activity Synthesis
“What is the same about each expression?” (They are all 10.)
Write
\(10 = 7 + 3\)
.
“There are 10 counters, 7 red counters and 3 yellow counters. We can write that as 10 is 7 plus 3. When we write
\(10 = 7 + 3\)
, it is called an
equation
.”
Repeat the steps with the next 2 images.


correct_option_index: 20