few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Mathematical concept/skill options: 
A. Write expressions in equivalent forms to solve problems.
B. Understand properties of multiplication and the relationship between multiplication and division.
C. Interpret the structure of expressions.
D. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
E. Use polynomial identities to solve problems.
F. Understand the relationship between zeros and factors of polynomials.
G. Write and interpret numerical expressions.
H. Work with equal groups of objects to gain foundations for multiplication.
I. Perform arithmetic operations on polynomials.
J. Create equations that describe numbers or relationships
K. Generate and analyze patterns.
L. Analyze and solve linear equations and pairs of simultaneous linear equations.
M. Understand solving equations as a process of reasoning and explain the reasoning.
N. Apply and extend previous understandings of arithmetic to algebraic expressions.
O. Rewrite rational expressions.
P. Represent and solve problems involving multiplication and division.
Q. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
R. Reason about and solve one-variable equations and inequalities.
S. Understand and apply properties of operations and the relationship between addition and subtraction.
T. Understand the connections between proportional relationships, lines, and linear equations.
U. Multiply and divide within 100.
V. Gain familiarity with factors and multiples.
W. Use the four operations with whole numbers to solve problems.
X. Work with addition and subtraction equations.
Y. Represent and solve problems involving addition and subtraction.
Z. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
AA. Solve equations and inequalities in one variable.
AB. Solve systems of equations.
AC. Represent and analyze quantitative relationships between dependent and independent variables.
AD. Work with radicals and integer exponents.
AE. Represent and solve equations and inequalities graphically.
AF. Analyze patterns and relationships.
AG. Use properties of operations to generate equivalent expressions.
AH. Add and subtract within 20.


Your response, in json format:
{
  "explanation": "This set of problems involves solving linear equations and pairs of linear equations.",
  "answer": "L"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001392

8
options: Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve equations and inequalities in one variable.

Use polynomial identities to solve problems.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving addition and subtraction.

Write and interpret numerical expressions.

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

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

Perform arithmetic operations on polynomials.

Represent and solve problems involving multiplication and division.

Analyze patterns and relationships.

Rewrite rational expressions.

Create equations that describe numbers or relationships

Generate and analyze patterns.

Use properties of operations to generate equivalent expressions.

Solve systems of equations.

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

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

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

Multiply and divide within 100.

Work with addition and subtraction equations.

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

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

Use the four operations with whole numbers to solve problems.

Write expressions in equivalent forms to solve problems.

Add and subtract within 20.

Represent and solve equations and inequalities graphically.

Interpret the structure of expressions.

Work with radicals and integer exponents.

Represent and analyze quantitative relationships between dependent and independent variables.

Gain familiarity with factors and multiples.

Understand the relationship between zeros and factors of polynomials.

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

Work with equal groups of objects to gain foundations for multiplication.
problem_activity: Problem 1
At a market, long-grain rice can be purchased in any weight, measured in pounds. The cost and weight are proportional, for example, 5 pounds of rice costs $4.
a.   Write an equation to represent the cost,
$$y$$
, to purchase
$$x$$
pounds of long-grain rice.
b.   Determine the cost of 1, 10, and 15 pounds of rice.
c.   Graph the relationship between cost and weight of rice in the coordinate plane.
d.   What is the slope of the graph? What does it mean as a unit rate?
Problem 2
Nia and Trey both had a sore throat so their mom told them to gargle with warm salt water.
Nia mixed 1 teaspoon salt with 3 cups water.
Trey mixed
$${1\over 2}$$
teaspoon salt with 1
$${{1\over2}}$$
cups of water.
Nia tasted Trey’s salt water. She said,
“I added more salt so I expected that mine would be more salty, but they taste the same.”
a.   Explain why the salt water mixtures taste the same.
b.   Find an equation that relates
$$s$$
, the number of teaspoons of salt, with
$$w$$
, the number of cups of water, for both of these mixtures.
c.   Draw the graph of your equation from part (b).
d.   Your graph in part (c) should be a line. Interpret the slope as a unit rate.


correct_option_index: 17