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:
Thought: 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: Reason about and solve one-variable equations and inequalities.

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

Multiply and divide within 100.

Interpret the structure of expressions.

Gain familiarity with factors and multiples.

Analyze patterns and relationships.

Use the four operations with whole numbers to solve problems.

Create equations that describe numbers or relationships

Work with radicals and integer exponents.

Represent and solve problems involving addition and subtraction.

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

Write expressions in equivalent forms to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve systems of equations.

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

Understand the relationship between zeros and factors of polynomials.

Represent and solve problems involving multiplication and division.

Write and interpret numerical expressions.

Use properties of operations to generate equivalent expressions.

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

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

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

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

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

Perform arithmetic operations on polynomials.

Rewrite rational expressions.

Add and subtract within 20.

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

Generate and analyze patterns.

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

Use polynomial identities to solve problems.

Represent and solve equations and inequalities graphically.
problem_activity: Problem 1
Sondra says
$$3\times223=696$$
. Use what you know about the product of two odd numbers to explain why Sondra is wrong.
Problem 2
Explain two ways you could find the next number in the highlighted diagonal below. You don’t need to actually compute it!
| **            ×           **  | **            1           ** | **            2           ** | **            3           ** | **            4           ** | **            5           ** | **            6           ** | **            7           ** | **            8           ** | **            9           ** | **            10           ** |   |
|-------------------------------|------------------------------|------------------------------|------------------------------|------------------------------|------------------------------|------------------------------|------------------------------|------------------------------|------------------------------|-------------------------------|---|
| **            1           **  |              1               |              2               |              3               |              4               |              5               |              6               |              7               |              8               |              9               |              10               |   |
| **            2           **  |              2               |              4               |              6               |              8               |              10              |              12              |              14              |              16              |              18              |              20               |   |
| **            3           **  |              3               |              6               |              9               |              12              |              15              |              18              |              21              |              24              |              27              |              30               |   |
| **            4           **  |              4               |              8               |              12              |              16              |              20              |              24              |              28              |              32              |              36              |              40               |   |
| **            5           **  |              5               |              10              |              15              |              20              |              25              |              30              |              35              |              40              |              45              |              50               |   |
| **            6           **  |              6               |              12              |              18              |              24              |              30              |              36              |              42              |              48              |              54              |              60               |   |
| **            7           **  |              7               |              14              |              21              |              28              |              35              |              42              |              49              |              56              |              63              |              70               |   |
| **            8           **  |              8               |              16              |              24              |              32              |              40              |              48              |              56              |              64              |              72              |              80               |   |
| **            9           **  |              9               |              18              |              27              |              36              |              45              |              54              |              63              |              72              |              81              |              90               |   |
| **            10           ** |              10              |              20              |              30              |              40              |              50              |              60              |              70              |              80              |              90              |              100              |   |
|                               |                              |                              |                              |                              |                              |                              |                              |                              |                              |                               |   |


correct_option_index: 1