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: Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Work with numbers 11–19 to gain foundations for place value.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)

Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Understand place value.

Use place value understanding and properties of operations to add and subtract.

Extend the counting sequence.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Understand the place value system.
problem_activity: Task
Your teacher was just awarded \$1,000 to spend on materials for your classroom.  She asked all 20 of her students in the class to help her decide how to spend the money.  Think about which supplies will benefit the class the most.
|                                                    Supplies                                                    | Cost  |
|----------------------------------------------------------------------------------------------------------------|-------|
|                                              A box of 20 markers                                               |  \$5  |
|                                              A box of 100 crayons                                              |  \$8  |
|                                              A box of 60 pencils                                               |  \$5  |
|                                     A box of 5,000 pieces of printer paper                                     | \$40  |
|                                      A package of 10 pads of lined paper                                       | \$15  |
|                                    A box of 50 pieces of construction paper                                    | \$32  |
|                                                 Books and maps                                                 |       |
|                                        A set of 20 books about science                                         | \$250 |
|                                       A set of books about the 50 states                                       | \$400 |
|                                   A story book (there are 80 to choose from)                                   |  \$8  |
| A map: there is one of your city, one for every state, one of the country, and one of the world to choose from | \$45  |
|                                               Puzzles and games                                                |       |
|                                     Puzzles (there are 30 to choose from)                                      | \$12  |
|                                   Board games (there are 40 to choose from)                                    | \$15  |
|                                 Interactive computer games (math and reading)                                  | \$75  |
|                                                 Special Items                                                  |       |
|                                    A bean bag chair for the reading corner                                     | \$350 |
Write down the different items and how many of each you would choose. Find the total for each category.
Supplies
Books and maps
Puzzles and games
Special items
Create a bar graph to represent how you would spend the money.  Scale the vertical axis by \$100.  Write all of the labels.
What was the total cost of all your choices?  Did you have any money left over?  If so, how much?
Compare your choices with a partner. How much more or less did you choose to spend on each category than your partner? How much more or less did you choose to spend in total than your partner?


correct_option_index: 2