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: Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Measure and estimate lengths in standard units.

Convert like measurement units within a given measurement system.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Work with time and money.

Geometric measurement: understand concepts of angle and measure angles.

Describe and compare measurable attributes.

Represent and interpret data.

Classify objects and count the number of objects in each category.

Relate addition and subtraction to length.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Tell and write time.

Measure lengths indirectly and by iterating length units.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
problem_activity: Narrative
The purpose of this activity is for students to learn stage 1 of the Jump the Line center. In this stage, students take turns making strategic choices about numbers to add or subtract to reach target numbers. Students choose 3 target numbers and mark them on the number line. Both players start at the beginning of the number line. They spin all 3 spinners and decide which of the moves they want to use on their turn. Students take turns spinning and moving, trying to land exactly on the target numbers. The first player to land on 2 target numbers wins.
Required Materials
Materials to Gather
Dry erase markers
Paper clips
Sheet protectors
Materials to Copy
Jump the Line Stage 1 Gameboard
Jump the Line Stage 1 Spinners
Launch
Groups of 2
Give each group a spinner, paper clip, dry erase marker and gameboard.
Display spinners and gameboard.
“You and your partner will choose 3 target numbers and mark them on your number line.”
“Then you will take turns spinning all 3 spinners. On your turn you can decide which spin to use. Your goal is to jump to one of the numbers you and your partner marked.”
“The first player to land exactly on 2 of the target numbers wins.”
Play a round with the class, if needed.
Activity
15 minutes: partner work time
Activity Synthesis
Display a gameboard with 3 target numbers. Spin the three spinners.
“This is my gameboard and my spins. Which spin would you use? Why?”


correct_option_index: 9