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: Extend the counting sequence.

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

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.

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

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.)

Understand the place value system.

Understand place value.

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.
problem_activity: Narrative
The purpose of this activity is for students to compare methods that can be used to count numbers between 100 and 999. Students see images of beans that are put in groups of 5 and another in groups of 10. A third image uses groups of 100, groups of 10, and single beans. Students make connections to place value and their understanding of the base-ten structure (MP2, MP7). They also consider opportunities for accuracy and efficiency when they articulate pros and cons for each method.
Launch
Groups of 2
Display image of a cup of beans or display a cup of beans.
Read the context aloud.
Activity
1 minute: quiet think time
5 minutes: small-group discussion
Monitor for students who:
describe the organization and group sizes in each method
describe Clare’s method in terms of hundreds, tens, and ones
discuss ideas such as efficiency (how long it takes) and accuracy (chances of mistakes)
Student Facing
[IMG]
Clare, Noah, and Jada counted a cup of dried beans. They each came up with 529 beans. The following pictures show how each of them counted.
Jada’s counting strategy:
[IMG]
Noah’s counting strategy:
[IMG]
Clare’s counting strategy:
[IMG]
What do you notice about each of their strategies?
What is helpful about each strategy?
What is challenging about each strategy?
Student Response
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Activity Synthesis
Invite previously selected students to share their observations.
“Which of these strategies do you believe would be the fastest or slowest? Explain.”
“Do you think it would be easier to make a mistake using one of these strategies? Which one and why?”
“Which strategy do you prefer? Why?”


correct_option_index: 7