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?


Topic options: 
A. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
B. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
C. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
D. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
E. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
F. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.
G. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
H. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
I. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
J. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
K. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.


Your response:
F

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: fl_problem_001392

8
options: Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.
problem_activity: Task
Some of the problems below can be solved by multiplying $\frac18\times\frac25$, while others need a different operation.  Select the ones that can be solved by multiplying these two numbers.  For the remaining, tell what operation is appropriate.  In all cases, solve the problem (if possible) and include appropriate units in the answer.
Two-fifths of the students in Anya’s fifth grade class are girls.  One-eighth of the girls wear glasses.  What fraction of Anya’s class consists of girls who wear glasses?
A farm is in the shape of a rectangle $\frac18$ of a mile long and $\frac25$ of a mile wide.  What is the area of the farm?
There is $\frac25$ of a pizza left.  If Jamie eats another  $\frac18$ of the original whole pizza, what fraction of the original pizza is left over?
In Sam’s fifth grade class, $\frac18$ of the students are boys.  Of those boys, $\frac25$ have red hair.  What fraction of the class is red-haired boys?
Only $\frac{1}{20}$ of the guests at the party wore both red and green.  If $\frac18$ of the guests wore red, what fraction of the guests who wore red also wore green?
Alex was planting a garden. He planted $\frac25$ of the garden with potatoes and $\frac18$ of the garden with lettuce. What fraction of the garden is planted with potatoes or lettuce?
At the start of the trip, the gas tank on the car was $\frac25$ full.  If the trip used $\frac18$ of the remaining gas, what fraction of a tank of gas is left at the end of the trip?
On Monday, $\frac18$ of the students in Mr. Brown’s class were absent from school.  The nurse told Mr. Brown that $\frac25$ of those students who were absent had the flu.  What fraction of the absent students had the flu?
Of the children at Molly’s daycare, $\frac18$ are boys and $\frac25$ of the boys are under 1 year old.  How many boys at the daycare are under one year old?
The track at school is $\frac25$ of a mile long.  If Jason has run $\frac18$ of the way around the track, what fraction of a mile has he run?


correct_option_index: 4