few_shots: Example:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response, in json format:
{
  "explanation": "This problem involves understanding fractions as numbers by comparing their quantities.",
  "answer": "F"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000157

3
options: Write and interpret numerical expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Work with addition and subtraction equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

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

Use the four operations with whole numbers to solve problems.

Generate and analyze patterns.

Analyze patterns and relationships.

Write expressions in equivalent forms to solve problems.

Add and subtract within 20.

Represent and solve problems involving multiplication and division.

Perform arithmetic operations on polynomials.

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

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

Rewrite rational expressions.

Create equations that describe numbers or relationships

Use properties of operations to generate equivalent expressions.

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

Use polynomial identities to solve problems.

Represent and solve equations and inequalities graphically.

Understand the relationship between zeros and factors of polynomials.

Solve equations and inequalities in one variable.

Reason about and solve one-variable equations and inequalities.

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

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

Solve systems of equations.

Represent and solve problems involving addition and subtraction.

Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

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

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

Multiply and divide within 100.

Interpret the structure of expressions.
problem_activity: Task
When Marcus started high school, his grandmother opened a college savings account. On the first day of each school year she deposited money into the account:  \$1000 in his freshmen year, \$600 in his sophomore year, \$1100 in his junior year and \$900 in his senior year. The account earns interest of $r\%$ at the end of each year. When Marcus starts college after four years, he gets the balance of the savings account plus an extra \$500.
If $r$ is the annual interest rate of the bank account, the at the end of the year the balance in the account is multiplied by a growth factor of $x=1+r$. Find an expression for the total amount of money Marcus receives from his grandmother as a function of this annual growth factor $x.$
Suppose that altogether he receives \$4400 from his grandmother.  Use appropriate technology to find the interest rate that the bank account earned.
How much total interest did the bank account earn over the four years?
Suppose the bank account had been opened when Marcus started Kindergarten. Describe how the expression for the amount of money at the start of college would change. Give an example of what it might look like.


correct_option_index: 16

20