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: Apply and extend previous understandings of arithmetic to algebraic expressions.

Perform arithmetic operations on polynomials.

Solve equations and inequalities in one variable.

Add and subtract within 20.

Interpret the structure of expressions.

Gain familiarity with factors and multiples.

Use properties of operations to generate equivalent expressions.

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

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

Multiply and divide within 100.

Use the four operations with whole numbers to solve problems.

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Rewrite rational expressions.

Work with radicals and integer exponents.

Represent and solve problems involving multiplication and division.

Solve systems of equations.

Work with addition and subtraction equations.

Analyze patterns and relationships.

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

Represent and solve equations and inequalities graphically.

Represent and solve problems involving addition and subtraction.

Write and interpret numerical expressions.

Use polynomial identities to solve problems.

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

Write expressions in equivalent forms to solve problems.

Create equations that describe numbers or relationships

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

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

Generate and analyze patterns.

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

Reason about and solve one-variable equations and inequalities.

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

Understand the connections between proportional relationships, lines, and linear equations.
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: 20

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