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: Create equations that describe numbers or relationships

Use polynomial identities to solve problems.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve equations and inequalities graphically.

Work with radicals and integer exponents.

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

Solve systems of equations.

Rewrite rational expressions.

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

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

Analyze patterns and relationships.

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

Interpret the structure of expressions.

Use properties of operations to generate equivalent expressions.

Add and subtract within 20.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand the relationship between zeros and factors of polynomials.

Multiply and divide within 100.

Represent and solve problems involving addition and subtraction.

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

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving multiplication and division.

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

Perform arithmetic operations on polynomials.

Solve equations and inequalities in one variable.

Write and interpret numerical expressions.

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

Work with addition and subtraction equations.

Gain familiarity with factors and multiples.

Generate and analyze patterns.

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

Understand properties of multiplication and the relationship between multiplication and division.
problem_activity: Problem 1
Which strategy would you use to solve each of the following problems? Justify your answer. (You do not need to solve them.)
$${\left\{\begin{matrix}2x-6y=24 \\ x+4y=16 \end{matrix}\right.}$$
$${\left\{\begin{matrix}4x-3y=15 \\ 2x+9y=32 \end{matrix}\right.}$$
Problem 2
Greg wants to buy a new car. He looks at two different models. Car A costs $40,000, and he estimates it will cost $2,000 per year for gas and maintenance. Car B costs $60,000, and he estimates it will cost about $1,000 per year for gas and maintenance. Under what circumstances would it make sense for Greg to buy Car A? Under what circumstances would it make sense for Greg to buy Car B? Justify your answer.


correct_option_index: 6

8

24