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

Gain familiarity with factors and multiples.

Represent and solve problems involving multiplication and division.

Perform arithmetic operations on polynomials.

Multiply and divide within 100.

Use polynomial identities to solve problems.

Generate and analyze patterns.

Write and interpret numerical expressions.

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

Represent and solve problems involving addition and subtraction.

Reason about and solve one-variable equations and inequalities.

Solve systems of equations.

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

Represent and solve equations and inequalities graphically.

Understand the relationship between zeros and factors of polynomials.

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

Write expressions in equivalent forms to solve problems.

Work with radicals and integer exponents.

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

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

Use the four operations with whole numbers to solve problems.

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

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

Add and subtract within 20.

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

Rewrite rational expressions.

Interpret the structure of expressions.

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

Create equations that describe numbers or relationships

Use properties of operations to generate equivalent expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Analyze patterns and relationships.

Represent and analyze quantitative relationships between dependent and independent variables.
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: 11

12

17