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:
Thought: 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: Interpret the structure of expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Use properties of operations to generate equivalent expressions.

Use polynomial identities to solve problems.

Multiply and divide within 100.

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

Represent and solve equations and inequalities graphically.

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

Write and interpret numerical expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve equations and inequalities in one variable.

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

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

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

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

Perform arithmetic operations on polynomials.

Create equations that describe numbers or relationships

Generate and analyze patterns.

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

Work with radicals and integer exponents.

Add and subtract within 20.

Reason about and solve one-variable equations and inequalities.

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

Represent and solve problems involving multiplication and division.

Solve systems of equations.

Work with addition and subtraction equations.

Rewrite rational expressions.

Write expressions in equivalent forms to solve problems.

Understand the relationship between zeros and factors of polynomials.

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

Gain familiarity with factors and multiples.

Use the four operations with whole numbers to solve problems.
problem_activity: Task
The following is a student solution to the inequality $$ \frac{5}{18} - \frac{x-2}{9} \leq \frac{x-4}{6}. $$ $$ \begin{align} \frac{5}{18} - \frac{x-2}{9} & \leq \frac{x-4}{6} \newline \frac{5}{18} - \frac22 \frac{x-2}{9} & \leq \frac33 \frac{x-4}{6} \newline \frac{5}{18} - \frac{2x-2}{18} & \leq \frac{3x-4}{18} \newline 5 - (2x - 2) & \leq 3x - 4 \newline 5 - 2x + 2 & \leq 3x - 4 \newline 7 - 2x & \leq 3x - 4 \newline -5x & \leq -11 \newline x & \leq \frac{11}{5} \newline \end{align} $$
There are two mathematical errors in this work. Identify at what step each mathematical error occurred and explain why it is mathematically incorrect.
The first mathematical error occurred going from line ____ to line ____.
Why it is incorrect:
The second mathematical error occurred going from line ____ to line ____.
Why it is incorrect:
How would you help the student understand his mistakes?
Solve the inequality correctly.


correct_option_index: 12

13