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:
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: Add and subtract within 20.

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

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

Represent and solve equations and inequalities graphically.

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.

Use the four operations with whole numbers to solve problems.

Understand the relationship between zeros and factors of polynomials.

Perform arithmetic operations on polynomials.

Solve equations and inequalities in one variable.

Solve systems of equations.

Rewrite rational expressions.

Represent and solve problems involving multiplication and division.

Write expressions in equivalent forms to solve problems.

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

Represent and solve problems involving addition and subtraction.

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

Write and interpret numerical expressions.

Analyze patterns and relationships.

Multiply and divide within 100.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use polynomial identities to solve problems.

Gain familiarity with factors and multiples.

Work with addition and subtraction equations.

Create equations that describe numbers or relationships

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

Reason about and solve one-variable equations and inequalities.

Generate and analyze patterns.

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

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

Work with radicals and integer exponents.

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

Use properties of operations to generate equivalent expressions.

Interpret the structure of expressions.
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: 9

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