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: Interpret the structure of expressions.

Multiply and divide within 100.

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

Analyze patterns and relationships.

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

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

Create equations that describe numbers or relationships

Use properties of operations to generate equivalent expressions.

Use polynomial identities to solve problems.

Write and interpret numerical expressions.

Add and subtract within 20.

Gain familiarity with factors and multiples.

Solve systems of equations.

Represent and solve problems involving addition and subtraction.

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

Perform arithmetic operations on polynomials.

Work with radicals and integer exponents.

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.

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

Rewrite rational expressions.

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

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve equations and inequalities graphically.

Generate and analyze patterns.

Represent and solve problems involving multiplication and division.

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

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

Understand properties of multiplication and the relationship between multiplication and division.
problem_activity: Problem 1
Evaluate the following numerical expressions.
a.
$${-2(5+(3)(-2)+4)}$$
b.
$${-2((5+3)(-2+4))}$$
c.
$${-2(5+3(-2+4))}$$
d.   Can the parentheses in any of these expressions be removed without changing the value of the expression?
Problem 2
An expression is shown below with three expressions that are
not
equivalent to it. Explain the error(s) that were made in writing each expression.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
a.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
$$\neq \frac{3(-4)}{2(3)^2}$$
b.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
$$\neq \frac{6-3(-4)}{(6)^2}$$
c.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
$$\neq \frac{6-12}{(2+4)^2}$$
d.   Evaluate the expression.
Problem 3
Evaluate:
$${\frac{1}{2}(-3-1)^2-\left ( 10 \div \frac{5}{6} \right )}$$


correct_option_index: 8