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: Write expressions in equivalent forms to solve problems.

Represent and solve equations and inequalities graphically.

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

Gain familiarity with factors and multiples.

Work with addition and subtraction equations.

Analyze patterns and relationships.

Create equations that describe numbers or relationships

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

Generate and analyze patterns.

Write and interpret numerical expressions.

Interpret the structure of expressions.

Add and subtract within 20.

Represent and solve problems involving addition and subtraction.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand the relationship between zeros and factors of polynomials.

Multiply and divide within 100.

Solve systems of equations.

Perform arithmetic operations on polynomials.

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

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving multiplication and division.

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

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

Rewrite rational expressions.

Reason about and solve one-variable equations and inequalities.

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

Solve equations and inequalities in one variable.

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

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

Use the four operations with whole numbers to solve problems.

Use polynomial identities to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Work with radicals and integer exponents.

Understand the connections between proportional relationships, lines, and linear equations.
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: 19