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, in json format:
{
  "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 and apply properties of operations and the relationship between addition and subtraction.

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

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

Perform arithmetic operations on polynomials.

Multiply and divide within 100.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use properties of operations to generate equivalent expressions.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving multiplication and division.

Create equations that describe numbers or relationships

Work with radicals and integer exponents.

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

Interpret the structure of expressions.

Use the four operations with whole numbers to solve problems.

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

Work with addition and subtraction equations.

Write and interpret numerical expressions.

Gain familiarity with factors and multiples.

Write expressions in equivalent forms to solve problems.

Solve systems of equations.

Analyze patterns and relationships.

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.

Understand the relationship between zeros and factors of polynomials.

Rewrite rational expressions.

Represent and solve problems involving addition and subtraction.

Use polynomial identities to solve problems.

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

Add and subtract within 20.

Reason about and solve one-variable equations and inequalities.

Solve equations and inequalities in one variable.

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

Generate and analyze patterns.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
problem_activity: Find the roots by factoring each of the following quadratic equations.
Additionally, for each equation, identify:
If the function has symmetry around the
y
-axis
If the root is a double root and the same as the vertex
The
y
-intercept
The vertex
a.
$${3x^2-27=0}$$
b.
$${2x^2+7x-15=0}$$
c.
$${4x^2-10x+25=0}$$


correct_option_index: 12

18