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: Reason about and solve one-variable equations and inequalities.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Rewrite rational expressions.

Represent and solve equations and inequalities graphically.

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

Write and interpret numerical expressions.

Analyze patterns and relationships.

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.

Gain familiarity with factors and multiples.

Represent and solve problems involving addition and subtraction.

Write expressions in equivalent forms to solve problems.

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

Solve equations and inequalities in one variable.

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

Multiply and divide within 100.

Use polynomial identities to solve problems.

Generate and analyze patterns.

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

Understand the relationship between zeros and factors of polynomials.

Use properties of operations to generate equivalent expressions.

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

Work with radicals and integer exponents.

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving multiplication and division.

Interpret the structure of expressions.

Perform arithmetic operations on polynomials.

Create equations that describe numbers or relationships

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

Solve systems of equations.

Work with addition and subtraction equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Add and subtract within 20.
problem_activity: Potassium-40 has a half-life of
$${1.28\times 10^9}$$
years, which means that after that many years, half of a sample has decayed into a different isotope of carbon. If a sample began with
$${115}$$
grams of potassium-40
$${30,000,000}$$
years ago, how much is left today? How long will it be until there are only
$${50}$$
grams remaining?


correct_option_index: 26