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: Work with radicals and integer exponents.

Represent and solve problems involving multiplication and division.

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

Use the four operations with whole numbers to solve problems.

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

Solve equations and inequalities in one variable.

Reason about and solve one-variable equations and inequalities.

Gain familiarity with factors and multiples.

Represent and solve problems involving addition and subtraction.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Analyze patterns and relationships.

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

Generate and analyze patterns.

Use polynomial identities to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Write expressions in equivalent forms to solve problems.

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

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

Interpret the structure of expressions.

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

Create equations that describe numbers or relationships

Use properties of operations to generate equivalent expressions.

Write and interpret numerical expressions.

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

Add and subtract within 20.

Solve systems of equations.

Rewrite rational expressions.

Work with addition and subtraction equations.

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

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

Understand the relationship between zeros and factors of polynomials.

Multiply and divide within 100.

Represent and solve equations and inequalities graphically.

Perform arithmetic operations on polynomials.
problem_activity: A bakery sells small cakes for
$${ {{$1}}0}$$
each. At this price, the bakery typically sells
$${100}$$
cakes per week.
The owner of the bakery wants to increase the price of the cake in order to maximize revenue. She determines that for each
$${{$1}}$$
increase in price, she sells
$$5$$
fewer cakes per week.
a.  Which function represents the weekly revenue,
$${R(x)}$$
, the owner of the bakery can expect to earn from the cakes based on
$$x$$
increases in price by
$${{$1}}$$
.
i.
$${R(x)}=(10-x)({100}+5x)$$
ii.
$${R(x)}=(10+x)({100}-5x)$$
iii.
$${R(x)}=(10-5x)({100}+x)$$
iv.
$${R(x)}=(10+5x)({100}-x)$$
b.  At what price will the owner of the bakery earn the maximum weekly revenue from sales of the small cakes?


correct_option_index: 20