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

Represent and solve problems involving addition and subtraction.

Represent and solve problems involving multiplication and division.

Reason about and solve one-variable equations and inequalities.

Use properties of operations to generate equivalent expressions.

Create equations that describe numbers or relationships

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

Analyze patterns and relationships.

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

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

Write expressions in equivalent forms to solve problems.

Use the four operations with whole numbers to solve problems.

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

Work with radicals and integer exponents.

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

Understand the relationship between zeros and factors of polynomials.

Gain familiarity with factors and multiples.

Interpret the structure of expressions.

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

Solve systems of equations.

Generate and analyze patterns.

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

Perform arithmetic operations on polynomials.

Represent and solve equations and inequalities graphically.

Write and interpret numerical expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Add and subtract within 20.

Rewrite rational expressions.

Use polynomial identities to solve problems.

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

Multiply and divide within 100.

Apply and extend previous understandings of arithmetic to algebraic expressions.
problem_activity: Problem 1
You and a friend are going for a run along a path. You both run at the same exact speed, but your friend starts 100 yards ahead of the starting point which is where you start.
The graph below is a sketch of your and your friend’s distance traveled from the starting point over time. When will you and your friend be the same distance from the starting point? Explain your answer using the graph.
[IMG]
Problem 2
Graph the system of equations below.
{"table": [{"_attributes": {"class": ["table"], "style": "width:100%"}, "tbody": [{"tr": [{"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${y={1\\over3}(x-6)}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${6y=2x-12}$$"}]}]}, {"_attributes": {"style": "text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d21royfkw9g4l6.cloudfront.net/uploads/2022/09/23/slice-1-2022-09-23t114209772.png", "style": "width: 375px; height: 380px;"}}]}]}]}]}]}
Anika was not sure how to interpret the graph of the system. She thought that since there was only one line visible in the graph then there were no solutions to the system of equations. Do you agree with Anika's reasoning? Explain why or why not.
Problem 3
Consider the equation
$$y = \frac{2}{5} x + 1$$
. Write a second linear equation to create a system of equations that has:
a.   Exactly one solution
b.   No solutions
c.   Infinite solutions


correct_option_index: 14