few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Your response, in json format:
{
  "explanation": "This problem focuses on the ratio between two ingredients. Students do not have to analyze proportional relationships in-depth, which is reserved for a higher grade level, but rather use ratios to find missing values.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6
options: Understand the connections between proportional relationships, lines, and linear equations.

Use the four operations with whole numbers to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve problems involving multiplication and division.

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

Rewrite rational expressions.

Use properties of operations to generate equivalent expressions.

Write expressions in equivalent forms to solve problems.

Gain familiarity with factors and multiples.

Write and interpret numerical expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Solve equations and inequalities in one variable.

Represent and solve problems involving addition and subtraction.

Use polynomial identities to solve problems.

Understand the relationship between zeros and factors of polynomials.

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

Work with radicals and integer exponents.

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

Multiply and divide within 100.

Perform arithmetic operations on polynomials.

Generate and analyze patterns.

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

Represent and solve equations and inequalities graphically.

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

Solve systems of equations.

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

Add and subtract within 20.

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

Work with addition and subtraction equations.

Analyze patterns and relationships.

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

Interpret the structure of expressions.

Create equations that describe numbers or relationships

Reason about and solve one-variable equations and inequalities.
problem_activity: Problem 1
Consider the three situations shown below.
$${|x|=5}$$
$${|x|<5}$$
$${|x|>5}$$
For each situation, let
$${{f(x)}=|x|}$$
and
$${{g(x)}=5}$$
. Graph each relationship between
$${f(x)}$$
and
$${g(x)}$$
in the coordinate plane and then use each graph to determine the solution to each situation.
Problem 2
Solve each absolute value inequality algebraically and verify the solution graphically.
a.
$${\left|x-{1\over2}\right|<3}$$
b.
$${\left|2x\right|>{7\over2}}$$
c.
$${\left|{1\over3}x\right|-4<-1}$$


correct_option_index: 11

17

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