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:
Thought: 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: Gain familiarity with factors and multiples.

Understand the relationship between zeros and factors of polynomials.

Interpret the structure of expressions.

Write and interpret numerical expressions.

Represent and solve problems involving addition and subtraction.

Work with radicals and integer exponents.

Create equations that describe numbers or relationships

Rewrite rational expressions.

Multiply and divide within 100.

Perform arithmetic operations on polynomials.

Write expressions in equivalent forms to solve problems.

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

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

Use properties of operations to generate equivalent expressions.

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

Represent and solve equations and inequalities graphically.

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

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

Add and subtract within 20.

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

Work with addition and subtraction equations.

Analyze patterns and relationships.

Solve systems of equations.

Reason about and solve one-variable equations and inequalities.

Generate and analyze patterns.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving multiplication and division.

Use the four operations with whole numbers to solve problems.

Use polynomial identities to solve problems.

Solve equations and inequalities in one variable.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Understand and apply properties of operations and the relationship between addition and subtraction.
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: 15

19

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