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:
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: Use the four operations with whole numbers to solve problems.

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

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

Perform arithmetic operations on polynomials.

Generate and analyze patterns.

Solve systems of equations.

Represent and solve problems involving multiplication and division.

Write and interpret numerical expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Work with addition and subtraction equations.

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

Gain familiarity with factors and multiples.

Reason about and solve one-variable equations and inequalities.

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

Create equations that describe numbers or relationships

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

Analyze patterns and relationships.

Solve equations and inequalities in one variable.

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

Use polynomial identities to solve problems.

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

Interpret the structure of expressions.

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

Multiply and divide within 100.

Use properties of operations to generate equivalent expressions.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving addition and subtraction.

Rewrite rational expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with radicals and integer exponents.

Understand the relationship between zeros and factors of polynomials.

Add and subtract within 20.

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

Write expressions in equivalent forms to solve problems.
problem_activity: Problem 1
Below is the graph and equation of the function
$$f$$
.
$$f(x)=(x-2)(x-5)\over(x-2)(x+1)$$
[IMG]
And below is the graph and equation of the function
$$g$$
.
$$g(x)={(x-5)\over(x+1)}$$
[IMG]
How are the functions
$$f$$
and
$$g$$
similar Different?
Problem 2
How are the functions
$${g(x)}$$
and
$${h(x)}$$
different? Similar?
$${g(x)}={x^2\over{x-2}}$$
$${h(x)}={x^2-4\over{(x-2)(x+3)}}$$


correct_option_index: 27