options: Generate and analyze patterns.

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

Work with radicals and integer exponents.

Use polynomial identities to solve problems.

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

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

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

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

Interpret the structure of expressions.

Represent and solve equations and inequalities graphically.

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

Represent and solve problems involving addition and subtraction.

Create equations that describe numbers or relationships

Solve equations and inequalities in one variable.

Represent and solve problems involving multiplication and division.

Use properties of operations to generate equivalent expressions.

Solve systems of equations.

Analyze patterns and relationships.

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

Perform arithmetic operations on polynomials.

Write and interpret numerical expressions.

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

Work with addition and subtraction equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Write expressions in equivalent forms to solve problems.

Multiply and divide within 100.

Add and subtract within 20.

Understand the relationship between zeros and factors of polynomials.

Gain familiarity with factors and multiples.

Rewrite rational expressions.

Reason about and solve one-variable equations and inequalities.

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

Use the four operations with whole numbers to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.
problem_activity: Task
The first three steps of three visual patterns are shown below.
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Here are functions that define how many tiles are in step $n$, in no particular order: $$f(n)=3n^2$$ $$g(n)=n^2+4$$ $$h(n)=n^2-1$$
Decide which function defines which pattern.
One of these patterns has a step with $432$ tiles in it, one has a step with $195$ tiles in it, and one of these patterns has a step with $404$ tiles in it. Decide which is which, find the step that contains that number of tiles, and explain how you know.
Describe and justify the steps to solve this equation for $x$. $$ax^2+c=d$$


correct_option_index: 13