options: Analyze patterns and relationships.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Use polynomial identities to solve problems.

Solve equations and inequalities in one variable.

Represent and solve problems involving multiplication and division.

Add and subtract within 20.

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

Understand the relationship between zeros and factors of polynomials.

Represent and solve problems involving addition and subtraction.

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

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

Write expressions in equivalent forms to solve problems.

Work with radicals and integer exponents.

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

Create equations that describe numbers or relationships

Use properties of operations to generate equivalent expressions.

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

Solve systems of equations.

Multiply and divide within 100.

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

Gain familiarity with factors and multiples.

Represent and analyze quantitative relationships between dependent and independent variables.

Perform arithmetic operations on polynomials.

Work with addition and subtraction equations.

Interpret the structure of expressions.

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

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

Represent and solve equations and inequalities graphically.

Use the four operations with whole numbers to solve problems.

Rewrite rational expressions.

Generate and analyze patterns.

Reason about and solve one-variable equations and inequalities.

Write and interpret numerical expressions.
problem_activity: Task
The first three steps of two visual patterns are shown below.
[IMG]
[IMG]
The number of tiles in step $n$ of Pattern D is defined by $d(n)=(n+3)^2$. The number of tiles in step $n$ of Pattern E is defined by $e(n)=(n+1)^2-2$.
For each pattern, decide whether there is a step with 167 tiles in it. If so, which step is it? If not, explain how you know.
For each pattern, decide whether there is a step with 169 tiles in it. If so, which step is it? If not, explain how you know.
Describe and justify the steps for solving the following equation for $x$: $$a(x-h)^2=k$$


correct_option_index: 4