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

Represent and analyze quantitative relationships between dependent and independent variables.

Create equations that describe numbers or relationships

Use the four operations with whole numbers to solve problems.

Add and subtract within 20.

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

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

Gain familiarity with factors and multiples.

Reason about and solve one-variable equations and inequalities.

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

Solve systems of equations.

Understand the relationship between zeros and factors of polynomials.

Use properties of operations to generate equivalent expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use polynomial identities to solve problems.

Write and interpret numerical expressions.

Analyze patterns and relationships.

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

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

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

Write expressions in equivalent forms to solve problems.

Perform arithmetic operations on polynomials.

Represent and solve problems involving addition and subtraction.

Represent and solve equations and inequalities graphically.

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

Work with radicals and integer exponents.

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

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

Generate and analyze patterns.

Multiply and divide within 100.

Rewrite rational expressions.

Represent and solve problems involving multiplication and division.

Interpret the structure of 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: 10