options: Write expressions in equivalent forms to solve problems.

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

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

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

Multiply and divide within 100.

Rewrite rational expressions.

Generate and analyze patterns.

Use properties of operations to generate equivalent expressions.

Solve equations and inequalities in one variable.

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

Understand the relationship between zeros and factors of polynomials.

Use polynomial identities to solve problems.

Work with addition and subtraction equations.

Perform arithmetic operations on polynomials.

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

Gain familiarity with factors and multiples.

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

Use the four operations with whole numbers to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving addition and subtraction.

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

Represent and solve equations and inequalities graphically.

Add and subtract within 20.

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

Create equations that describe numbers or relationships

Write and interpret numerical expressions.

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

Solve systems of equations.

Reason about and solve one-variable equations and inequalities.

Analyze patterns and relationships.

Interpret the structure of expressions.

Work with radicals and integer exponents.

Represent and solve problems involving multiplication and division.
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: 8