options: Write expressions in equivalent forms to solve problems.

Represent and solve problems involving multiplication and division.

Use the four operations with whole numbers to solve problems.

Interpret the structure of expressions.

Use polynomial identities to solve problems.

Generate and analyze patterns.

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

Perform arithmetic operations on polynomials.

Solve systems of equations.

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

Represent and solve problems involving addition and subtraction.

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

Use properties of operations to generate equivalent expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Gain familiarity with factors and multiples.

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

Multiply and divide within 100.

Represent and solve equations and inequalities graphically.

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

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

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

Rewrite rational expressions.

Work with radicals and integer exponents.

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

Represent and analyze quantitative relationships between dependent and independent variables.

Create equations that describe numbers or relationships

Reason about and solve one-variable equations and inequalities.

Analyze patterns and relationships.

Add and subtract within 20.

Understand the relationship between zeros and factors of polynomials.

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

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: 25