options: Represent and analyze quantitative relationships between dependent and independent variables.

Generate and analyze patterns.

Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

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

Solve equations and inequalities in one variable.

Use polynomial identities to solve problems.

Interpret the structure of expressions.

Write expressions in equivalent forms to solve problems.

Write and interpret numerical expressions.

Represent and solve equations and inequalities graphically.

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

Multiply and divide within 100.

Add and subtract within 20.

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

Create equations that describe numbers or relationships

Represent and solve problems involving addition and subtraction.

Reason about and solve one-variable equations and inequalities.

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.

Solve systems of equations.

Use properties of operations to generate equivalent expressions.

Work with addition and subtraction equations.

Rewrite rational expressions.

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

Represent and solve problems involving multiplication and division.

Perform arithmetic operations on polynomials.

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

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

Analyze patterns and relationships.

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

Use the four operations with whole numbers to solve problems.

Work with radicals and integer exponents.
problem_activity: Problem 1
A rectangular garden has a width of
$$x$$
feet. The length of the garden is
$$4$$
feet longer than the width. Around the garden there is a pathway that measures
$$3$$
feet across the path.
[IMG]
The expression below represents the area of the pathway, not including the garden.
$$(x+6)(x+10)-x(x+4)$$
Explain what each part of the expression represents in context of the situation.
a.
$$x$$
b.
$$x+4$$
c.
$$x+10$$
d.
$$x(x+4)$$
e.
$$(x+6)(x+10)$$
Problem 2
An artist has a strip of wood
$$8$$
feet long to make a large rectangular picture frame. The possible dimensions of the frame that the artist can create can be represented as
$$x$$
and
$$4-x$$
, as seen in the diagram below.
[IMG]
What is the largest area the artist can frame with the
$$8$$
feet of wood?


correct_option_index: 16