options: Write and interpret numerical expressions.

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

Multiply and divide within 100.

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

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

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

Analyze patterns and relationships.

Work with addition and subtraction equations.

Reason about and solve one-variable equations and inequalities.

Generate and analyze patterns.

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

Perform arithmetic operations on polynomials.

Understand the relationship between zeros and factors of polynomials.

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

Solve equations and inequalities in one variable.

Solve systems of equations.

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

Work with radicals and integer exponents.

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

Interpret the structure of expressions.

Rewrite rational expressions.

Add and subtract within 20.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Create equations that describe numbers or relationships

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving addition and subtraction.

Use the four operations with whole numbers to solve problems.

Write expressions in equivalent forms to solve problems.

Use properties of operations to generate equivalent expressions.

Represent and solve equations and inequalities graphically.

Use polynomial identities to solve problems.

Represent and solve problems involving multiplication and division.

Gain familiarity with factors and multiples.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
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: 23