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

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

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

Multiply and divide within 100.

Interpret the structure of expressions.

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Solve systems of equations.

Use polynomial identities to solve problems.

Solve equations and inequalities in one variable.

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

Analyze patterns and relationships.

Add and subtract within 20.

Generate and analyze patterns.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Create equations that describe numbers or relationships

Represent and solve problems involving multiplication and division.

Write and interpret numerical expressions.

Reason about and solve one-variable equations and inequalities.

Work with radicals and integer exponents.

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

Represent and solve problems involving addition and subtraction.

Represent and solve equations and inequalities graphically.

Work with addition and subtraction equations.

Write expressions in equivalent forms to solve problems.

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.

Gain familiarity with factors and multiples.

Rewrite rational expressions.

Perform arithmetic operations on polynomials.

Use properties of operations to generate equivalent expressions.

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

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

Use the four operations with whole numbers to solve problems.
problem_activity: Problem 1
A balance is shown below.
[IMG]
a.   Describe how you can use the balance to find the value of
$$x$$
.
b.   Write an equation to represent the situation shown in the balance.
c.   Use the equation to model the actions you did in part A with the balance.
d.   Repeat parts A–C using the balance shown below.
[IMG]
Problem 2
Yoshiro has a new puppy. She decides to create an enclosure for her puppy in her backyard. The enclosure is in the shape of a hexagon, with one pair of opposite sides running the same distance along the length of two parallel flowerbeds. A sketch of the enclosure is shown below.
[IMG]
If the perimeter of the enclosure is 137 feet, what is the length of each side that runs along the flowerbed, labeled
$$n$$
in the diagram? Write an equation to represent the situation, and solve using algebraic properties.
Problem 3
Solve the equations:
a.
$${12(x-2)=72}$$
b.
$${- {1\over3}x+4=-2}$$
c.
$${5.6-2p=13}$$


correct_option_index: 10