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

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

Use properties of operations to generate equivalent expressions.

Add and subtract within 20.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve equations and inequalities in one variable.

Use polynomial identities to solve problems.

Gain familiarity with factors and multiples.

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Multiply and divide within 100.

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

Analyze patterns and relationships.

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

Perform arithmetic operations on polynomials.

Solve systems of equations.

Work with radicals and integer exponents.

Write expressions in equivalent forms to solve problems.

Represent and solve equations and inequalities graphically.

Interpret the structure of expressions.

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

Generate and analyze patterns.

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

Represent and solve problems involving multiplication and division.

Write and interpret numerical expressions.

Reason about and solve one-variable equations and inequalities.

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

Create equations that describe numbers or relationships

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

Represent and solve problems involving addition and subtraction.

Use the four operations with whole numbers to solve problems.

Work with addition and subtraction equations.

Rewrite rational expressions.
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: 21