options: Add and subtract within 20.

Work with addition and subtraction equations.

Solve systems of equations.

Rewrite rational expressions.

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

Understand the relationship between zeros and factors of polynomials.

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

Represent and solve problems involving multiplication and division.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Gain familiarity with factors and multiples.

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

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

Use the four operations with whole numbers to solve problems.

Write and interpret numerical expressions.

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

Generate and analyze patterns.

Analyze patterns and relationships.

Reason about and solve one-variable equations and inequalities.

Interpret the structure of expressions.

Multiply and divide within 100.

Perform arithmetic operations on polynomials.

Represent and solve equations and inequalities graphically.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Solve equations and inequalities in one variable.

Represent and solve problems involving addition and subtraction.

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

Use polynomial identities to solve problems.

Use properties of operations to generate equivalent expressions.

Write expressions in equivalent forms to solve problems.

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

Work with radicals and integer exponents.

Create equations that describe numbers or relationships
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: 15