options: Rewrite rational expressions.

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

Use the four operations with whole numbers to solve problems.

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

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

Gain familiarity with factors and multiples.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.

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

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

Multiply and divide within 100.

Represent and solve problems involving addition and subtraction.

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

Solve systems of equations.

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

Work with addition and subtraction equations.

Perform arithmetic operations on polynomials.

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

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

Understand the relationship between zeros and factors of polynomials.

Use properties of operations to generate equivalent expressions.

Generate and analyze patterns.

Write and interpret numerical expressions.

Use polynomial identities to solve problems.

Analyze patterns and relationships.

Represent and analyze quantitative relationships between dependent and independent variables.

Write expressions in equivalent forms to solve problems.

Solve equations and inequalities in one variable.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Create equations that describe numbers or relationships

Add and subtract within 20.

Interpret the structure of expressions.

Work with equal groups of objects to gain foundations for multiplication.
problem_activity: Problem 1
In equations (a)–(d) below, the solution,
$$x$$
, to the equation depends on the constant,
$$a$$
. Assuming
$$a$$
is positive, what is the effect of increasing
$$a$$
on the solution? Does it increase, decrease, or remain unchanged?
Give a reason for your answer that can be understood without solving the equation.
a.
$$x-a=0$$
b.
$$ax=1$$
c.
$$ax=a$$
d.
$$\frac{x}{a}=1$$
Problem 2
Which of the following equations have the same solution(s)? Give reasons for your answer that do not depend on solving the equations.
a.
$${x+3=5x-4}$$
b.
$${x-3=5x+4}$$
c.
$${2x+8=5x-3}$$
d.
$${10x+6=2x-8}$$
e.
$${10x-8=2x+6}$$


correct_option_index: 1