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

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

Represent and solve equations and inequalities graphically.

Use polynomial identities to solve problems.

Gain familiarity with factors and multiples.

Solve equations and inequalities in one variable.

Work with addition and subtraction equations.

Rewrite rational expressions.

Write expressions in equivalent forms to solve problems.

Use the four operations with whole numbers to solve problems.

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.

Represent and solve problems involving multiplication and division.

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

Multiply and divide within 100.

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

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

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

Create equations that describe numbers or relationships

Generate and analyze patterns.

Write and interpret numerical expressions.

Analyze patterns and relationships.

Represent and analyze quantitative relationships between dependent and independent variables.

Perform arithmetic operations on polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve systems of equations.

Interpret the structure of expressions.

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

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

Use properties of operations to generate equivalent expressions.

Understand the relationship between zeros and factors of polynomials.

Work with radicals and integer exponents.

Add and subtract within 20.

Reason about and solve one-variable equations and inequalities.
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: 15