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

Gain familiarity with factors and multiples.

Multiply and divide within 100.

Use the four operations with whole numbers to solve problems.

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

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

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

Reason about and solve one-variable equations and inequalities.

Solve systems of equations.

Create equations that describe numbers or relationships

Analyze patterns and relationships.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving addition and subtraction.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with addition and subtraction equations.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Rewrite rational expressions.

Represent and solve problems involving multiplication and division.

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

Solve equations and inequalities in one variable.

Write and interpret numerical expressions.

Interpret the structure of expressions.

Use properties of operations to generate equivalent expressions.

Understand the relationship between zeros and factors of polynomials.

Write expressions in equivalent forms to solve problems.

Work with radicals and integer exponents.

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

Add and subtract within 20.

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

Perform arithmetic operations on polynomials.

Generate and analyze patterns.

Use polynomial identities to solve problems.
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: 4