In this topic, students will:
identify equations and variables
use substitution to find solutions to equations
use the properties of equality to keep both sides of the equation equal
identify which properties of equality are used to write equivalent expressions
write one-variable addition and subtraction equations
use inverse relationships and properties of equality to solve one-step addition and subtraction equations
write one-variable multiplication and division equations
use inverse relationships and propertiese of equality to solve one-step multiplication and division equations
write and solve equations that involve fractions, decimals, and mixed numbers
understand the symbols required to write an inequality
write inequalities to describe or real-world situations
describe solutions to an inequality represent solutions to an inequality on a number line
use mathematical modeling to represent a problem situation and to propose a solution
test and verify the appropriateness of math models
explain why the results from mathematical models may not align exactly to the problem situations
identify dependent variables
identify independent variables
analyze the relationships between variables by using tables
write equations to represent the relationships between variables
analyze the relationship between dependent and independent variables using tables, graphs, and equations
Vocabulary:
Equation - statement of equality between two expressions consisting of variables and/or numbers
Solution of an equation - the solution of an equation makes the equation true
Addition property of equality - if the same number or value is added to both sides of an equation, then the equality still holds true after addition
Subtraction property of equality - subtracting the same number from both sides of an equation does not affect the equality
Multiplication property of equality - if both sides of an equation are multiplied by the same number, the expressions on both sides of the equation remain equal to each other
Division property of equality - if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal
Inverse - pairs of mathematical manipulations in which one operation undoes the action of the other
Relationship - a relation between two sets is a collection of ordered pairs containing one object from each set
Inequality - a statement that contains <, >, ≥, ≤, or ≠ to compare two expressions
dependent variable - the variable that depends on the value of some other number
independent variable - a variable that stands alone and isn't changed by the other variables you are trying to measure