Math101 · Independent Ontario learning library
02 · Subject library
Pre-Algebra
The bridge from numerical thinking to expressions, equations, patterns, and functions.
Start with Coefficient →21 complete · 21 total lessons
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01CoefficientA coefficient is the numerical factor multiplying a variable or variable product in a term. In $-7x^2y$, the coefficient is $-7$; in $x$, the understood coefficient is $1$; in $-x$, it is $-1$.Full lesson + sheet02Combining Like TermsCombining like terms rewrites repeated copies of the same variable part as one term while preserving the expression’s value.Full lesson + sheet03ConstantA constant is a quantity whose value does not vary within the problem under discussion. A constant term contains no variable, so in $4x^2-3x+9$, the constant term is $9$.Full lesson + sheet04Coordinate PlaneThe coordinate plane locates points with ordered pairs and turns numerical relationships into visible geometry and graphs.Full lesson + sheet05Distributive PropertyThe distributive property connects multiplication with addition and subtraction, allowing brackets to be expanded or common factors to be revealed.Full lesson + sheet06EquationAn equation is a mathematical statement that two expressions have equal value. The equals sign expresses a relationship, not a command to calculate.Full lesson + sheet07Evaluating ExpressionsTo evaluate an expression is to find its value for specified variable inputs. Evaluation replaces each variable consistently, preserves grouping, and then applies the order of operations.Full lesson + sheet08ExpressionAn algebraic expression combines numbers, variables, and operations to represent a quantity without asserting that it equals something else.Full lesson + sheet09FormulaA formula is an equation that expresses a general relationship among quantities. Each symbol stands for a defined quantity, often with units and conditions.Full lesson + sheet10InequalityAn inequality compares values that need not be equal. Symbols $<$ and $>$ are strict; $\le$ and $\ge$ include equality.Full lesson + sheet11Introduction to FunctionsA function assigns exactly one output to each allowed input and provides a precise language for relationships, graphs, tables, and models.Full lesson + sheet12Linear InequalitiesA linear inequality in one variable compares linear expressions and has a solution set that is an interval, ray, all real numbers, or no solution.Full lesson + sheet13Literal EquationsA literal equation contains two or more variables and is often a formula. Solving for one variable rewrites the same relationship with that variable isolated.Full lesson + sheet14Ordered PairAn ordered pair $(x,y)$ records two coordinates in a fixed order. In the Cartesian plane, $x$ gives horizontal displacement from the origin and $y$ gives vertical displacement.Full lesson + sheet15Patterns and SequencesA sequence is an ordered list whose terms follow a rule. A pattern is the regularity used to generate or relate those terms.Full lesson + sheet16RelationsA relation is any set of ordered pairs connecting inputs with outputs. The domain is the set of first coordinates and the range is the set of second coordinates.Full lesson + sheet17Solving Multi-Step EquationsMulti-step equations combine brackets, like terms, fractions, and variables on both sides while preserving equality through reversible operations.Full lesson + sheet18Solving One-Step EquationsA one-step equation isolates its variable with one inverse operation. The goal is not to “move” a term mysteriously but to preserve equality by applying the same legal operation to both sides.Full lesson + sheet19Solving Two-Step EquationsA two-step equation requires undoing two operations to isolate the variable. Work in reverse order of how the expression was built while performing the same transformation on both sides.Full lesson + sheet20TermA term is a single number, variable, or product of numbers and variables separated from other terms by top-level addition or subtraction.Full lesson + sheet21VariableA variable is a symbol that represents a number—sometimes unknown, sometimes changing, and sometimes chosen freely.Full lesson + sheet
