Algebra 1

A Contemplanda online course.

Algebra 1 covers a first year of algebra in ten units. It starts with expressions and the real numbers, then treats linear equations and inequalities, functions and linear functions, and systems of linear equations and inequalities. The course continues with exponents and exponential functions, polynomials and factoring, and quadratic functions and equations, and it closes with radical and rational expressions and a unit on data analysis and statistics.

Most answers are worked out rather than chosen from a list: students fill in area models, solve an equation one step per line, place points on a graph, enter expressions, and write the solution sets of inequalities. Most practice problems carry hints, and each skill's practice continues until four answers in a row are correct.

Course at a glance

Course title: Algebra 1
Publisher: Contemplanda
Structure: 10 units over two semesters
Lessons: 69 lessons
Credit: Not awarded by Contemplanda
Enrollment: Through the student's school
Course page: www.contemplanda.com/courses/algebra-1

Credit and enrollment

Contemplanda does not award high school credit. A student who wants credit for the course should ask their own school whether it will accept it.

Schools order course seats for their students by writing to info@contemplanda.com, and a student enrolls through their school.

Students enrolled through Contemplanda Direct sign in at direct.contemplanda.com. A student whose school delivers the course signs in on the school's own portal instead.

Units and lessons

Every published lesson, by semester and unit.

Semester 1

Expressions, variables, and the real numbers

Variables and expressions
Order of operations
The real numbers
Operations with rational numbers
Properties of real numbers
Evaluating and translating expressions

Linear equations and inequalities

Solving one- and two-step equations
Multi-step equations and special cases
Literal equations and formulas
Absolute-value equations
Linear inequalities
Compound inequalities
Absolute-value inequalities

Functions and linear functions

Relations and functions
Function notation and evaluation
Domain, range, and interval notation
Slope as rate of change
Slope-intercept and point-slope forms
Graphing linear equations
Linear models

Systems of linear equations and inequalities

Solving systems by graphing
Solving systems by substitution
Solving systems by elimination
Special systems and choosing a method
Applications of linear systems
Linear inequalities in two variables
Systems of linear inequalities

Exponents and exponential functions

Product and power properties of exponents
Quotient and negative exponents
Scientific notation
Exponential functions and their graphs
Exponential growth
Exponential decay
Linear versus exponential

Semester 2

Polynomials and factoring

Adding and subtracting polynomials
Multiplying polynomials
Special products
GCF and factoring by grouping
Factoring trinomials
Factoring with leading coefficients
Special patterns and factoring completely

Quadratic functions and equations

Quadratic functions and parabolas
Graphing from standard form
Vertex form and transformations
Solving by graphing and square roots
Solving by factoring
Completing the square and the quadratic formula
Choosing a method and modeling with quadratics

Radical expressions and equations

Square roots and cube roots
Simplifying radical expressions
Adding and subtracting radical expressions
Multiplying radical expressions
Dividing radicals and rationalizing denominators
Square-root functions and their graphs
Solving radical equations

Rational expressions and equations

Simplifying rational expressions
Multiplying and dividing rational expressions
Adding and subtracting rational expressions
Dividing polynomials and complex fractions
Solving rational equations
Rational functions and inverse variation
Applications: work and rate problems

Data analysis and statistics

Mean, median, and mode
Dot plots, histograms, and shape
The five-number summary and box plots
Range and standard deviation
Two-way tables
Scatter plots and trend lines
Checkpoint: analyzing a data set

Assessment

Contemplanda publishes no grade weighting for this course. A school that decides to grant credit for it also decides how the work counts toward a grade.

Academic integrity

Work in the course must be the student's own.

Answer keys for graded questions are never sent to the student's device.

Materials and technology

Where the course runs: In a web browser, through Contemplanda Direct or inside a school's own platform
Textbook: None required. The course's own lessons are the text.