Algebra I
A grade 9 Algebra I course designed for homeschool learners. Students solve and graph linear equations and inequalities, operate on polynomials and factor expressions, and solve quadratic equations by multiple methods through structured lessons, guided practice, and real-world projects that build confidence and academic strength.
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Program Features
- Start date:
- Online Prerequisite:
- Successful completion of Pre-Algebra or equivalent.
- Interactive LMS Content
- Blockchain-based Certificate
Assessments
- Academy for Independent Study with 1 credits
Program Features
- Start date:
- Online Prerequisite:
- Successful completion of Pre-Algebra or equivalent.
- Interactive LMS Content
- Blockchain-based Certificate
Assessments
- Academy for Independent Study with 1 credits
Description
Algebra I is a comprehensive grade 9 course built for homeschool families and self-directed learners. Students move through eight focused modules — from variables, expressions, and order of operations to real-world modeling with algebra — gaining the conceptual foundation, skills, and confidence to succeed at the next level. Lessons combine clear direct instruction with guided practice, projects, and real-world application so learners not only know the material, they can use it.
Throughout the course, students develop habits of careful reasoning, clear communication, and self-directed study. By the end, learners are prepared to analyze and interpret functions and model real situations with systems of equations, with a portfolio of work that demonstrates mastery. Algebra I fits naturally into a four-year homeschool plan and pairs well with co-ops, tutoring, and family-led learning.
Program Syllabus
Course Overview
| Course Code (NCES SCED): | 02052 |
| Grade Level: | Grade 9 |
| Credit: | 1.0 Carnegie unit |
| Instructional Hours: | 120 hours over 32 weeks |
| Delivery: | Online, teacher-led (not self-paced) |
| Prerequisites: | Successful completion of Pre-Algebra or equivalent. |
| Issuing Institution: | Academy for Independent Study (AIS) |
Course Description
Algebra I is a grade 9 course designed for homeschool learners pursuing a credit-bearing high-school transcript. Students engage with the material through teacher-led instruction, guided practice, projects, and regular assessments. The course is built to meet recognized academic standards and prepares students for college and career readiness.
Learning Outcomes
By the end of this course, students will be able to:
- Solve and graph linear equations and inequalities.
- Operate on polynomials and factor expressions.
- Solve quadratic equations by multiple methods.
- Analyze and interpret functions.
- Model real situations with systems of equations.
- Reason quantitatively with algebraic structure.
Course Schedule & Modules
Module 1 — Variables, Expressions, and Order of Operations
Time on Task: Weeks 1–4 (16–24 hours of instruction and practice)
Learning Objectives:
- Explain the core concepts and vocabulary of variables, expressions, and order of operations.
- Apply variables, expressions, and order of operations to solve representative problems and real-world scenarios.
- Demonstrate mastery of variables, expressions, and order of operations through written, oral, or project-based work.
Key Topics: Variables, Expressions, and Order of Operations — concept introduction, core terminology, foundational skills, and connections to prior modules.
Activities & Practice: Direct instruction, guided practice, independent practice, small projects, and discussion. Students keep a course notebook and complete short weekly reflections.
Materials & Resources: Textbook chapter readings, instructor video lessons, supplementary articles, and online practice tools. Materials list is published at the start of each module.
Assessment: Module 1 assessment includes a quiz on key concepts (20%), a graded application activity or short project (40%), and contribution to discussion or peer review (10%). Cumulative midterm and final exams contribute to the remaining 30% of the course grade.
Module 2 — Linear Equations in One Variable
Time on Task: Weeks 5–8 (16–24 hours of instruction and practice)
Learning Objectives:
- Explain the core concepts and vocabulary of linear equations in one variable.
- Apply linear equations in one variable to solve representative problems and real-world scenarios.
- Demonstrate mastery of linear equations in one variable through written, oral, or project-based work.
Key Topics: Linear Equations in One Variable — concept introduction, core terminology, foundational skills, and connections to prior modules.
Activities & Practice: Direct instruction, guided practice, independent practice, small projects, and discussion. Students keep a course notebook and complete short weekly reflections.
Materials & Resources: Textbook chapter readings, instructor video lessons, supplementary articles, and online practice tools. Materials list is published at the start of each module.
Assessment: Module 2 assessment includes a quiz on key concepts (20%), a graded application activity or short project (40%), and contribution to discussion or peer review (10%). Cumulative midterm and final exams contribute to the remaining 30% of the course grade.
Module 3 — Linear Inequalities and Compound Inequalities
Time on Task: Weeks 9–12 (16–24 hours of instruction and practice)
Learning Objectives:
- Explain the core concepts and vocabulary of linear inequalities and compound inequalities.
- Apply linear inequalities and compound inequalities to solve representative problems and real-world scenarios.
- Demonstrate mastery of linear inequalities and compound inequalities through written, oral, or project-based work.
Key Topics: Linear Inequalities and Compound Inequalities — concept introduction, core terminology, foundational skills, and connections to prior modules.
Activities & Practice: Direct instruction, guided practice, independent practice, small projects, and discussion. Students keep a course notebook and complete short weekly reflections.
Materials & Resources: Textbook chapter readings, instructor video lessons, supplementary articles, and online practice tools. Materials list is published at the start of each module.
Assessment: Module 3 assessment includes a quiz on key concepts (20%), a graded application activity or short project (40%), and contribution to discussion or peer review (10%). Cumulative midterm and final exams contribute to the remaining 30% of the course grade.
Module 4 — Functions and Graphs
Time on Task: Weeks 13–16 (16–24 hours of instruction and practice)
Learning Objectives:
- Explain the core concepts and vocabulary of functions and graphs.
- Apply functions and graphs to solve representative problems and real-world scenarios.
- Demonstrate mastery of functions and graphs through written, oral, or project-based work.
Key Topics: Functions and Graphs — concept introduction, core terminology, foundational skills, and connections to prior modules.
Activities & Practice: Direct instruction, guided practice, independent practice, small projects, and discussion. Students keep a course notebook and complete short weekly reflections.
Materials & Resources: Textbook chapter readings, instructor video lessons, supplementary articles, and online practice tools. Materials list is published at the start of each module.
Assessment: Module 4 assessment includes a quiz on key concepts (20%), a graded application activity or short project (40%), and contribution to discussion or peer review (10%). Cumulative midterm and final exams contribute to the remaining 30% of the course grade.
Module 5 — Systems of Linear Equations
Time on Task: Weeks 17–20 (16–24 hours of instruction and practice)
Learning Objectives:
- Explain the core concepts and vocabulary of systems of linear equations.
- Apply systems of linear equations to solve representative problems and real-world scenarios.
- Demonstrate mastery of systems of linear equations through written, oral, or project-based work.
Key Topics: Systems of Linear Equations — concept introduction, core terminology, foundational skills, and connections to prior modules.
Activities & Practice: Direct instruction, guided practice, independent practice, small projects, and discussion. Students keep a course notebook and complete short weekly reflections.
Materials & Resources: Textbook chapter readings, instructor video lessons, supplementary articles, and online practice tools. Materials list is published at the start of each module.
Assessment: Module 5 assessment includes a quiz on key concepts (20%), a graded application activity or short project (40%), and contribution to discussion or peer review (10%). Cumulative midterm and final exams contribute to the remaining 30% of the course grade.
Module 6 — Exponents and Polynomials
Time on Task: Weeks 21–24 (16–24 hours of instruction and practice)
Learning Objectives:
- Explain the core concepts and vocabulary of exponents and polynomials.
- Apply exponents and polynomials to solve representative problems and real-world scenarios.
- Demonstrate mastery of exponents and polynomials through written, oral, or project-based work.
Key Topics: Exponents and Polynomials — concept introduction, core terminology, foundational skills, and connections to prior modules.
Activities & Practice: Direct instruction, guided practice, independent practice, small projects, and discussion. Students keep a course notebook and complete short weekly reflections.
Materials & Resources: Textbook chapter readings, instructor video lessons, supplementary articles, and online practice tools. Materials list is published at the start of each module.
Assessment: Module 6 assessment includes a quiz on key concepts (20%), a graded application activity or short project (40%), and contribution to discussion or peer review (10%). Cumulative midterm and final exams contribute to the remaining 30% of the course grade.
Module 7 — Factoring and Quadratic Equations
Time on Task: Weeks 25–28 (16–24 hours of instruction and practice)
Learning Objectives:
- Explain the core concepts and vocabulary of factoring and quadratic equations.
- Apply factoring and quadratic equations to solve representative problems and real-world scenarios.
- Demonstrate mastery of factoring and quadratic equations through written, oral, or project-based work.
Key Topics: Factoring and Quadratic Equations — concept introduction, core terminology, foundational skills, and connections to prior modules.
Activities & Practice: Direct instruction, guided practice, independent practice, small projects, and discussion. Students keep a course notebook and complete short weekly reflections.
Materials & Resources: Textbook chapter readings, instructor video lessons, supplementary articles, and online practice tools. Materials list is published at the start of each module.
Assessment: Module 7 assessment includes a quiz on key concepts (20%), a graded application activity or short project (40%), and contribution to discussion or peer review (10%). Cumulative midterm and final exams contribute to the remaining 30% of the course grade.
Module 8 — Real-World Modeling with Algebra
Time on Task: Weeks 29–32 (16–24 hours of instruction and practice)
Learning Objectives:
- Explain the core concepts and vocabulary of real-world modeling with algebra.
- Apply real-world modeling with algebra to solve representative problems and real-world scenarios.
- Demonstrate mastery of real-world modeling with algebra through written, oral, or project-based work.
Key Topics: Real-World Modeling with Algebra — concept introduction, core terminology, foundational skills, and connections to prior modules.
Activities & Practice: Direct instruction, guided practice, independent practice, small projects, and discussion. Students keep a course notebook and complete short weekly reflections.
Materials & Resources: Textbook chapter readings, instructor video lessons, supplementary articles, and online practice tools. Materials list is published at the start of each module.
Assessment: Module 8 assessment includes a quiz on key concepts (20%), a graded application activity or short project (40%), and contribution to discussion or peer review (10%). Cumulative midterm and final exams contribute to the remaining 30% of the course grade.
Assessment & Grading
Course grade is calculated from:
- Module quizzes and weekly assignments — 30%
- Module projects, papers, or labs — 30%
- Midterm exam — 15%
- Final exam or capstone — 20%
- Class participation, discussion, and engagement — 5%
The final letter grade is recorded on the AIS transcript using a standard A–F scale (A: 90–100%, B: 80–89%, C: 70–79%, D: 60–69%, F: below 60%). Students must earn a passing grade (60% or higher) to receive course credit.
Materials & Resources
Students will need: textbook (provided digitally), notebook for note-taking, internet access for online portal and video lessons, and any subject-specific tools listed at the start of each module (e.g., calculator, lab supplies, art materials). All required materials are listed in the course portal before each module begins.
Academic Integrity & Conduct
All work must be the student's own. AIS follows standard academic-integrity expectations: original work, proper citation, no AI-generated submissions presented as original work, and respectful engagement with peers and instructors. Violations may result in loss of credit.
Standards Alignment
This course aligns with: algebra 1, linear equations, inequalities, polynomials, factoring, quadratic equations, functions, graphing, homeschool, SCED 02052 (Algebra I), Credit: 1.0, Hours: 120. Specific lesson-level alignment is documented in the instructor's pacing guide.