Math With Avrila

Homeschool Course Guide

Hello mathematicians, puzzlers, and other curious people!

If you’re homeschooling or thinking about homeschooling in the future, and you’d like math class to be one less thing on your list, you might wonder how my monthly unit modules translate into classes for transcripts and other requirements. In general, 8-9 modules cover a year’s study. While schools and organizations that examine your transcript may have their own requirements and preferences, this is one reasonable way you can handle that.

Please let me know if there are any other classes you have questions about.

Calc You Later!

These classes are not typically credit-bearing for high school, but might be considered for purposes like applying to selective junior high or high schools, state compliance, or high school programs including below grade level coursework.

For learners who have already completed a thorough and modern elementary math curriculum, the first class is optional, and will probably be too easy for learners who have excelled with elementary math. It includes a good deal of review and consolidation of key elementary math topics, and is suitable for learners who missed mastery of important topics because of less thorough schools or doing less bookwork at home, as well as those who prefer another year to gain confidence with the basics. Younger advanced learners who want to accelerate by skipping past a year or two of elementary math can also benefit from taking this class to avoid learning gaps from the skipped courses.

Arithmetic and Applications

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Available for full-year enrollment at The Scholar Cube.

  • Problem Solving and Graphs
    • Upcoming Outschool section, beginning August 11
    • asynchronous, to be released by August 11
  • Decimal Calculations and Angles
    • Upcoming Outschool section, beginning September 8
    • asynchronous, to be released by September 8
  • More Decimal Calculations and Patterns
    • Upcoming Outschool section, beginning October 13
    • asynchronous, to be released by October 13
  • Area, Perimeter, and Fractions
    • Upcoming Outschool section, beginning November 10
    • asynchronous, to be released by November 10
  • Collecting Data and Calculations
  • Patterns, Time, and Negative Numbers
  • Linear Equations and Parts of Wholes
  • Data, Scale, and Fractions
  • Probability and Volume

General Mathematics

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Available for full-year enrollment at The Scholar Cube.

  • Area and Surface Area
  • Ratios, Rates, and Percentages
    • Upcoming Outschool session, beginning September 8
    • asynchronous, to be released by September 8
  • Fractions and Decimals
    • Upcoming Outschool session, beginning October 13
    • asynchronous, to be released by October 13
  • Equations and Expressions
    • Upcoming Outschool session, beginning November 10
    • asynchronous, to be released by November 10
  • Proportions
  • Percentage Changes
  • Rational Numbers
  • Data and Distributions

Prealgebra

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  • Transformations and Congruence
  • Scale, Similarity, and Slope
  • Writing and Solving Equations
  • Expressions, Equations, and Inequalities
  • Linear Relationships
  • Introduction to Functions
  • Solid Geometry
  • Exponents and Scientific Notation
  • Roots and Other Irrational Numbers

After Prealgebra

Junior high learners will often take some modules toward their first high school math class, either Algebra 1 or Integrated Math 1. If learners will continue homeschooling through high school, the difference between the two is unimportant at this point, as is the number of high school modules they complete in junior high. However, if they will enroll in a conventional high school, they should coordinate their strategy with that school’s enrollment counselor, or equivalent, if getting credit from homeschooling included on their high school transcript or considered for placement beyond introductory level is a goal.

Even if neither of those goals applies, learners who finish the junior high math curriculum early and will attend a conventional high school should continue to whatever number of high school modules the available time permits, so that the inevitable challenges of any major transition will be relieved by their math class being easier because it is review, rather than further stressed by their math class being additionally challenging because they took a longer break and forgot more than their new classmates.

The high school curriculum’s modular design allows for either acceleration or slow-and-steady growth toward college readiness and lifelong understanding.

For transcript purposes, students/families should choose one path or the other rather than mix classes from the two paths. It is not essential for all units from each class to be taken consecutively in the stated order — some units can be studied in various orders.

AGA (Traditional, Algebra-Geometry-Algebra) Path

Algebra 1

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  • Sequences and Functions
  • Linear and Exponential Functions
  • Features of Functions
  • Equations and Inequalities
  • Systems of Equations and Inequalities
  • Quadratic Functions
  • Structure of Expressions
  • More Functions, More Features
  • Modeling Data

Geometry

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on Geometry
  • Transformations and Symmetry
  • Congruence, Construction, and Proof
    • Upcoming Outschool section starting September 8
  • Geometric Figures
    • Upcoming Outschool section starting October 13
  • Circles
    • Upcoming Outschool section starting November 10
  • Similarity and Right Triangle Trigonometry
  • Connecting Algebra and Geometry
  • Circles and Other Conic Sections
  • Probability

Algebra 2

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  • Functions and their Inverses
  • Quadratic Equations
  • Logarithmic Functions
  • Polynomial Functions
  • Rational Functions and Expressions
  • Modeling Periodic Behavior
  • Trigonometric Functions, Equations, and Identities
  • Modeling with Functions
  • Statistics

Integrated Math Path

Integrated Math 1

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on integrated math 1
  • Sequences and Functions
  • Linear and Exponential Functions
  • Features of Functions
  • Equations and Inequalities
  • Systems of Equations and Inequalities
  • Transformations and Symmetry
  • Congruence, Construction, and Proof
  • Connecting Algebra and Geometry
  • Modeling Data

Integrated Math 2

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on Integrated Math 2
  • Quadratic Functions
  • Structure of Expressions
  • Quadratic Equations
  • More Functions, More Features
  • Geometric Figures
  • Similarity and Right Triangle Trigonometry
  • Circles from a Geometric Perspective
  • Circles and Other Conics
  • Probability

Integrated Math 3

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on Integrated Math 3
  • Functions and their Inverses
  • Logarithmic Functions
  • Polynomial Functions
  • Rational Expressions and Functions
  • Modeling with Geometry
  • Modeling Periodic Behavior
  • Trig Functions, Equations, and Identities
  • Modeling with Functions
  • Statistics

Many universities expect learners to complete four credits of high school mathematics. Choosing a fourth credit also allows learners to specialize based on their interests and goals.

Precalculus

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A common 1-credit high school capstone class, which summarizes and expands upon key algebra topics from previous coursework. Potentially college credit bearing through a CLEP or AP exam.

  • Beginning-of-Year Review (optional, take an additional topics unit if skipping)
    • Upcoming Outschool section, beginning August 11
    • asynchronous, available by August 11
  • Function Basics and Linear Functions
    • Upcoming Outschool section, beginning September 8
    • asynchronous, available by September 8
  • Nonlinear Functions
    • Upcoming Outschool section, beginning October 13
    • asynchronous, available by October 13
  • Systems of Equations and Further Nonlinear Functions
    • Upcoming Outschool section, beginning November 10
    • asynchronous, available by November 10
  • Intro to Trigonometry
  • Further Trigonometry
  • Geometry, Analytically
  • One of these topics units (two without Beginning-of-Year Review):
    • Sequences and Series
    • Combinatorics and Probability
    • A Few Ideas From Calculus

Calculus 1

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on Calculus

Potentially college credit bearing through a CLEP or AP exam. Usually this will be a one semester class for a half credit.

  • Limits
  • Introduction to Derivatives
  • Applications of Derivatives
  • Antiderivatives and Introduction to Integration

Many universities expect learners to complete four credits of high school mathematics. Choosing a fourth credit also allows learners to specialize based on their interests and goals.

Precalculus (1 credit, potentially college credit bearing through a CLEP or AP exam)

  • Beginning-of-Year Review (optional, take an additional topics unit if skipping)
    • Upcoming Outschool Section
  • Function Basics and Linear Functions
  • Nonlinear Functions
  • Systems of Equations and Further Nonlinear Functions
  • Intro to Trigonometry
  • Further Trigonometry
  • Geometry, Analytically
  • One of these topics units (two without Beginning-of-Year Review):
    • Sequences and Series
    • Combinatorics and Probability
    • A Few Ideas From Calculus

Calculus 1 (0.5 credit, potentially college credit bearing through CLEP or AP exams)

  • Limits
  • Introduction to Derivatives
  • Applications of Derivatives
  • Antiderivatives and Introduction to Integration