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Coming soon Grades 6–7 For homeschool families

Pre-Algebra

Everything students need to enter Algebra 1 with confidence.

A complete pre-algebra course, from whole numbers and the language of algebra through integers, fractions, decimals, percents, equations, geometry, data and a first look at polynomials and graphing. It meets students where they are, builds algebraic thinking early, and checks mastery before moving on.

Level
Grades 6–7
Units
12
Lessons
59
Read the syllabus Join the founding families

Included

What’s in Pre-Algebra the course.

  • A readable textbook

    Short sections in plain language, with figures and examples every few paragraphs.

  • Worked examples

    Every new idea comes with an example that shows each step, including the one students usually miss.

  • Video lessons

    Short animated lessons from Orbital, our math video studio, that show the idea moving.

  • Homework practice

    Every lesson has homework, from skill drills to word problems, with answers and full solutions to check work.

  • Mastery checks

    A check at the end of each unit. Students move on at 85% or higher, and review what they missed before a retake.

  • Progress view

    See what’s finished, how each mastery check went and what to review next.

Syllabus

12 units, 59 lessons, 123 objectives.

Open any section for the details. Every lesson lists its objectives and the Arizona / Common Core and Texas TEKS standards it covers.

01Course description

Meridian Pre-Algebra is a complete, self-paced course that prepares students for Algebra 1 in one school year. It is built on the grade 6 and 7 math standards, with selected grade 8 topics, and written and tested by Clayton Ragsdale, a college mathematics instructor.

Standards
Grade 6–7, plus selected grade 8 topics
Typically taken
Grade 6, 7 or 8
Length
36 weeks, 4 days a week
Daily time
30–45 minutes
Prerequisites
Whole-number operations and basic fractions
Format
Online, self-paced, parent-supervised

By the end of the course, students can:

  1. 01Compute fluently with integers, fractions, decimals and percents, and explain why the procedures work.
  2. 02Translate words into expressions and equations, and solve one-, two- and multi-step linear equations.
  3. 03Use ratios, rates, proportions and percents to solve real-world problems, including tax, discounts and simple interest.
  4. 04Apply properties of real numbers and the rules of exponents, and write numbers in scientific notation.
  5. 05Solve geometry problems with angles, triangles, the Pythagorean theorem, area, circumference, volume and surface area.
  6. 06Summarize data with mean, median and mode, read and build data displays, and find simple probabilities.
  7. 07Add, subtract and multiply polynomials and begin factoring.
  8. 08Graph linear equations on the coordinate plane and describe slope and intercepts.
02Scope and sequence, with objectives and standards

Standards marked grade 8 or Algebra 1 are enrichment beyond the grade 6–7 core; codes from grades 3–5 are review.

01 Whole Numbers

  1. 1.1Place Value and Number Sense

    AZ 4.NBT.A.2AZ 5.NBT.A.1 TEKS 4.2(B)TEKS 4.2(C)
    • Read and write whole numbers in standard, word and expanded form.
    • Compare and order whole numbers using place value and the symbols <, > and =.

  2. 1.2Addition and Subtraction

    AZ 4.NBT.B.4 TEKS 4.4(A)TEKS 5.3(A)
    • Add and subtract multi-digit whole numbers with the standard algorithm.
    • Check sums and differences with estimation and inverse operations.

  3. 1.3Multiplication and Division

    AZ 5.NBT.B.5AZ 6.NS.B.2AZ 4.OA.A.3 TEKS 5.3(B)TEKS 5.3(C)TEKS 4.4(H)TEKS 6.3(E)
    • Multiply multi-digit whole numbers fluently.
    • Divide multi-digit whole numbers with the standard algorithm and interpret remainders in context.

  4. 1.4Order of Operations

    AZ 6.EE.A.1AZ 5.OA.A.1 TEKS 6.7(A)TEKS 5.4(E)
    • Evaluate numerical expressions with grouping symbols and whole-number exponents using the order of operations.
    • Insert grouping symbols to make an expression equal a given value.

  5. 1.5Rounding and Estimation

    AZ 4.NBT.A.3AZ 7.EE.B.3 TEKS 4.2(D)TEKS 5.3(A)TEKS 6.1(B)
    • Round whole numbers to any place.
    • Use estimation to predict results and judge whether an answer is reasonable.
  6. ✓ Unit 1 mastery check (pass at 85%)
02 The Language of Algebra

  1. 2.1Variables and Expressions

    AZ 6.EE.A.2aAZ 6.EE.A.2bAZ 6.EE.B.6 TEKS 6.7(B)
    • Use a variable to stand for an unknown or changing quantity.
    • Identify the terms, coefficients and constants of an expression.

  2. 2.2Evaluating Expressions

    AZ 6.EE.A.2c TEKS 6.7(A)TEKS 6.8(D)TEKS 7.4(A)
    • Evaluate algebraic expressions for given values of their variables.
    • Evaluate formulas from real-world situations, such as area and distance.

  3. 2.3Translating Words to Math

    AZ 6.EE.A.2aAZ 6.EE.B.6AZ 6.EE.B.7AZ 6.EE.B.8 TEKS 6.7(B)TEKS 6.9(A)
    • Translate verbal phrases into algebraic expressions.
    • Translate verbal sentences into equations and inequalities.

  4. 2.4Factors, Multiples, and Primes

    AZ 5.OA.B.4AZ 6.NS.B.4aAZ 6.NS.B.4bAZ 6.NS.B.4c TEKS 5.4(A)TEKS 6.7(A)TEKS 6.7(D)
    • Classify whole numbers as prime or composite and write prime factorizations.
    • Find the greatest common factor and least common multiple of two whole numbers.
    • Use the distributive property to factor out a common factor, such as 36 + 8 = 4(9 + 2).
  5. ✓ Unit 2 mastery check (pass at 85%)
03 Integers

  1. 3.1Introduction to Integers

    AZ 6.NS.C.5AZ 6.NS.C.6aAZ 6.NS.C.6cAZ 6.NS.C.7aAZ 6.NS.C.7bAZ 6.NS.C.7c TEKS 6.2(B)TEKS 6.2(C)TEKS 6.2(D)
    • Use integers to describe real-world quantities such as temperature, elevation and money.
    • Place, compare and order integers on a number line.
    • Find and interpret absolute value as distance from zero.

  2. 3.2Adding and Subtracting Integers

    AZ 7.NS.A.1bAZ 7.NS.A.1c TEKS 6.3(C)TEKS 6.3(D)TEKS 7.3(A)
    • Add integers using a number line and the rules for signs.
    • Subtract integers by adding the opposite.
    • Find the distance between two integers using absolute value.

  3. 3.3Multiplying and Dividing Integers

    AZ 7.NS.A.2aAZ 7.NS.A.2b TEKS 6.3(C)TEKS 6.3(D)TEKS 7.3(A)
    • Multiply and divide integers using the rules for signs.
    • Explain why the product of two negatives is positive.

  4. 3.4Order of Operations with Integers

    AZ 7.NS.A.3 TEKS 6.3(D)TEKS 7.3(A)TEKS 7.3(B)
    • Evaluate expressions with integers using the order of operations.
    • Solve real-world problems involving integer operations.

  5. 3.5Solving Equations with Integers

    AZ 6.EE.B.5AZ 6.EE.B.7AZ 7.EE.B.4a TEKS 6.10(A)TEKS 6.10(B)
    • Solve one-step equations whose solutions are integers.
    • Check a solution by substituting it into the equation.
  6. ✓ Unit 3 mastery check (pass at 85%)
04 Fractions

  1. 4.1Understanding Fractions

    AZ 3.NF.A.1AZ 3.NF.A.2AZ 6.NS.C.6cAZ 6.NS.C.7aAZ 6.NS.C.7b TEKS 4.3(G)TEKS 6.2(C)
    • Represent fractions as parts of a whole, parts of a set and points on a number line.
    • Place positive and negative fractions on a number line and compare them.

  2. 4.2Equivalent Fractions and Simplifying

    AZ 4.NF.A.1AZ 6.NS.B.4a TEKS 4.3(C)TEKS 6.4(G)
    • Generate equivalent fractions by multiplying or dividing by a form of one.
    • Write fractions in simplest form using the GCF.

  3. 4.3Multiplying and Dividing Fractions

    AZ 5.NF.B.4AZ 5.NF.B.6AZ 6.NS.A.1 TEKS 6.3(A)TEKS 6.3(E)
    • Multiply fractions and mixed numbers.
    • Divide fractions by multiplying by the reciprocal and explain why it works.
    • Solve word problems that require dividing fractions.

  4. 4.4Adding and Subtracting Fractions

    AZ 5.NF.A.1AZ 7.NS.A.1 TEKS 5.3(K)TEKS 7.3(A)
    • Add and subtract fractions with unlike denominators using a common denominator.
    • Add and subtract positive and negative fractions.

  5. 4.5Mixed Numbers and Complex Fractions

    AZ 5.NF.A.1AZ 5.NF.B.6AZ 7.NS.A.3 TEKS 7.3(A)TEKS 7.3(B)
    • Convert between mixed numbers and improper fractions.
    • Compute with mixed numbers and simplify complex fractions.

  6. 4.6Solving Equations with Fractions

    AZ 6.EE.B.7AZ 7.EE.B.4a TEKS 6.10(A)TEKS 7.11(A)
    • Solve one- and two-step equations that contain fractions.
    • Clear fractions from an equation by multiplying by the least common denominator.
  7. ✓ Unit 4 mastery check (pass at 85%)
05 Decimals

  1. 5.1Decimal Concepts

    AZ 5.NBT.A.3AZ 5.NBT.A.4 TEKS 5.2(A)TEKS 5.2(B)TEKS 5.2(C)TEKS 6.2(D)
    • Read, write and compare decimals using place value.
    • Round decimals to a given place.

  2. 5.2Operations with Decimals

    AZ 6.NS.B.3 TEKS 5.3(K)TEKS 6.3(E)
    • Add, subtract, multiply and divide multi-digit decimals fluently.
    • Solve real-world problems with money and measurement using decimals.

  3. 5.3Decimals and Fractions

    AZ 7.NS.A.2d TEKS 6.4(G)
    • Convert fractions to decimals using long division.
    • Identify terminating and repeating decimals.

  4. 5.4Solving Equations with Decimals

    AZ 6.EE.B.7AZ 7.EE.B.4a TEKS 6.10(A)TEKS 7.10(A)TEKS 7.11(A)
    • Solve one- and two-step equations with decimal coefficients and constants.
    • Solve real-world problems by writing and solving decimal equations.

  5. 5.5Square Roots

    AZ 8.EE.A.2aAZ 8.NS.A.2 TEKS 8.2(B)
    • Find square roots of perfect squares.
    • Estimate square roots of non-perfect squares and place them on a number line.
  6. ✓ Unit 5 mastery check (pass at 85%)
06 Ratios, Proportions, and Percents

  1. 6.1Ratios and Rates

    AZ 6.RP.A.1AZ 6.RP.A.2AZ 6.RP.A.3bAZ 7.RP.A.1 TEKS 6.4(B)TEKS 6.4(C)TEKS 6.4(D)TEKS 7.4(B)
    • Write ratios in three forms and describe ratio relationships.
    • Find unit rates, including unit rates with fractions, and use them to compare.

  2. 6.2Proportions

    AZ 6.RP.A.3aAZ 7.RP.A.2aAZ 7.RP.A.2b TEKS 6.5(A)TEKS 7.4(A)TEKS 7.4(C)TEKS 8.5(F)
    • Decide whether two quantities are proportional using tables and graphs.
    • Find the constant of proportionality and solve proportions.

  3. 6.3Understanding Percents

    AZ 6.RP.A.3c TEKS 6.4(E)TEKS 6.4(F)TEKS 6.4(G)TEKS 6.5(C)
    • Understand a percent as a rate per 100.
    • Convert among percents, fractions and decimals.

  4. 6.4Percent Problems

    AZ 6.RP.A.3cAZ 7.RP.A.3 TEKS 6.5(B)TEKS 7.4(D)
    • Find a percent of a number, a whole from a part, and what percent one number is of another.
    • Find percent increase and decrease.

  5. 6.5Sales Tax, Discounts, and Simple Interest

    AZ 7.RP.A.3 TEKS 7.4(D)TEKS 7.13(A)TEKS 7.13(E)TEKS 7.13(F)
    • Calculate sales tax, tips, discounts and markups.
    • Calculate simple interest and compare it with compound interest.

  6. 6.6Proportions and Percent Applications

    AZ 7.RP.A.3AZ 7.G.A.1 TEKS 7.4(D)TEKS 7.5(C)
    • Solve multi-step ratio and percent problems.
    • Use scale drawings to find actual lengths and areas.
  7. ✓ Unit 6 mastery check (pass at 85%)
07 Properties of Real Numbers

  1. 7.1Rational and Irrational Numbers

    AZ 8.NS.A.1AZ 8.NS.A.2 TEKS 6.2(A)TEKS 7.2TEKS 8.2(A)TEKS 8.2(D)
    • Classify numbers as natural, whole, integer, rational or irrational.
    • Compare and order rational and irrational numbers.

  2. 7.2Commutative and Associative Properties

    AZ 6.EE.A.3AZ 6.EE.A.4 TEKS 6.7(C)TEKS 6.7(D)
    • Use the commutative and associative properties to rewrite expressions.
    • Use these properties to compute mentally.

  3. 7.3The Distributive Property

    AZ 6.EE.A.3AZ 7.EE.A.1AZ 7.EE.A.2 TEKS 6.7(D)TEKS A.10(D)
    • Expand expressions with the distributive property.
    • Combine like terms to simplify expressions.
    • Factor linear expressions with rational coefficients.

  4. 7.4Properties of Identity, Inverses, and Zero

    AZ 6.EE.A.3AZ 7.NS.A.1bAZ 7.NS.A.1cAZ 7.NS.A.2c TEKS 6.3(A)TEKS 6.7(D)
    • Identify additive and multiplicative identities and inverses.
    • Use the zero property and inverse operations to simplify and solve.
  5. ✓ Unit 7 mastery check (pass at 85%)
08 Solving Equations

  1. 8.1One-Step Equations

    AZ 6.EE.B.5AZ 6.EE.B.7 TEKS 6.9(A)TEKS 6.10(A)
    • Solve one-step equations with inverse operations.
    • Write and solve one-step equations for real-world problems.

  2. 8.2Two-Step Equations

    AZ 7.EE.B.4a TEKS 7.10(A)TEKS 7.11(A)
    • Solve two-step equations of the form px + q = r and p(x + q) = r.
    • Write and solve two-step equations for word problems.

  3. 8.3Multi-Step Equations

    AZ 7.EE.B.4aAZ 8.EE.C.7bAZ A1.A-REI.A.1 TEKS 7.11(A)TEKS 7.11(B)TEKS A.5(A)
    • Solve equations that require the distributive property and combining like terms.
    • Check solutions and explain each step.

  4. 8.4Equations with Variables on Both Sides

    AZ 8.EE.C.7aAZ 8.EE.C.7b TEKS 8.8(A)TEKS 8.8(C)TEKS A.5(A)
    • Solve equations with variables on both sides.
    • Recognize equations with one solution, no solution and infinitely many solutions.

  5. 8.5Equations with Fraction and Decimal Coefficients

    AZ 7.EE.B.4aAZ 8.EE.C.7b TEKS 7.11(A)TEKS 8.8(C)
    • Solve equations with fraction and decimal coefficients.
    • Choose an efficient strategy, such as clearing fractions first.
  6. ✓ Unit 8 mastery check (pass at 85%)
09 Geometry and Measurement

  1. 9.1Angles and Triangles

    AZ 7.G.B.5AZ 8.G.A.5 TEKS 6.8(A)TEKS 7.11(C)TEKS 8.8(D)
    • Use supplementary, complementary, vertical and adjacent angles to find unknown angles.
    • Use the triangle angle sum to find unknown angles.

  2. 9.2The Pythagorean Theorem

    AZ 8.G.B.7AZ 8.G.B.8 TEKS 8.7(C)TEKS 8.7(D)
    • Use the Pythagorean theorem to find a missing side of a right triangle.
    • Apply the theorem to real-world problems and to distance on the coordinate plane.

  3. 9.3Perimeter and Area

    AZ 6.G.A.1AZ 7.G.B.6 TEKS 6.8(B)TEKS 6.8(D)TEKS 7.9(C)
    • Find the area of triangles, parallelograms and trapezoids.
    • Find the perimeter and area of composite figures.

  4. 9.4Circles

    AZ 7.G.B.4 TEKS 7.5(B)TEKS 7.8(C)TEKS 7.9(B)TEKS 7.9(C)
    • Find the circumference and area of a circle.
    • Solve problems with semicircles and composite figures that include circles.

  5. 9.5Volume and Surface Area

    AZ 6.G.A.2AZ 6.G.A.4AZ 7.G.B.6AZ 8.G.C.9 TEKS 7.8(A)TEKS 7.8(B)TEKS 7.9(A)TEKS 7.9(D)TEKS 8.7(A)
    • Find the volume and surface area of prisms and pyramids.
    • Find the volume of cylinders, cones and spheres.

  6. 9.6Solving Geometry Problems

    AZ 7.G.B.6AZ 8.G.C.9 TEKS 7.9(A)TEKS 7.9(C)TEKS 7.9(D)TEKS 8.7(A)TEKS 8.7(B)
    • Solve multi-step real-world problems with area, surface area and volume.
    • Choose the right formula and units for a problem.
  7. ✓ Unit 9 mastery check (pass at 85%)
10 Data and Statistics

  1. 10.1Collecting and Organizing Data

    AZ 6.SP.A.1AZ 6.SP.B.5aAZ 6.SP.B.5bAZ 7.SP.A.1 TEKS 6.12(D)TEKS 6.13(B)TEKS 7.6(F)TEKS 8.11(C)
    • Recognize statistical questions and collect data to answer them.
    • Organize data in frequency tables and recognize when a sample is representative.

  2. 10.2Mean, Median, and Mode

    AZ 6.SP.A.3AZ 6.SP.B.5cAZ 6.SP.B.5d TEKS 6.12(C)TEKS 6.12(D)
    • Find the mean, median, mode and range of a data set.
    • Choose the measure of center that best describes a data set.

  3. 10.3Graphs and Data Displays

    AZ 6.SP.A.2AZ 6.SP.B.4 TEKS 6.12(A)TEKS 6.12(B)TEKS 6.13(A)
    • Make and interpret dot plots, histograms and box plots.
    • Describe the center, spread and shape of a distribution.

  4. 10.4Probability Basics

    AZ 7.SP.C.5AZ 7.SP.C.6AZ 7.SP.C.7 TEKS 7.6(C)TEKS 7.6(D)TEKS 7.6(H)TEKS 7.6(I)
    • Find the probability of simple events as a number from 0 to 1.
    • Compare experimental and theoretical probability.
  5. ✓ Unit 10 mastery check (pass at 85%)
11 Introduction to Polynomials

  1. 11.1Exponent Rules

    AZ 8.EE.A.1 TEKS A.11(B)
    • Apply the product, quotient and power rules for exponents.
    • Simplify expressions with zero and negative exponents.

  2. 11.2Adding and Subtracting Polynomials

    AZ 7.EE.A.1AZ A1.A-SSE.A.1aAZ A1.A-APR.A.1 TEKS A.10(A)
    • Identify the degree and terms of a polynomial.
    • Add and subtract polynomials by combining like terms.

  3. 11.3Multiplying Polynomials

    AZ A1.A-APR.A.1AZ A1.A-SSE.A.2 TEKS A.10(B)TEKS A.10(D)
    • Multiply a polynomial by a monomial.
    • Multiply two binomials.

  4. 11.4Scientific Notation

    AZ 8.EE.A.3AZ 8.EE.A.4 TEKS 8.2(C)
    • Write very large and very small numbers in scientific notation.
    • Multiply and divide numbers in scientific notation and compare their sizes.

  5. 11.5Introduction to Factoring

    AZ 6.EE.A.3AZ 7.EE.A.1AZ A1.A-SSE.A.2 TEKS 6.7(D)TEKS A.10(D)
    • Find the greatest common factor of the terms of a polynomial.
    • Factor out the GCF from a polynomial.
  6. ✓ Unit 11 mastery check (pass at 85%)
12 Graphing

  1. 12.1The Coordinate Plane

    AZ 6.NS.C.6bAZ 6.NS.C.6cAZ 6.NS.C.8AZ 6.G.A.3 TEKS 6.11
    • Plot and name points in all four quadrants.
    • Find horizontal and vertical distances between points.

  2. 12.2Graphing Linear Equations

    AZ 6.EE.C.9AZ 7.RP.A.2dAZ 8.EE.B.5AZ 8.F.A.3 TEKS 7.7TEKS 8.4(B)TEKS 8.5(A)TEKS 8.5(B)
    • Make a table of values from a linear equation and graph it.
    • Graph proportional relationships and interpret the point (1, r).

  3. 12.3Intercepts

    AZ 8.EE.B.6AZ 8.F.B.4AZ A1.F-IF.B.4 TEKS 8.4(C)TEKS A.3(C)
    • Find the x- and y-intercepts of a line from its equation or graph.
    • Graph a line using its intercepts.

  4. 12.4Introduction to Slope

    AZ 8.EE.B.6AZ 8.F.B.4 TEKS 8.4(A)TEKS 8.4(C)
    • Find slope from a graph, a table or two points.
    • Interpret slope as a rate of change in context.
  5. ✓ Unit 12 mastery check and final assessment (pass at 85%)
03Assessment and grading

Tracked, not graded

Homework practice

Every lesson

Answers and full solutions after each attempt.

70% of the grade

Unit mastery check

End of each of the 12 units

Pass at 85% or higher; unlimited retakes with new questions after reviewing what was missed.

30% of the grade

Final assessment

After Unit 12

Cumulative across all 12 units.

  • Mastery: students move to the next unit at 85% or higher on its mastery check. Each result shows which objectives were missed, so review is targeted.
  • Grade scale: A 90–100, B 80–89, C 70–79, D 60–69. The best mastery-check score counts.
  • Parents decide: parents remain the grading authority for their homeschool and see every attempt and score.
04Pacing: 36 weeks, 4 days a week

A typical week

  1. Day 1Lesson A: read the section, watch the video, work the examples
  2. Day 2Lesson A: homework practice and check solutions
  3. Day 3Lesson B: read, watch, work the examples
  4. Day 4Lesson B: homework practice, or the mastery check at the end of a unit

30–45 minutes a day, about 90–110 hours for the year. A 5-day plan finishes in about 29 weeks; a summer plan of one lesson a day takes about 15.

Weeks per unit

  1. 1. Whole Numbers3 wk
  2. 2. The Language of Algebra2 wk
  3. 3. Integers3 wk
  4. 4. Fractions3 wk
  5. 5. Decimals3 wk
  6. 6. Ratios, Proportions, and Percents3 wk
  7. 7. Properties of Real Numbers2 wk
  8. 8. Solving Equations3 wk
  9. 9. Geometry and Measurement3 wk
  10. 10. Data and Statistics2 wk
  11. 11. Introduction to Polynomials3 wk
  12. 12. Graphing2 wk
  13. Catch-up and review2 wk
  14. Final review and assessment2 wk
05Standards alignment

Arizona and Common Core: the course covers the grade 6 and 7 standards for ratios and proportional relationships, the number system, expressions and equations, geometry, and statistics and probability. Each lesson’s codes are listed in the scope and sequence.

Grade 8 topics included: irrational numbers, square roots, integer exponents, scientific notation, equations with variables on both sides, the Pythagorean theorem, volume of cylinders, cones and spheres, and an introduction to slope.

Texas TEKS: every lesson is mapped to specific TEKS student expectations (for example 7.3(A)), plus Algebra I where polynomials go beyond grade 8. Codes marked “review” revisit grade 3–5 skills.

Verified: standards were checked against the official Arizona Department of Education and Texas Education Agency documents in October 2026.

Not in the core course: grade 8 functions, systems of linear equations and transformations come in the planned Grade 8 extension.

06Planned add-ons

AI tutor

Hints and guiding questions instead of answers. Planned as an add-on after launch.

Grade 8 extension

Functions, systems of linear equations, transformations and repeating decimals as fractions, for families who want full grade 8 coverage.

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