30 written chapters · 1 published teaching videos

Grade 9, one chapter at a time.

Develop algebraic fluency while learning to justify rules and compare mathematical models. Connect powers, equations, functions, and geometry through carefully explained examples.

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26 sec
Grade 9 · AI-assisted teaching
Binomials: multiply every area part
AI-assisted presenter with an American male AI voice. Split a rectangle with sides x + 2 and x + 3 into four areas. When x = 2, those parts add to the same 20 square units as the full rectangle.
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1 short teaching clip is available above, each linked to its exact practice question. Every chapter below opens a written lesson with worked examples and practice. Full lesson recordings are being prepared; the interactive animations are available now.

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Each chapter follows an existing academy lesson. Numbers match the written study order; grade placement is a guide and school sequences may vary.

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30 of 30 chapters · in study order

Chapter 1 · Algebra
Explain exponent laws by matching factors
Use repeated factors to justify product and quotient laws for integer powers.
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Chapter 2 · Algebra
Interpret negative powers as reciprocals
Rewrite negative integer exponents without changing the sign of the base.
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Chapter 3 · Algebra
Keep scale and significant factor separate
Multiply scientific-notation quantities and normalize the coefficient.
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Chapter 4 · Algebra
Extract square factors from radicals
Separate perfect-square factors from a nonnegative radicand.
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Chapter 5 · Algebra
Prove a number is irrational
Use a lowest-terms contradiction to establish irrationality.
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Chapter 6 · Algebra
Distribute a negative factor carefully
Track signs while removing parentheses and combining terms.
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Chapter 7 · Algebra
Solve when the variable appears on both sides
Collect variable terms through equality-preserving operations.
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Chapter 8 · Algebra
An equation can have all, one, or no solutions
Interpret identities and contradictions after simplification.
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Chapter 9 · Algebra
Clear fractions in a linear inequality
Multiply by a positive common denominator before solving a linear inequality.
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Chapter 10 · Algebra
Solve a two-sided bound
Apply the same operation to every part of a compound inequality.
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Chapter 11 · Algebra
Solve a distance equation with two directions
Translate absolute value into distance from a center.
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Chapter 12 · Algebra
One input must have one output
Test a relation against the definition of a function.
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Chapter 13 · Algebra
Find inputs excluded by an expression
Intersect denominator and real-square-root restrictions.
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Chapter 14 · Algebra
Follow the order of two function machines
Evaluate a composition and distinguish it from reversing the order.
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Chapter 15 · Algebra
Compute a signed rate from two points
Use consistent coordinate differences to calculate slope.
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Chapter 16 · Algebra
Build a line from a point and a rate
Use point-slope form and translate it into slope-intercept form.
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Chapter 17 · Algebra
Distinguish zero slope from undefined slope
Derive equations for horizontal and vertical lines.
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Chapter 18 · Geometry
Use slope to compare nonvertical directions
Find parallel and perpendicular line slopes with the appropriate exceptions.
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Chapter 19 · Algebra
Shade a half-plane from a linear inequality
Use a boundary line and a test point to identify a solution region.
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Chapter 20 · Algebra
Recover three quantities from pairwise totals
Use three independent pairwise conditions to recover three unknown quantities.
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Chapter 21 · Algebra
Eliminate a variable with matched coefficients
Add scaled equations to cancel one unknown.
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Chapter 22 · Algebra
Read a system's solution count from line geometry
Connect intersecting, parallel, and coincident lines to algebraic outcomes.
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Chapter 23 · Algebra
Test whether a table has constant rate
Compare output changes over equal input intervals.
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Chapter 24 · Algebra
Index an arithmetic sequence correctly
Derive a term formula from the first term and common difference.
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Chapter 25 · Algebra
Count repeated factors in a geometric sequence
Derive a term formula for a fixed-ratio sequence.
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Chapter 26 · Algebra
Turn repeated percentage growth into a multiplier
Model a constant percentage increase applied to the current amount.
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Chapter 27 · Algebra
Model a constant fraction remaining
Use a repeated retention factor to model proportional decay.
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Chapter 28 · Algebra
Combine polynomials by matching powers
Add and subtract polynomial expressions with aligned variable powers.
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Chapter 29 · Algebra
Multiply every pair of binomial terms
Use distribution to multiply two binomials and collect the result.
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Chapter 30 · Algebra
Reverse a product to solve a quadratic
Factor a monic quadratic and apply the zero-product property.
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Watch this grade’s teaching clips

Binomials: multiply every area part

Explore the complete written study sequence

Chapters and video availability

Explain exponent laws by matching factors

Interpret negative powers as reciprocals

Keep scale and significant factor separate

Extract square factors from radicals

Prove a number is irrational

Distribute a negative factor carefully

Solve when the variable appears on both sides

An equation can have all, one, or no solutions

Clear fractions in a linear inequality

Solve a two-sided bound

Solve a distance equation with two directions

One input must have one output

Find inputs excluded by an expression

Follow the order of two function machines

Compute a signed rate from two points

Build a line from a point and a rate

Distinguish zero slope from undefined slope

Use slope to compare nonvertical directions

Shade a half-plane from a linear inequality

Recover three quantities from pairwise totals

Eliminate a variable with matched coefficients

Read a system's solution count from line geometry

Test whether a table has constant rate

Index an arithmetic sequence correctly

Count repeated factors in a geometric sequence

Turn repeated percentage growth into a multiplier

Model a constant fraction remaining

Combine polynomials by matching powers

Multiply every pair of binomial terms

Reverse a product to solve a quadratic