30 written chapters · 1 published teaching videos

Grade 6, one chapter at a time.

Make the transition from arithmetic to algebra through ratios, expressions, signed numbers, and equations. Connect these ideas to geometry and data so the symbols describe something meaningful.

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26 sec
Grade 6 · AI-assisted teaching
Ratios: scale both quantities
AI-assisted presenter with an American male AI voice. Scale a 3:2 ratio by six to get 18:12, then compare the 18 blue counters with all 30 counters to find a fraction of 3/5.
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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
Distinguish part-to-part from part-to-whole
State what each side of a ratio compares.
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Chapter 2 · Algebra
Build a table of equivalent ratios
Scale both entries of a ratio by a common factor.
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Chapter 3 · Algebra
Compare rates per one unit
Calculate and compare unit rates with clear units.
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Chapter 4 · Algebra
Find a percentage of a quantity
Convert a percent to a multiplier and apply it to a specified whole.
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Chapter 5 · Algebra
Recover a whole from a percentage part
Solve for a reference amount when a part and its percent are known.
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Chapter 6 · Algebra
Divide by a fractional measure
Interpret and compute the ratio of two fractional quantities.
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Chapter 7 · Algebra
Use negative numbers relative to a reference
Interpret a signed value as a position relative to zero.
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Chapter 8 · Algebra
Order positive and negative values
Compare signed numbers using their positions on a number line.
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Chapter 9 · Algebra
Absolute value measures distance from zero
Distinguish a signed position from its nonnegative distance to zero.
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Chapter 10 · Algebra
Opposite numbers reflect across zero
Find additive opposites and distinguish them from reciprocals.
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Chapter 11 · Geometry
Plot points in all four quadrants
Interpret the signs of both coordinates.
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Chapter 12 · Geometry
Find horizontal or vertical coordinate distance
Use coordinate differences for points sharing one coordinate.
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Chapter 13 · Algebra
Represent a changing quantity with a variable
Translate a repeating cost and fixed cost into an expression.
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Chapter 14 · Algebra
Substitute a value into a rule
Evaluate an expression while preserving its grouping.
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Chapter 15 · Algebra
Combine terms with the same variable part
Use a shared variable unit to simplify an expression.
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Chapter 16 · Algebra
Explain and reverse distribution
Expand or factor an expression using a common multiplier.
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Chapter 17 · Algebra
Balance an equation with an inverse operation
Solve an additive equation by doing the same operation to both sides.
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Chapter 18 · Algebra
Solve for one equal group's size
Use division to solve a one-step multiplication equation.
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Chapter 19 · Algebra
Describe all values meeting a limit
Interpret an inequality as a set of allowed values.
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Chapter 20 · Algebra
Identify input and output variables
Use a rule to connect an independent input and dependent output.
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Chapter 21 · Geometry
Find triangle area from a rectangle
Use a perpendicular height in the triangle area formula.
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Chapter 22 · Geometry
Slide a triangle to measure a parallelogram
Explain why parallelogram area uses base times perpendicular height.
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Chapter 23 · Geometry
Average the parallel sides of a trapezoid
Derive trapezoid area by pairing congruent copies.
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Chapter 24 · Geometry
Count every face in surface area
Sum the six rectangular faces of a rectangular prism.
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Chapter 25 · Geometry
Use fractional edges in a volume model
Extend prism volume to positive fractional dimensions.
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Chapter 26 · Statistics
Ask a question that expects variation
Distinguish a statistical question from a single fixed-value question.
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Chapter 27 · Statistics
Find the middle and most frequent values
Compare median and mode as different summaries.
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Chapter 28 · Statistics
Measure overall and middle-half spread
Compute range and an interquartile range using a stated median-of-halves convention.
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Chapter 29 · Statistics
Average distances from the mean
Calculate mean absolute deviation for a small data set.
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Chapter 30 · Statistics
Count favorable outcomes under a fair model
Compute a simple probability when elementary outcomes are equally likely.
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Watch this grade’s teaching clips

Ratios: scale both quantities

Explore the complete written study sequence

Chapters and video availability

Distinguish part-to-part from part-to-whole

Build a table of equivalent ratios

Compare rates per one unit

Find a percentage of a quantity

Recover a whole from a percentage part

Divide by a fractional measure

Use negative numbers relative to a reference

Order positive and negative values

Absolute value measures distance from zero

Opposite numbers reflect across zero

Plot points in all four quadrants

Find horizontal or vertical coordinate distance

Represent a changing quantity with a variable

Substitute a value into a rule

Combine terms with the same variable part

Explain and reverse distribution

Balance an equation with an inverse operation

Solve for one equal group's size

Describe all values meeting a limit

Identify input and output variables

Find triangle area from a rectangle

Slide a triangle to measure a parallelogram

Average the parallel sides of a trapezoid

Count every face in surface area

Use fractional edges in a volume model

Ask a question that expects variation

Find the middle and most frequent values

Measure overall and middle-half spread

Average distances from the mean

Count favorable outcomes under a fair model