30 written chapters · 1 published teaching videos
Grade 7, one chapter at a time.
Strengthen proportional reasoning and use rational numbers to model change. Connect equations, geometry, and probability to practical questions where units and assumptions matter.
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Chapters and video availability
Each chapter follows an existing academy lesson. Numbers match the written study order; grade placement is a guide and school sequences may vary.
30 of 30 chapters · in study order
Chapter 1 · Algebra
Find a rate when both quantities are fractions
Dividing two measured fractions gives the amount per one unit of the denominator quantity.
Written lesson available · video pending
Study this chapterChapter 2 · Algebra
Recover the constant of proportionality
A proportional relationship has one output-to-input ratio and passes through the origin.
Written lesson available · video pending
Study this chapterChapter 3 · Algebra
Detect a fixed fee in a table
A constant rate of increase does not make a relationship proportional when there is a nonzero starting fee.
Written lesson available · video pending
Study this chapterChapter 4 · Geometry
Convert a map length with a scale
A map scale relates drawing length and actual length through consistent units.
Written lesson available · video pending
Study this chapterChapter 5 · Algebra
Choose the base of a percentage change
A percentage change compares a difference with the original value, so reversing a change uses a different base.
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Study this chapterChapter 6 · Algebra
Work backward from a discounted amount
A discounted price is a fraction of the original, so reverse percentages require division by the remaining fraction.
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Study this chapterChapter 7 · Algebra
Match time units in simple interest
In a simple-interest model, interest is proportional to principal, annual rate, and elapsed years.
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Study this chapterChapter 8 · Algebra
Add signed changes on a number line
Signed addition combines a starting position with a directed change.
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Study this chapterChapter 9 · Algebra
Explain subtraction of a negative number
Subtracting a number is adding its additive inverse; removing a negative change increases the result.
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Study this chapterChapter 10 · Algebra
Use a pattern to justify a negative product
The sign rules for multiplication preserve distributivity and consistent numerical patterns.
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Study this chapterChapter 11 · Algebra
Check division using a missing factor
A quotient is the factor that reproduces the dividend when multiplied by the nonzero divisor.
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Study this chapterChapter 12 · Algebra
Order negative fractions and decimals
On the negative side of a number line, the number closer to zero is greater.
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Study this chapterChapter 13 · Algebra
Distribute a negative factor to every term
Distributivity multiplies every term inside a grouped sum by the outside factor, including its sign.
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Study this chapterChapter 14 · Algebra
Combine quantities with matching variable parts
Like terms can be combined because they count the same variable quantity; constants form a separate group.
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Study this chapterChapter 15 · Algebra
Undo operations in a two-step equation
Solving an equation preserves equality while undoing operations in reverse order.
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Study this chapterChapter 16 · Algebra
Reverse an inequality when dividing by a negative
Multiplying or dividing an inequality by a negative reflects the number line and reverses order.
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Study this chapterChapter 17 · Geometry
Relate a wheel's turns to circumference
One full turn of an ideal rolling wheel covers one circumference, which is π times its diameter.
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Study this chapterChapter 18 · Geometry
Use the radius to find a circular area
Circular area scales with the square of the radius, making a length change larger in area terms.
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Study this chapterChapter 19 · Geometry
Find an L-shaped area by subtraction
A composite region can be measured by combining simple nonoverlapping regions or subtracting a missing part.
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Study this chapterChapter 20 · Geometry
Extend a triangular area into a prism
A prism's volume equals its constant cross-sectional area multiplied by its perpendicular length.
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Study this chapterChapter 21 · Geometry
Count all faces in a rectangular box
Surface area measures covering and requires adding the areas of the exposed faces.
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Study this chapterChapter 22 · Geometry
Build an equation from triangle angles
The interior angles of a Euclidean triangle total 180°, linking geometry to a linear equation.
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Study this chapterChapter 23 · Geometry
Distinguish supplementary and vertical angles
Adjacent angles on a straight line add to 180°, while opposite vertical angles at intersecting lines are equal.
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Study this chapterChapter 24 · Statistics
Find a probability through its complement
An event and its complement cover all possibilities without overlap, so their probabilities sum to one.
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Study this chapterChapter 25 · Statistics
Separate observed frequency from certainty
Relative frequency estimates a probability from observations but does not guarantee the next result.
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Study this chapterChapter 26 · Statistics
List compound outcomes before counting
A systematic outcome table prevents missing or duplicating possibilities in a two-stage experiment.
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Study this chapterChapter 27 · Statistics
Recognize who a survey leaves out
A sample can misrepresent a population when selection systematically favours particular members.
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Study this chapterChapter 28 · Statistics
Measure spread with mean absolute deviation
Mean absolute deviation averages distances from the mean, describing variability in the original units.
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Study this chapterChapter 29 · Statistics
Describe the middle half with an interquartile range
The interquartile range measures the spread of the middle half of ordered observations.
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Study this chapterChapter 30 · Statistics
Scale a sample proportion to an estimated count
A sample proportion can support a population estimate while leaving sampling uncertainty.
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