30 free lessons · Worked examples and practice
Grade 7 math
Strengthen proportional reasoning and use rational numbers to model change. Connect equations, geometry, and probability to practical questions where units and assumptions matter.
Your study guide
What you will explore.
- Calculate fractional rates and proportional relationships
- Reason with signed numbers and equations
- Use scale, geometry, and probability models
Before you begin
Review fraction operations, ratios, negative numbers, and one-step equations. These tools appear repeatedly throughout the lessons.
Review Grade 6How to study these lessons
Write the units in every rate and explain what one unit means. Before accepting an answer, test whether its size and sign make sense in the situation.
Work at your own pace. Open a hint when you need it, then try again before revealing the complete explanation.
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Your Grade 7 lesson collection.
The lessons appear in their suggested study order. Choose the first lesson for a starting point, or use the search and subject filters to review a particular skill. Read the prerequisites whenever you change topics.
Showing 12 of 30 matching lessons · All free
AlgebraGrade 7 · Developing 8 min
Find a rate when both quantities are fractions
Dividing two measured fractions gives the amount per one unit of the denominator quantity.
Read, practice, and reflectAlgebraGrade 7 · Developing 8 min
Recover the constant of proportionality
A proportional relationship has one output-to-input ratio and passes through the origin.
Read, practice, and reflectAlgebraGrade 7 · Developing 8 min
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.
Read, practice, and reflectGeometryGrade 7 · Developing 8 min
Convert a map length with a scale
A map scale relates drawing length and actual length through consistent units.
Read, practice, and reflectAlgebraGrade 7 · Developing 8 min
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.
Read, practice, and reflectAlgebraGrade 7 · Developing 8 min
Work backward from a discounted amount
A discounted price is a fraction of the original, so reverse percentages require division by the remaining fraction.
Read, practice, and reflectAlgebraGrade 7 · Developing 8 min
Match time units in simple interest
In a simple-interest model, interest is proportional to principal, annual rate, and elapsed years.
Read, practice, and reflectAlgebraGrade 7 · Developing 8 min
Add signed changes on a number line
Signed addition combines a starting position with a directed change.
Read, practice, and reflectAlgebraGrade 7 · Developing 8 min
Explain subtraction of a negative number
Subtracting a number is adding its additive inverse; removing a negative change increases the result.
Read, practice, and reflectAlgebraGrade 7 · Developing 8 min
Use a pattern to justify a negative product
The sign rules for multiplication preserve distributivity and consistent numerical patterns.
Read, practice, and reflectAlgebraGrade 7 · Developing 8 min
Check division using a missing factor
A quotient is the factor that reproduces the dividend when multiplied by the nonzero divisor.
Read, practice, and reflectAlgebraGrade 7 · Developing 8 min
Order negative fractions and decimals
On the negative side of a number line, the number closer to zero is greater.
Read, practice, and reflect