30 free lessons · Worked examples and practice
Grade 8 math
Connect algebraic expressions to lines, equations, and functions. Explore geometric relationships and data, using multiple representations to explain why a method works.
Your study guide
What you will explore.
- Interpret linear relationships and systems
- Use exponents, roots, and scientific notation
- Connect geometry, graphs, and data
Before you begin
Be comfortable with proportional relationships, signed arithmetic, and solving simple equations. Revisit a prerequisite whenever the symbols hide the underlying idea.
Review Grade 7How to study these lessons
Translate a problem between words, a table, a graph, and an equation when possible. Use one representation to check a result found with another.
Work at your own pace. Open a hint when you need it, then try again before revealing the complete explanation.
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750 guided practice chapters for Grade 8.
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Your Grade 8 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 8 · Developing 8 min
Count factors to combine powers
Multiplication adds exponents of a common base, while division cancels matching nonzero factors.
Read, practice, and reflectAlgebraGrade 8 · Developing 8 min
Distinguish a power of a power from a product
Raising a power to another integer power multiplies the exponents, and an outside power acts on every factor of a product.
Read, practice, and reflectAlgebraGrade 8 · Developing 8 min
Extend exponent patterns through zero
For a nonzero base, the zero power is one and a negative integer exponent represents a reciprocal.
Read, practice, and reflectAlgebraGrade 8 · Developing 8 min
Normalize very small numbers in scientific notation
Scientific notation writes a positive number as a coefficient from 1 up to but not including 10 times a power of ten.
Read, practice, and reflectAlgebraGrade 8 · Developing 8 min
Align powers of ten before adding
Adding quantities in scientific notation requires expressing them with the same power of ten.
Read, practice, and reflectAlgebraGrade 8 · Developing 8 min
Multiply and renormalize scientific notation
Products in scientific notation combine coefficients and powers separately, then restore the standard coefficient range.
Read, practice, and reflectAlgebraGrade 8 · Developing 8 min
Distinguish a square root from solving a squared equation
The square-root symbol denotes the nonnegative root, while a positive squared equation has two real solutions.
Read, practice, and reflectAlgebraGrade 8 · Developing 8 min
Use cube roots to recover a signed input
Cubing preserves a real number's sign, so a negative real number has one negative real cube root.
Read, practice, and reflectAlgebraGrade 8 · Developing 8 min
Locate an irrational square root between decimals
Comparing squares gives reliable bounds on a positive square root without pretending a decimal approximation is exact.
Read, practice, and reflectGeometryGrade 8 · Developing 8 min
Recover a right triangle's missing leg
When the hypotenuse is known, the Pythagorean theorem finds a missing leg by subtraction of squares.
Read, practice, and reflectGeometryGrade 8 · Developing 8 min
Test whether three sides form a right triangle
The converse of the Pythagorean theorem recognizes a right triangle from a square-sum equality.
Read, practice, and reflectGeometryGrade 8 · Developing 8 min
Turn coordinate differences into a distance
The straight-line distance between two points is the hypotenuse formed by their horizontal and vertical differences.
Read, practice, and reflect