Public learning track
Real Numbers: Exponents, Squares, Cubes, and Roots
7th Grade · Math · Open Global Math
8 lessons
Goal
Evaluate square and cube roots of perfect and non-perfect values, distinguish rational from irrational numbers, and convert repeating decimals to fractions.
Featured Diagrams
Understanding Perfect Squares and Evaluating Square Roots
8 lessons
0 of 8 done
- 1Understanding Perfect Squares and Evaluating Square RootsUp nextStart
- 2Understanding Perfect Cubes and Evaluating Cube RootsPremiumNot started yet
- 3Cube Roots of Negative Integers and Rational NumbersNot started yet
- 4Evaluating Expressions with Square and Cube NumbersNot started yet
- 5Rational Numbers as Fractions and Terminating or Repeating DecimalsNot started yet
- 6Converting Terminating and Repeating Decimals to FractionsNot started yet
- 7Defining Irrational Numbers and Non-Repeating DecimalsNot started yet
- 8Classifying Numbers in the Real Number SystemNot started yet
Standards Covered
- OGM.8.NO.5Open Global Math Standards 2026™ · Math · Level 8 / Grade 7 (Age 12) · Grade 7Understand perfect squares, square roots, cubes, and cube roots; explore the real number continuum comprising rational and irrational numbers, represent real numbers on the number line, and approximate irrational numbers with rational bounds.
- OGM.8.NO.4Open Global Math Standards 2026™ · Math · Level 8 / Grade 7 (Age 12) · Grade 7Apply and extend multiplication and division to rational numbers (fractions, terminating/repeating decimals, and signed numbers) using properties of operations; understand that -(p/q) = (-p)/q = p/(-q) for non-zero divisors, and convert fractions to decimals using long division.
Curriculum Framework
7th Grade · Math · Open Global Math
1
9 lessons
Prime Factorization, Index Notation, and Expanded Powers of Ten
Decompose natural numbers into prime factors using exponent notation and express numbers in expanded decimal form with powers of 10.
2
8 lessons
The Structure of Integers, Rational Numbers, and Absolute Value
Model additive inverses, plot signed numbers on horizontal and vertical lines, and interpret absolute value as distance from zero.
3
8 lessons
Addition and Subtraction of Rational Numbers
Add and subtract signed fractions and decimals, interpret subtraction as adding the opposite, and calculate distance as |p - q|.
4
8 lessons
Multiplication and Division of Rational Numbers
Multiply and divide signed fractions and decimals, understand the placement of negative signs in quotients, and convert fractions using long division.
5
8 lessons
Real Numbers: Exponents, Squares, Cubes, and Roots
Evaluate square and cube roots of perfect and non-perfect values, distinguish rational from irrational numbers, and convert repeating decimals to fractions.
6
6 lessons
Approximating Irrationals and the Real Number Continuum
Estimate the value of irrational square roots using rational bounds, place irrationals on number lines, and solve geometric radical problems.
7
9 lessons
Estimation, Significant Figures, and Scientific Notation
Round numbers to specified decimal places or significant figures, check calculation reasonableness, and compute with scientific notation.
8
5 lessons
Applied Problem Solving with Rational and Real Numbers
Solve complex, multi-step real-world problems combining fractions, decimals, signed numbers, exponents, and estimation.