OGM.13.NUM
Open Global Math Standards 2026™ · 12th Grade
Real Number Systems, Algebraic Expressions, Sequences, and Series
Grade12th Grade
SubjectMath
Levelstrand
Child standards (5)
- OGM.13.NUM.1Analyze decimal and non-decimal representations of real numbers to differentiate rational and irrational numbers; demonstrate the density and incompleteness of the rational numbers and compare structural properties across number systems (natural, integer, rational, real).
- OGM.13.NUM.2Manipulate algebraic expressions with rational exponents and surds, including rationalizing denominators; apply algebraic operations to polynomials (expansion, factor theorem, polynomial long division) and simplify complex algebraic fractions.
- OGM.13.NUM.3Decompose rational functions into partial fractions with linear and repeated linear factors in the denominator for constant and linear numerators.
- OGM.13.NUM.4Expand binomial expressions $(a + bx)^n$ using factorial notation and combinations $\binom{n}{r}$ for positive integers, and generalize to rational exponents $n \in \mathbb{Q}$ with convergence criterion $|\frac{bx}{a}| < 1$ to approximate numerical and functional values.
- OGM.13.NUM.5Analyze arithmetic and geometric sequences and series, including explicit and recursive relations $x_{n+1} = f(x_n)$, sigma notation $\sum$, sum of finite series, sum to infinity of convergent geometric series ($|r| < 1$), and classification of increasing, decreasing, and periodic sequences in theoretical and real-world modeling.