National Council of Teachers of Mathematics (NCTM) Standards
Visit http://www.nctm.org/ to view the standards.
Instructional programs from prekindergarten through grade 12 should enable all students
- to organize and consolidate their mathematical thinking through communication;
- to communicate their mathematical thinking coherently and clearly to peers, teachers, and
- to analyze and evaluate the mathematical thinking and strategies of others;
- to use the language of mathematics to express mathematical ideas precisely.
California State Mathematics Standards
- 1.0 Students identify and use the arithmetic properties of subsets of integers
and rational, irrational, and real numbers, including closure properties for
the four basic arithmetic operations where applicable:
- 1.1 Students use properties of numbers to demonstrate whether
assertions are true or false.
- 2.0 Students understand and use such operations as taking the opposite,
finding the reciprocal, taking a root, and raising to a fractional power.
They understand and use the rules of exponents.
- 4.0 Students simplify expressions before solving linear equations and inequalities
in one variable.
- 5.0 Students solve multistep problems, including word problems, involving linear
equations and linear inequalities in one variable and provide justification
for each step.
- 11.0 Students apply basic factoring techniques to second- and simple third-degree
polynomials. These techniques include finding a common factor for all terms in a polynomial,
recognizing the difference of two squares, and recognizing perfect squares of binomials.
- 14.0 Students solve a quadratic equation by factoring or completing the square.
- 19.0 Students know the quadratic formula and are familiar with its proof by
completing the square.
- 20.0 Students use the quadratic formula to find the roots of a second-degree
polynomial and to solve quadratic equations.
- 25.0 Students use properties of the number system to judge the validity of results, to
justify each step of a procedure, and to prove or disprove statements:
- 25.2 Students judge the validity of an argument according to whether the properties
of the real number system and the order of operations have been applied correctly at each step.
Mid-continent Research for Education and Learning (McREL)
McREL's Content Knowledge: A Compendium of Standards and Benchmarks for K-12 Education
addresses 14 content areas. To view the standards and benchmarks, visit http://www.mcrel.org/compendium/
Understands and applies basic and advanced properties of
functions and algebra
World History: Understands how Islamic civilization contributed to mathematics