Note: All MCPT core courses may be applied towards the earning of a supplementary authorization to teach mathematics through Grade 9/Algebra, which requires the completion of 30-quarter units of college level mathematics. Math X462A and Math X462B meet the requirements for a course in the real number system; Math X468A, Math X468B, or Math X464A meet the requirements for a course in algebra; Math X464B meets the requirements for a course in advanced algebra; Math X467 meets the requirement for a course in geometry; Math X465 meets the requirements for a course in statistics.

• Math X462A - NUMBER POWER 1 (4 units)
  This course focuses primarily on whole-number concepts and operations, including sense-making strategies for single-digit and multidigit addition, subtraction, multiplication, and division. Other topics include various number systems (Babylonian, Egyptian, Mayan) and base-5 arithmetic, which are used to help diagnose difficulties children face as they learn our Hindu-Arabic number system. The course follows a problem-solving approach, in which participants learn to express solutions to problems in multiple ways: visually, algebraically, numerically, and verbally (the fourfold way). Prerequisite: Intermediate Algebra
  

• Math X462B - NUMBER POWER 2 (4 units)
  This course focuses primarily on fraction concepts and operations. Area, set, and linear models are used to explore equivalence, ordering, and procedures for the basic arithmetic operations on fractions. Other topics include the decimal expansions of fractions; basic probability concepts; and integer concepts and operations. The course follows a problem-solving approach, in which participants learn to express solutions to problems in multiple ways: visually, algebraically, numerically, and verbally (the fourfold way). Prerequisite: Intermediate Algebra
  

• Math X468A - PERSPECTIVES ON ALGEBRA (4 units)
  This course examines ideas associated with algebraic thinking and algebra. Topics include functions, variables, graphs, equations, linear equations, and systems of linear equations. Emphasis is placed on the interpretation of graphs. The course follows a problem-solving approach, in which participants learn to express the solution to a problem in multiple ways: visually, algebraically, numerically, and verbally (the fourfold way). Prerequisite: Intermediate Algebra
  

• Math X 468B - TOPICS IN ALGEBRA AND GEOMETRY (4 units)
  This course focuses on several topics that cut across algebra and geometry. Emphasis is placed on using models to gain insight into concepts and using the graphing calculator as a problem-solving tool. Topics include the function concept, linear and quadratic functions and relations, systems of equations, Pythagorean theorem, the distance formula, and right-triangle trigonometry. Prerequisite: Math X468A
  

• Math X467 - PERSPECTIVES ON GEOMETRY (4 units)
  This course examines ideas associated with two- and three-dimensional geometric figures, including polygons, polyhedra, circles, cylinders, and spheres. Topics include the vocabulary of geometric figures; spatial visualization, representation by nets and isometric drawings; basic notions and constructions of Euclidean geometry; isometric transformations, congruence, and similarity; length, area, and volume; and perimeter and surface area. Prerequisite: Intermediate Algebra
  

• Math X464A - PERSPECTIVES ON FUNCTIONS 1 (4 units)
  This course examines the families of linear, quadratic, power, polynomial, exponential, and trigonometric functions. Emphasis is placed on studying functions as bridges between the mathematics and the situations they model. Graphing calculator skills are reinforced and expanded. Prerequisite: Math X468B
  

• Math X464B - PERSPECTIVES ON FUNCTIONS 2 (4 units)
  This course examines the families of polynomial, exponential, inverse, logarithmic, rational, and periodic functions. Emphasis is placed on studying functions as bridges between the mathematics and the situations they model. Graphing calculator skills are reinforced and expanded. Prerequisite: Math X464A
  

• Math X465 - DEALING WITH DATA (4 units)
  This course focuses on the gathering, description, and analysis of data. Each lesson is developed around questions generated from published or collected data sets, and a recurring theme of the course is to “let the data tell a story.” Techniques for one-variable and bivariate data analysis are included. Participants also explore randomness and sampling through probability experiments and data collection. Basic concepts of probability, such as techniques for determining the sample space, independence, and mathematical expectation, are included. Prerequisites: Math X462B

• Math X469 - MORE (ADVANCED) TOPICS IN ALGEBRA (4 units)
  Participants will study topics in high school mathematics from a mature perspective. Topics include algebraic structures, vectors, complex numbers, and trigonometry. Connections to classroom practice will be included. Prerequisite: Math X464B
  

• Math X470 - MORE (ADVANCED) TOPICS IN GEOMETRY (4 units)
  Participants will study topics in high school mathematics from a mature perspective. Topics include Euclidean and non-Euclidean geometries, coordinate geometry, conic sections, proof. Connections to classroom practice will be included. Prerequisites: Math X467 and Math X464A
  
  

• Math X471 - MORE (ADVANCED) TOPICS IN DATA (4 units)
  This course will review descriptive data techniques and focus on statistical inference. Participants will apply techniques to analyze data and prepare a project that illustrates sound statistical reasoning. Access to a computer and the Internet is required. A laptop computer is required. Prerequisites: Math X465 and Math X464A
  
  

• Math X472 - MATH AND TECHNOLOGY (4 units)
  Participants will learn to use commonly available technology tools and applications to improve the quality and efficiency of their professional work and increase student understanding of important mathematical concepts.  Some of the applications planned for exploration include creating professional documents using POWERPOINT, MATHTYPE, and graphics from MSWORD, exploring algebraic relationships with EXCEL, downloading internet data and analyzing it using FATHOM, exploring geometric relationships with GEOMETER SKETCHPAD, and analysis of rates of motion using a the TI calculator-based ranger.  A laptop computer is recommended. Prerequisite: Math X468B
  

• Math X461A - TOPICS FROM HIGH SCHOOL MATHEMATICS 1A: ADVANCED ALGEBRA (4 units)
  Participants study topics tested on the California Subject Examination for Teachers (CSET Mathematics Subtest 1: Algebra; Number Theory) that are related to algebra and functions from an advanced perspective. Topics include: analysis of polynomial, rational, and exponential functions; and computation with complex numbers. Prerequisite: Intermediate Algebra and Math X464A (recommended)
  

• Math X461B - TOPICS FROM HIGH SCHOOL MATHEMATICS 1B: LINEAR ALGEBRA AND NUMBER THEORY (4 units)
  Participants study topics tested on the California Subject Examination for Teachers (CSET Mathematics Subtest 1: Algebra; Number Theory) that are related to algebraic structures, linear algebra, and number theory from an advanced perspective. Topics include: rings and fields, properties of real and complex numbers, vectors and matrices, properties of natural numbers, and Mathematical Induction. Prerequisite: Intermediate Algebra and Math X461A (recommended)
  

• Math X461C - TOPICS FROM HIGH SCHOOL MATHEMATICS 2A: PLANE EUCLIDEAN GEOMETRY (4 units)
  Participants study topics tested on the California Subject Examination for Teachers (CSET Mathematics Subtest 2: Geometry; Probability and Statistics) that are related to Euclidean Geometry from an advanced perspective. Topics include: classic constructions, parallel postulate, similarity and congruence, properties of polygons, Pythagorean theorem, and triangle trigonometry. Prerequisite: Intermediate Algebra, Math X467 (recommended), and Math X464A (recommended)
  

• Math X461D - TOPICS FROM HIGH SCHOOL MATHEMATICS 2B: GEOMETRY, PROBABILITY, AND STATISTICS (4 units)
  Participants study topics tested on the California Subject Examination for Teachers (CSET Mathematics Subtest 2: Geometry; Probability and Statistics) from an advanced perspective. Geometry topics include: non-Euclidean geometries, three-dimensional geometry, and transformational geometry. Probability and statistics topics include: permutations and combinations, finding probabilities, the use of distributions to solve probability problems, computation and interpretation of descriptive statistics, linear regression and correlation, and chi square tests. Prerequisite: Intermediate Algebra, Math X465 (recommended), and Math X461C (recommended)