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Math Content Review

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by

Jessica Rodriguez

on 16 October 2014

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Transcript of Math Content Review

Domain I

Number Concepts
Domain II
Patterns and Algebra
Domain III
Geometry and Measurement
Domain IV
Probability and Statistics
Domain V
Mathematical Processes and Perspectives
Domain VI
Mathematical Learning, Instruction and Assessment
GOAL!
Math Qualifier Review
235: 7-12 Mathematics
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Place Value
Number Systems Bases
binary, ternary, etc
Real Numbers
natural, whole, integers, rationals, irrationals
Fields, Rings, Groups
Operations
Algorithms
Complex Numbers
Properties
Algebraic Structure
Representations
Vectors, ordered pairs, polar, etc
Operations
Divisibility Rules
Fundamental Theorem of Arithmetic
Modular Arithmetic
Front-End Estimation
Compensation
Calculating a Range
Reasonableness
Sequences
Tables
Converting between Recursive and Closed Forms
Mathematical Induction
Series (arithmetic, geometric)
Modeling Phenomena with Sequences and Series (compound interest)
Relation
Function
Mapping
Domain & Range
Shifts
Scaling
Adding & Subtracting Functions
Composition of Functions
Inverses of Functions
Slopes
Equations of lines
Factoring
Completing the square
Quadratic formula
Graphing
Linear models
Quadratic models
Functions
Polynomial
Rational
Absolute Value
Radical
Piecewise
Fundamental Theorem of Algebra
Real number system
Complex number system
Number theory concepts
Patterns to model and solve problems
Attributes of functions, relations, and their graphs
Linear and quadratic functions
Algebraic and graphical properties of functions
Algebraic and graphical properties
Using assessment to monitor and guide student learning
Formative & Summative Assessment
Aligning Learning Objectives and Assessment
Understanding learning theories and understanding TEKS
Constructivism - building on prior knowledge
Use of manipulatives
Bloom's Taxonomy
Piaget's Stages of Cognitive Development
Making connections within and outside of mathematics
Multiple representations of a math concept
Modeling math in other disciplines
e.g. art, music, science...
Understanding the "language" of math symbols
Mathematical reasoning (proofs)
Indirect & Direct proofs
Inductive & Deductive reasoning
Problem-solving process
Guess-and-check
Reasonableness
Does this answer make sense?
Working backward
e.g. prove (sinx)^2) = 1/2(1-cos2x)
Coordinate, transformational, and vector geometry
Transformations
Apply transformations on the coordinate plane
Conic sections
Euclidean geometry
Properties
polygons, quadrilaterals, circles
Cross sections & nets
cube, tetrahedron, octahedron, ...
Trigonometric and circular functions
Unit Circle
Degrees & Radians
Periodic functions, period, phase shift
Inverse trig functions
Trig identities
Solving equations with trig
Differential and integral calculus
Measurement as a process
Geometries as axiomatic systems
Concepts & applications of probability
Probability theory, sampling, and statistical inference
Limits
Continuity
Difference quotient
Derivative
Differentiation rules
Slope of a tangent line
Extrema
Integration
Explore data, characterize patterns, describe departures from patterns
Conversion Factors
length, weight, volume
Area & perimeter
Volume & surface area
Pythagorean Theorem
Proportional Reasoning
Algebraic postulates
Properties of parallel lines
Properties of triangles
Congruence & similarity
Construction
Parallel lines, perpendicular lines, bisectors, angle bisectors
Scales
Nominal, ordinal, interval, ratio
Plots
Line, scatter, stem & leaf, box-and-whisker
Graphs
Line, bar, pictographs
Pie charts, histograms
Measures of central tendency
Measures of dispersion
Permutations & combinations
Addition rule
Multiplication rule
Finite probability
Dependent and independent events
Normal, binomial, and exponential distribution
Systematic Random Sampling vs. Nonrandom Sampling
The method of least squares
Linear least squares regression
The Law of Large Numbers
Statistical Hypothesis Testing
z-test
t-test
chi-square test
Exponential & Logarithmic functions
Intercepts
Asymptotes
Graphing
Laws & Properties
Exponential Growth & Decay
Real World Applications
The Richter Scale measuring earthquakes
The Decibel Scale measuring sound
Full transcript