**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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Detailed Description of Competency 001

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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