Generalist Ec-6

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SITUATED LEARNING THEORY

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STUDENTS LEARN MORE EASILY FROM INSTRUCTION INVOLVING RELEVANT, REAL-WORLD SITUATIONS AND APPLICATIONS THAN FROM ABSTRACT CONCEPTS

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CONSTRUCTIVISM

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PRIOR KNOWLEDGE GREATLY INFLUENCES THE LEARNING OF MATH, AND LEARNING IS CUMULATIVE AND VERTICALLY STRUCTURED. BE AWARE OF THE KNOWLEDGE AND IDEAS STUDENTS ALREADY HAVE ABOUT A SUBJECT.

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CONCRETE-TO-REPRESENTATIONAL-TO-ABSTRACT SEQUENCE OF INSTRUCTION

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1. INTRODUCE A CONCEPT BY MODELING WITH CONCRETE MATERIALS

2. TRANSLATE CONCRETE MODELS INTO REPRESENTATIONAL DIAGRAMS OR PICS.

3. TRANSLATE REPRESENTATIONAL MODELS INTO ABSTRACT MODELS USING ONLY NUMBERS AND SYMBOLS

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FORMATIVE ASSESSMENTS

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STUDENTS CREATE A RESPONSE RATHER THAN CHOOSE AN ANSWER

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SUMMATIVE ASSESSMENT

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OCCURS PERIODICALLY AND CONSISTS OF TEMPORARY INTERACTION BETWEEN TEACHER AND STUDENT

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ALTERNATIVE ASSESSMENT

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SHORT RESPONSE AND ESSAY QUESTIONS

STUDENT PORTFOLIOS

PROJECTS, DEMONSTRATIONS, AND ORAL PRESENTATIONS

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WHOLE NUMBER

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ONE OF THE COUNTING NUMBERS

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INTEGER

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A POSITIVE OR NEGATIVE NUMBER

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REAL NUMBER

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A MEMBER OF THE SET OF ALL NUMBERS, RATIONAL AND IRRATIONAL

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IRRATIONAL NUMBER

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ANY REAL NUMBER THAT CANNOT BE EXPRESSED AS THE QUOTIENT A/B OF TWO INTEGERS

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PRIME NUMBER

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A NUMBER WITH EXACTLY TWO FACTORS, ITSELF AND ONE

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COMPOSITE

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A NUMBER WITH MORE THAN TWO FACTORS

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ALGORITHMS

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METHODS OR STRATEGIES FOR SOLVING PROBLEMS

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PERMUTATION

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ONE OF A NUMBER OF POSSIBLE SELECTIONS OF ITEMS, WITHOUT REPETITION, WHERE ORDER OF SELECTION IS IMPORTANT

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COMBINATION

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ONE OF A NUMBER OF POSSIBLE SELECTIONS, WITHOUT REPETITION, WHERE ORDER OF SELECTION IS NOT IMPORTANT

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LINEAR FUNCTION

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A FUNCTION DEFINED BY THE EQUATION Y=MX+B

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SEQUENCE

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PATTERN OF NUMBERS OR SYMBOL ARRANGED IN A PARTICULAR ORDER

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ARITHMETIC SEQUENCE

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SET OF NUMBERS WITH A COMMON DIFFERENCE BETWEEN THE TERMS

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GEOMETRIC SEQUENCE

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SERIES OF NUMBERS IN WHICH A COMMON RATIO CAN BE MULTIPLIED BY A TERM TO YIELD THE NEXT TERM

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MODELS

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MEANS OF REPRESENTING MATHEMATICAL CONCEPTS BY RELATING THE CONCEPTS TO REAL-WORLD SITUATIONS

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PROPORTION

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AN EQUATION IN WHICH A FRACTION IS SET EQUAL TO ANOTHER

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LINEAR PROGRAMMING

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THE OPTIMIZATION OF A LINEAR QUANTITY THAT IS SUBJECT TO CONSTRAINTS EXPRESSED AS LINEAR EQUATIONS OR INEQUALITIES

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NET

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TWO-DIMENSIONAL FIGURE THAT CAN BE CUT OUT AND FOLDED UP TO MAKE A THREE-DIMENSIONAL SOLID

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CONGRUENT FIGURES

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FIGURES THAT HAVE THE SAME SIZE AND SHAPE

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PERIMETER

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THE SUM OF THE LENGTHS OF THE SIDES OF THE FIGURE

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AREA

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THE NUMBER OF SQUARE UNITS COVERED BY THE FIGURE

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POINT

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A DIMENSIONLESS LOCATION WITH NO LENGTH, WIDTH, OR HEIGHT

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LINE

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CONNECTS A SERIES OF POINTS AND CONTINUES "STRAIGHT" INFINITELY IN TWO DIRECTIONS

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LINE SEGMENT

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A PORTION OF A LINE

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RAY

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A PORTION OF A LINE THAT HAS ONLY ONE END POINT AND CONTINUES INFINITELY IN ONE DIRECTION

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PLANE

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A FLAT SURFACE DEFINED BY THREE POINTS; PLANES EXTEND INDEFINITELY IN TWO DIMENSIONS

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PARALLEL LINES

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LINES THAT DO NOT INTERSECT

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PERPENDICULAR LINES

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LINES THAT INTERSECT AT A POINT AND FORM 90 DEGREE ANGLES

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POLYGON

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SIMPLE, CLOSED FIGURE COMPOSED OF LINE SEGMENTS

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QUADRILATERAL

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POLYGON WITH 4 SIDES

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TRAPEZOID

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QUADRILATERAL WITH ONE PAIR OF PARALLEL SIDES

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PARALLELOGRAM

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QUADRILATERAL WITH TWO PAIRS OF PARALLEL SIDES

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CIRCUMFERENCE

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DISTANCE AROUND THE PERIMETER OF A CIRCLE

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TRANSFORMATIONAL GEOMETRY

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STUDY OF MANIPULATING OBJECT BY FLIPPING, TWISTING, TURNING, AND SCALING

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SYMMETRY

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EXACT CORRESPONDENCE BETWEEN TWO PARTS OR HALVES, AS IF ONE WERE A MIRROR IMAGE OF THE OTHER

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TESSELLATION

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ARRANGEMENT OF CLOSED SHAPES THAT COMPLETELY COVERS A PLANE WITHOUT OVERLAPPING OR LEAVING GAPS

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PRECISION

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INDICATION OF HOW EXACT A MEASUREMENT IS, WITHOUT REFERENCE TO A TRUE OR REAL VALUE

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ACCURACY

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MEASURE OF HOW CLOSE THE RESULT OF MEASUREMENT COMES TO THE TRUE VALUE

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THEOREMS

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MATHEMATICAL STATEMENTS THAT CAN BE PROVEN TO BE TRUE BASED ON POSTULATES, DEFINITIONS, ALGEBRAIC PROPERTIES, GIVEN INFO, AND PREVIOUSLY PROVED THEOREMS

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MEAN

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THE AVG VALUE OF A DATA SET

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MEDIAN

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MIDDLE VALUE OF A DATA SET

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MODE

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VALUE THAT APPEARS MOST OFTEN IN A DATA SET

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RANGE

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DIFFERENCE BETWEEN THE HIGHEST AND LOWEST VALUE OF DATA IN A SET

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VARIANCE

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AVG SQUARED DISTANCE FROM EACH VALUE OF A DATA SET TO THE MEAN

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STANDARD DEVIATION

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SQUARE ROOT OF THE VARIANCE

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SAMPLE STATISTICS

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IMPORTANT GENERALIZATIONS ABOUT THE ENTIRE SAMPLE, SUCH AS MEAN, MEDIAN, MODE, AND RANGE, AND SAMPLING ERROR (STANDARD DEVIATION)

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PROBABILITY

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THE CHANCE OF AN EVENT OCCURING

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GEOMETRIC PROBABILTY

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DESCRIBES SITUATIONS THAT INVOLVE SHAPES AND MEASURES

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STATISTICAL HYPOTHESIS TESTING

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METHOD OF DETERMINING, TO WITHIN A CERTAIN CONFIDENCE LEVEL, WHETHER A PARTICULAR CONCLUSION CAN BE ACCEPTED ACCORDING TO A CERTAIN SET OF DATA

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NORMAL DISTRIBUTION

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THE DISTRIBUTION ASSOCIATED WITH MOST SETS OF REAL-WORLD DATA

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Z-SCORE

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MEASURE OF THE DISTANCE IN STANDARD DEVIATIONS OF A SAMPLE FROM THE MEAN

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INDUCTION

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PROCESS OF FINDING A PATTERN FROM A GROUP OF EXAMPLES

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DEDUCTION

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PROCESS OF ARRIVING AT A CONCLUSION BASED ON STATEMENT THAT ARE KNOWN TO BE TRUE

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HYPOTHESIS

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THE INFO THAT IS ASSUMED TO BE TRUE

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CONCLUSION

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WHAT MUST BE PROVEN TRUE

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PARABOLA

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SET OF ALL POINTS IN A PLANE THAT ARE EQUIDISTANT FROM A FIXED POINT AND A LINE