Math 156 for Elementary Teachers

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Problem Solving

Identifying the Problem (Understanding the Problem)

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Divising a Plan

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Guess and checkFind a resource to assistUse a formula if one ecistsMake an organized list/ tableSolve a simpler problemDraw a modelUse tools (ruler, protractor, compass, etc)Loofor a patternWork backwordsAct it out (using manipulatives)Change your point of view

Using/ Carrying out the Plan

Looking Back/ Reflecting on the Answer

Numberal Systems

Tally System

Egyptian System

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Symbolic/ non-positional

Mayans/ Babylonians

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Mayans had first symbol for "zero". Babylonians used Base 60

Roman Symbolic

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Letters represent numbers. Positional.

Hindu- Arabic (what we use)

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Base 10.

Bases

Operations

Subtraction (-)

"Take Away" Problems

Comparison Problems

Missing- Addend Problems

Addition (+)

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2 Basic models we consider for addition are: Discrete, andContinuous.

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Closure Property

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Commutative Property

Associative Property

Identity Property

Multiplication (x)

Repeated Addition

Discrete

Continuous

Area Model (Array Model)

Cartesian Product Model

Division (/)

Partition (Sharing)

Measurement (Repeated Subtraction)

Scaffolding

Column Division

Four Fact Families

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a + b = cb + a + cc - a = bc - b = a

Prime/ Composite Numbers

Prime

Composite

Fundamental Theorem of Arithmetic

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Every composite number can be written as the product of prime numbers in one and only one way.

Number Theory

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Characteristcs of a number.

Even numbers

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2n

Odd numbers

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2n+1

Divisibility

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If we writ "a divides b", there are 4 equivalent statements that are useful based on this statement. 1.) a is a factor of b2.) b is a multiple of a3.) a is a divisor of b4.) b is divisible by a

Sequences

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Sequence- an ordered list

Elements

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Element- a memeber in the sequence

Arithmetic Sequences

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Sequences of numbers with a common difference.

Geometric Sequences

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Sequences of numbers with a common ratio.

Recurrence Relationship Sequences

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A sequence in which the current term is dependent on previous terms.

Sets

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Collection of objects

Universal Set

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Collection of objects under consideration (U)

Subset

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Set of objects in which all of those objects are contained within another set. (⊆)

Proper Subset

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A subset of another set and there is atleast one element of the other set that is not in the subset. (⊂)

Empty Set

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No elements

Equal Sets

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Have identical elements

Equivalent Sets

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Same cardinal number

Compliment of a Set

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Opposite.

Greatest Common Factor

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aka GCD

GCF (a,b) = n

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The greatest common factor of both a and b is equal to n. The largest number that is a factor of both a and b is n.

Least Common Multiple

LCM (a,b) = m

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The smallest number that is a multiple of both a and b is m.

Ratios

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Part-to-whole

Rational number

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A number that can be written as the ratio of two integers. Often referred to as fractions, BUT not all fractions are RATIONAL fractions.