Kategorie: Wszystkie - division - prime - number - operations

przez Katie Brandt 13 lat temu

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Math 156 for Elementary Teachers

What I have learned.

Math 156 for Elementary Teachers

Math 156 for Elementary Teachers

Ratios

Part-to-whole

Rational number

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

Least Common Multiple

LCM (a,b) = m

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

Greatest Common Factor

aka GCD

GCF (a,b) = n

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.

Sets

Collection of objects

Compliment of a Set

Opposite.

Equivalent Sets

Same cardinal number

Equal Sets

Have identical elements

Empty Set

No elements

Proper Subset

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

Subset

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

Universal Set

Collection of objects under consideration (U)

Sequences

Sequence- an ordered list

Recurrence Relationship Sequences

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

Geometric Sequences

Sequences of numbers with a common ratio.

Arithmetic Sequences

Sequences of numbers with a common difference.

Elements

Element- a memeber in the sequence

Number Theory

Characteristcs of a number.

Divisibility

If we writ "a divides b", there are 4 equivalent statements that are useful based on this statement.

1.) a is a factor of b

2.) b is a multiple of a

3.) a is a divisor of b

4.) b is divisible by a

Odd numbers

2n+1

Even numbers

2n

Prime/ Composite Numbers

Fundamental Theorem of Arithmetic

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

Composite
Prime

Operations

Four Fact Families

a + b = c

b + a + c

c - a = b

c - b = a

Division (/)
Column Division
Scaffolding
Measurement (Repeated Subtraction)
Partition (Sharing)
Multiplication (x)
Cartesian Product Model
Area Model (Array Model)
Repeated Addition

Continuous

Discrete

Addition (+)

2 Basic models we consider for addition are:

Discrete, and

Continuous.

Identity Property
Associative Property
Commutative Property
Closure Property
Subtraction (-)
Missing- Addend Problems
Comparison Problems
"Take Away" Problems

Numberal Systems

Bases
Hindu- Arabic (what we use)

Base 10.

Roman Symbolic

Letters represent numbers. Positional.

Mayans/ Babylonians

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

Egyptian System

Symbolic/ non-positional

Tally System

Problem Solving

Looking Back/ Reflecting on the Answer
Using/ Carrying out the Plan
Divising a Plan

Guess and check

Find a resource to assist

Use a formula if one ecists

Make an organized list/ table

Solve a simpler problem

Draw a model

Use tools (ruler, protractor, compass, etc)

Loofor a pattern

Work backwords

Act it out (using manipulatives)

Change your point of view

Identifying the Problem (Understanding the Problem)