Kategorier: Alla - division - prime - number - operations

av Katie Brandt för 12 årar sedan

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Math 156 for Elementary Teachers

The document provides an overview of several fundamental mathematical concepts tailored for elementary teachers. It begins with the greatest common factor (GCD), emphasizing its role as the largest number that divides two given numbers.

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)