Elementary Mathematics

Number & Numeration Systems

Hindu-Arabic Number System

Positional Number System

Roman Numeral System

Venn Diagrams

Subtraction

Four Fact Families

a

Division

Major Models

Partition (sharing)

r

Distributing a given quantity among a specified number of partitions and determining the size of each partition

Measurement

r

using a given quantity to create partitions of a specified size and determining the number of partitions formed

Strategies

array

friendly division

scaffolding algorithm

traditional algorithm

Fractions

Constructs

r

Part-whole: two thirds of the class went on a field trip Measure: for 5/8 use five 1/8 unit fractions to count or measureDivision: sharing $10 with 4 people is 10/4Operator: 4/5 of 20 feetRatio: the fraction 1/4 can mean the probability of an event is one in four

Misconceptions

r

-Thinking of numerator and denominator as separate and not as a single value-Not recognizing equal parts-Thinking that 1/5 is smaller than 1/10 because it has a smaller denominator-Using the rules from whole numbers to compute

Models

r

-Region or area models-Length models-Set models

Fractions greater than 1 (Improper Fractions)

Equivalent Fractions

Decimals

Rules

r

-When going to the right of the decimal point you will divide by 10 and when going the left of the decimal point you will multiply by 10-When talking about decimal places make sure to add the "ths" to the end of the normal places

Terminating and Repeating Decimals

r

Terminating Decimals- decimals that have a specific end Repeating Decimals- decimals that keep going on with a repeating pattern and never ends (do not mistaken for an irrational number/decimal)

Multiplying Decimals

Bases

Place Value

a

Whole Number Addition

Properties of Addition

a

Algorithims

Multiplication

Three Major Models

Repeated Addition (Discrete)

repeated Addition (continuous)

Area Model

Properties

a

Integers

r

Integers are positive numbers, negative numbers, and zero

Negative numbers in real life

a

Absolute Value

distance from zero

Chip Method

Fraction Operations

a

Addition

r

Discrete: something you can put in a box (physical objects usually) Continuous: time or distance

Subtraction

r

Take away Missing addendComparison

Multiplication

r

Repeated addition (discrete)Repeated addition (continuous)

Division

r

Measurement (repeated subtraction)- know # in each groupParition (sharing, dealing cards)- know # of groups