Math 251

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Integers

Division

Negative / Positive

Positive / Negative

Negative / Negative

Positve / Positive

Negative * Positive

Positive * Negative

Negative * Negative

Positive * Positive

Subtraction

Negative - Positive

Positve - Negative

Negative - Negative

Positive - Positive

Positive or Negative

Addition

Negative + Positive

Negative or Posiitive

Positive + Negative

Negative or Positive

Negative +Negative

Negative

Posiitve + Positive

Positive

Division

Using Multiplication

Using the smaller number to find its multiples until the larger number is reached, a guess and check using mulitiplication

Partial Quotients

Using the "long seven" method guess multiples and then subract to get easier numbers to work with

Area Model

Repeated Subtraction

48/6 6,6,6,6,6,6,6,6

Drawing the smaller number as whole pieces until the amount of them reaches the larger number

Number Bonding

1512/3 1512 can be broken down to 1500 and 12 which are easy to divide 3 by

Breaking down the larger number to multiples of the smaller one

Multiplication

Models

Ratio Table

A table is drawn one number is slowing multiplied by smaller number until then other number is reached to easily find the answer

Partial Products

Like the traditional model except the zero is not dropped, the intagers are multiplied then added up at the end

Tree/Combinations Model

Array/Area Model

Drawing a box with the height one number and the width the other, breaking them down to solve the area

Repeated Addition Model

4*3=4+4+4

Drawing out one number by the amount of another

Properties

Distributive Property

a(b+c)=(a*b)+(a*c)

Identity Property

a*1=a

Associative Property

a(b*c)=(a*b)c

Communitive Property

a*b=b*a