Introducing Integers Copyright 2015 Scott Storla.

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Presentation transcript:

Introducing Integers Copyright 2015 Scott Storla

If all we have are the whole numbers, {0,1,2,3…}, we can find this difference 5 – 2 = 3 but we can’t find this difference 2 – 5 = ? To find the difference 2 – 5 we need to expand our set of numbers.

Copyright 2015 Scott Storla The Integers

Positive Money we have Yards gained Degrees above 0 Floors above ground Above sea level Negative Money we owe Yards lost Degrees below 0 Floors below ground Below sea level Copyright 2015 Scott Storla

The Integers

Introducing Integers Copyright 2015 Scott Storla

Absolute Value Copyright 2015 Scott Storla

Positive Money we have Yards gained Degrees above 0 Floors above ground Above sea level Negative Money we owe Yards lost Degrees below 0 Floors below ground Below sea level Copyright 2015 Scott Storla

Integers have two attributes, a “size” (how much, how many) and a sign (positive or negative). For instance $2 has a size of 2 and it’s positive, we have $2. – $2 also has a size of 2 and it’s negative, we owe $2. To discuss the size of a number we use the absolute value operator. Copyright 2015 Scott Storla

Absolute value is both an operator and an implicit grouping symbol. Copyright 2015 Scott Storla Absolute Value

Operations and Operators Copyright 2015 Scott Storla

Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Absolute Value Copyright 2015 Scott Storla

Multiplying and Dividing Integers Copyright 2015 Scott Storla

Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright Scott Storla 2015 Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Multiplying and Dividing Integers Copyright 2015 Scott Storla

Adding Integers With Similar Signs Copyright 2015 Scott Storla

Simplify

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright Scott Storla 2015 Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Adding Integers With Similar Signs Copyright 2015 Scott Storla

Adding Integers With Different Signs Copyright 2015 Scott Storla

Simplify

Copyright Scott Storla 2015 Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Adding Integers With Different Signs Copyright 2015 Scott Storla

Subtracting Integers Copyright 2015 Scott Storla

Introducing the Procedure Copyright 2015 Scott Storla

Simplify

Copyright 2015 Scott Storla Simplify

Copyright 2015 Scott Storla Simplify

Introducing the Procedure Copyright 2015 Scott Storla

Continuing With the Procedure Copyright 2015 Scott Storla

Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Continuing With the Procedure Copyright 2015 Scott Storla

Problems With a Factor of -1 Copyright 2015 Scott Storla

Simplify

Copyright 2015 Scott Storla Simplify

Copyright Scott Storla 2015 Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Simplify

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Copyright 2015 Scott Storla Count the number of operators, discuss the order of the operations and then simplify.

Problems With a Factor of -1 Copyright 2015 Scott Storla

See introductory algebra resources Copyright 2015 Scott Storla

Fill in each blank with the appropriate property

Copyright 2015 Scott Storla Fill in each blank with the appropriate property

Copyright 2015 Scott Storla Fill in each blank with the appropriate property

Copyright 2015 Scott Storla Fill in each blank with the appropriate property

Integer Automaticity Quiz Copyright 2015 Scott Storla

Simplify Copyright 2015 Scott Storla Answers

Simplify Copyright 2015 Scott Storla Answers

What’s the sign of the result? Copyright 2015 Scott Storla

What’s the sign of the result? Copyright 2015 Scott Storla

What’s the sign of the result? Copyright 2015 Scott Storla

What’s the sign of the result? Copyright 2015 Scott Storla

What’s the sign of the result? Copyright 2015 Scott Storla

What’s the sign of the result? Copyright 2015 Scott Storla

What’s the sign of the result? Copyright 2015 Scott Storla

What’s the sign of the result? Copyright 2015 Scott Storla

Simplify