The World of Integers

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Information and Resources about Integers

This is a fun video that does a great job introducing integers. It talks about positive and negative integers, the number line, greater than and less than values, and many other topics.

Division of Integers

Division Sign Practice

This website has descriptions and practice problems for positive and negative signs with multiplication and division.

Fact Families

If a, b and c are whole numbers, with b not equal to 0, then a/b = c if and only if a = bc.

Fact Family Practice for Multiplication and Division

This website has various worksheets for students where they can practice different fact families for multiplication and division.

Multiplication of Integers

Multiplication Using a Number Line

6 times 4 equals 24/4 times 6 equals 24

Multiplication Properties

This website has various worksheets and resources to practice the different properties of multiplication.

Multiplicative Property of 0 ((0)(r) = (r)(0) = 0)

Multiplicative-Identity Property of 1 ((1)(r) = (r)(1) = r)

The website here gives a mini lesson about the multiplicative-identity property of 1 and even includes a quiz students can take.

Distributive Property (r(s+t) = rs+rt)

This YouTube video explains the distributive property of multiplication using the example of distributing bracelets to friends. It is a perfect video for younger students.

Associative Property (r(st) = (rs)t)

Commutative Property (rs = sr)

The commutative property is explained in an easy and fun way with this website.

Closure Property (rs is an integer)

The Rule of Signs

The website here describes the various rules of signs when multiplying positive and negative integers together.

3. (-m)(-n) = mn

2. (-m)n = -mn

1. m(-n) = -mn

Number Line Representations

Number Line Practice

This website quizzes students on the number line and gives them extra practice and help.

Number lines are represented with zero in the middle, negative numbers to the left of the zero and positive numbers to the right of the zero.

Number Line Example

Ordering the Set of Integers

Law of Trichotomy

This website has a perfect definition and explanation of the law of trichotomy.

If a and b are any two integers, then precisely one of the following relations holds: a is greater than b, a is less than b or a is equal to b.

Subtraction of Integers

Subtracting by adding the opposite: a-b = a+(-b)

Fact families: (a-b = c), (a = c+b), (a = b+c), (a-c = b)

This website describes fact families for addition and subtraction. It also includes practice worksheets.

If a, b and c are integers, then (a-b = c) if and only if (a = c+b).

Subtraction is the "take away" representation of numbers and can be shown using a number line.

This YouTube video talks about subtraction in relation to the number line and gives various examples. The colors and characters in the video make it perfect for a younger audience.

Addition of Integers

Addition of Integers by Using a Number Line

You can add numbers on a number line by simply hopping or jumping from point to point to find the answer.

You can also add a negative number to a positive one using the same technique.

Addition Properties of Integers

Existence of Negatives ((-m)+m = m+(-m) = 0)

The additive inverse property is described in detail with this website.

It is also known as the Additive Inverse Property.

Additive-Identity Property of O (0+m = m+0 = m)

Associative Property (m+(n+r) = (m+n)+r)

This website gives a fun and exciting description of the associative property of addition.

Commutative Property (m+n = n+m)

Closure Property (m+n is an integer)

Closure and Commutative Properties

This is a descriptive YouTube video that talks about the closure and commutative properties of addition.

Absolute Value

Absolute value is also known as the magnitude of an integer.

This video uses lots of cartoons and animation to describe what absolute value is. It is the perfect video for elementary-aged students.

Absolute Value Problems and Resources

Resources

The website here defines absolute value is basic and helpful terms.

Practice Problems

The website here has lots of worksheets to help practice absolute value.