Integers are natural numbers and their negative counterparts. An integer can be a positive (1, 2, 3, 4) or a negative number (-1, -2, -3, -4). It can also be zero. These values do not contain a decimal or fractional part. They are often called counting numbers because they are whole units that differ by a complete value. You will often come across the term consecutive integers which indicates that these are numbers that come one after another (5, 6, 7, 8). These worksheets and lessons will have you work with integers in all types of different situations and operations.
- Absolute Value and Basic Operations - We look at how operations and absolute value measures can work hand in hand.
- Absolute Value in Word Problems - You will find a large number of problems that include measures of temperature and finance as they lend themselves to absolute value.
- Advanced Absolute Value Operations - These are normally two-step or more problems. It will help to organize them along every step.
- Adding and Subtracting Rational Numbers - This gives you a basic approach to follow and complete. It focuses on sum and difference operations only.
- Addition and Subtraction of Integers - This is normally under special circumstances. This will be a good skill to review prior to learning algebra.
- Consecutive Integer Problems - Where do you go about organizing these problems? Start with understanding the vocabulary that is being presented.
- Consecutive Numbers - How to spot them and where to go from here with them.
- Creating Reciprocals - Learn how to jump in a flip. As we move forward with exponents, this skill will be used more.
- Factors of an Integer - What is an integer built up of? See if you can pull a multiple out of it.
- Forms of Numbers (Numerals, Number Names, Expanded Form) - We look at different formats for expressing a value.
- Inequalities and Numbers Lines - This really helps students start to understand the true value of an inequality.
- Integer Word Problems - How to quickly set them up and solve them. We setup some interesting situations for you.
- Making Words With Calculator Fun - We all do this, as kids. These worksheets can make for a fun day.
- Multiplication and Division of Rational Numbers - This provides a concrete set solution for you.
- Multiplying and Adding Rational and Irrational Numbers - Some students will get a little lost with the irrational values.
- Naming Numbers - Matching the values to words that represent them and vice versa.
- Odd and Even Numbers - How to classify values. This concept helps students learn division and understand the concept of primes.
- Ordering For Rational Numbers - We start by comparing them and then we sort them.
- Ordinal Numbers - How to put these values in order. This skill is helpful for communicating your message.
- Prime and Composite Numbers - Primes have two factors which are themselves and one. Composites have factors besides themselves and one.
- Prime Factorization and Factor Trees - We look at what which primes you can multiply by one another to make an original value.
- Roman Numerals - You will learn how to convert between and use this form of numeracy.
- Understanding Cardinal Numbers - This is a way to state a relative position found within a series.
- Understanding Division of Integers - The goal is in the setup of the problem.
- Understanding Positive and Negative Numbers - The way in which the problems are setup count a great deal here.
- Understand A Rational Number As A Point - This relates to the use of number lines.
- Using Number Lines In Math - A very helpful and useful tool. This really is helpful when learning new skills.
- Working with Absolute Value - I always tell students to knock it off and calculate the absolute value first and then the rest of the problem.
What are Integers?
We all use and observe numbers every day. They all might look the same but there are different kinds of numbers. Each number shares some differences and similarities with each other. These similarities and differences help us in identifying them and keeping track of them. Therefore, to better understand these numbers, mathematicians have categorized them in different groups of: Natural, Real, Whole, Integers, ands Rational.
Integers are a group of numbers that consists of all numbers, positive or negative. Integers do not have fractions and decimals. For example, 1.23, 1/4, and 3.44 are not considered integers. Let work on understanding the basic numbers and integers around us.
We work heavily with numbers lines and use it to make sense of negative numbers.
Integers can be positive (1, 2, 3, 4...) and negative (-4, -3, -2, -1 ...). Remember, zero is also included as an integer.
There are few things to remember about integers when doing the addition and subtraction of integers.
1. Negative integer + negative integer result in negative integer.
2. Positive integer + positive integer results in a positive integer.
3. Negative integer + positive integer or positive integer + negative integer results in subtraction. The sign of the resulting integer will be of the larger integer.
How Do You Use Integers in Real Life?
Whether you realize it or not, in the modern world we are constantly being swamped with data. When you get in the car, you have a number of miles to travel and you maintain a certain speed along your way. All of these values are forms of integers. It is really tough to come into a situation where you are either trying to improve something or take it apart where integers do not play a factor of some sort. Being able to understand data to the point where you can either manipulate or make solid educated guesses is a highly desirable skill. This why understanding how these values interact is the key to being able to recognize trends. In most cases the single most important component of this is to understand if the value is presenting as positive or negative. Once you learn how to recognize this, everything just seems to fall into place for you.