Adding and Subtracting Integers Worksheets
A number line is a great tool that we can use to visualize adding or subtracting signed integers. When we add positive integers, we move to the right on the number line. If you were to add a negative integer, you would move in the opposite direction (left). The tricky part comes in when we look at the subtraction operation. You can consider subtraction the addition of the values opposite value. For example, if we consider the value as x; -(-x) = + x. When we add two negative values it results in a combination of the integers with a negative value. For example, -5 + -6 = -11. The opposite is true if we were to subtract these values. Just remember the phrase, "minus a minus equals a plus". For example, -5 - -6 = -5 + 6 = 1. These worksheets and lessons will explore the value of these types of values and how they are relative to one another when we consider these operations.
Aligned Standard: Grade 7 Number Systems - 7.NS.A.1
- Using a Numbers Line Step-by-step Lesson- Adding a negative number to a positive number. We show you how to do this with a numbers line. A great visual for students.
- Guided Lesson - More work with our favorite visual, but we also introduce the concept of debt and balances.
- Guided Lesson Explanation - The numbers line ninjas went all out on this one.
- Practice Worksheet - I plopped a numbers line at the top for you to work off of.
- Number line Expressions Five Worksheet Pack - Represent each problem on the numbers line. A neat way to review this skill.
- Matching Worksheet - This makes for a great culminating activity for the kids.
- Answer Keys - These are for all the unlocked materials above.
As you can tell, I am a huge fan of having a number line handy when looking at this skill.
- Homework 1 - Use a number line to add -3 + 10 . This is a great way to see it before you.
- Homework 2 - Jenifer has 9 cupcakes. She made 2 more cupcakes. But her sister took 3 cupcakes. How many cupcakes does she have left?
- Homework 3 - We know that two like signs become a positive sign when they go through these operations.
The first 2 sheets have you draw the problems on a number line. The last sheet is a transition away from the number line.
- Practice 1 - Represent the operations: -2 - (-3) using the technique that we have discussed.
- Practice 2 - We will display a wide array of operations to help make sense of the outcomes.
- Practice 3 - Find the sum of negative values in this practice sheet.
Math Skill Quizzes
We cover this skill on all fronts including number lines, word problems, and integer sums and differences.
- Quiz 1 - It is time to see how far you can run with this skill.
- Quiz 2 - We expand to use larger values on this quiz.
- Quiz 3 - Roxy gave 15 chocolates to Mandy. Roxy originally had 25 chocolates, how many does Roxy have left?
What Are Integers?
Integers are a specific set of numbers that consist in a series. These are the counting values that we grew up with, but they also include the negative scale. These values do not include a fractional or decimal portion. That means that they are whole numbers. One thing to remember is that zero is in fact an integer and it the origin of the entire scale. Where students often get a little confused when classifying values in this group is the use of symbols such as brackets, parenthesis, and ellipses. Just because a value is encased or found outside one of these symbols, it does not change the fact that it is classified as an integer. When we are performing addition or subtraction operations with integers there are some common rules that often apply. When we are adding two positive integers the sum is positive as well. The same holds true for negative sums. When you are finding the sum of negative and positive value, it is best to rearrange the equation to make it a subtraction equation. When you are working with subtraction operations, just remember that subtracting a negative value turns it into a positive value.
What are Negative Numbers?
We all know the opposite of words in the English language. Thin and fat. Night and day. Beautiful and ugly. But do you know the opposites of numbers in math? We will explore that here. You know the integers that we use when counting, right? 1, 2, 3, 4, 5, 6, and so on. All the numbers that we are familiar with are called positive numbers. Why? Because there is no sign along with that value. The starting point of positive integers is 0. So, like any other opposite form of communication, the opposite of positive numbers are negative numbers. All the values that lie before 0 are called negatives, and they are written with a "-" sign. These numbers come before 0 because their value is smaller than 0. For example, the opposite of 1 is -1. The opposite of 2 is -2. The opposite of 3 is -3.
We use these values every day to express the concept of being above or below a standard level. Our temperature scales are based on standards. The Celsius temperature scale is based on phase changes of water. When a temperature that would freeze water is reached it said to be zero. The negative values would indicate that water is in solid (frozen) form. We use negative values in finance to indicate that money is owed. The standard in elevation is based on the standard of sea level. A negative value of elevation indicates that you are describing a height below sea level.