Do you know what integers are? Do you also know how to graph them on a number line? Let’s find out together!

Integers are whole numbers that can be positive, negative, or zero. For example, 3, -5, 0, 12, and -8 are all integers. A number line is a horizontal line that has numbers marked on it. The number zero is in the middle of the line, and the positive numbers are to the right of zero, while the negative numbers are to the left of zero.

To graph an integer on a number line, find the point corresponding to that number and make a dot or a circle on it. For example, to graph 3 on a number line, make a dot on the point that is three units to the right of zero. To graph -5 on a number line, make a dot on the point that is five units to the left of zero.

Positive and negative integers have different meanings depending on the context. For example;

• If we are talking about temperature, a positive integer means that it is above zero degrees Celsius. In contrast, a negative integer means that it is below zero degrees Celsius.
• If we are talking about elevation, a positive integer means that we are above sea level, while a negative integer means that we are below sea level.
• If we are talking about money, a positive integer means that we have gained or earned some amount, while a negative integer means that we have lost or spent some amount.

To compare two integers, we use the symbols > (greater than), < (less than), or = (equal to). For example:

• 3 > -5 means that 3 is greater than -5,
• -8 < 0 means that -8 is less than 0,
• 12 = 12 means that 12 is equal to

To compare two integers on a number line, we look at their relative positions. The integer that is closer to the right of the number line is greater than the integer that is closer to the left of the number line. For example, 3 is greater than -5 on a number line because 3 is closer to the right than -5. Similarly, -8 is less than 0 because -8 is closer to the left than 0.

The absolute value of an integer is its distance from zero on a number line. It is always positive or zero. To find the absolute value of an integer, we ignore its sign and write it as a positive number. For example, the absolute value of 3 is 3, the absolute value of -5 is 5, and the absolute value of 0 is 0. To find the distance between two integers on a number line, we can use their absolute values.

The distance between two integers equals the difference between their absolute values. For example, to find the distance between 3 and -5 on a number line, we can subtract their absolute values: |3| - |-5| = 3 - 5 = 2. The distance between 3 and -5 is 2 units.

We can use graphing and comparing integers to solve many real-world problems involving temperature, elevation, money, etc. For example, suppose we want to know how much warmer it was in Miami than in New York on a particular day; we can use a number line to graph the temperatures in both cities and compare them using symbols.

Suppose Miami had a temperature of 25°C and New York was -2°C.

We can graph these temperatures on a number line as shown below:

As we can see, Miami is warmer than New York because 25 is greater than -2 on the number line.

So, we can write this as 25 > -2.

To find out how much warmer Miami was than New York, we can subtract their temperatures: 25 - (-2) = 25 + 2 = 27.

Miami was 27°C warmer than New York.

Here are some tips and tricks for mastering integers in grade 6 math:

• Remember the rules for adding, subtracting, multiplying, and dividing integers. For example, when adding two integers with the same sign, we add their absolute values and keep their sign.

  When adding two integers with different signs, we subtract their absolute values and take the sign of the larger absolute value.

  The result is positive when multiplying or dividing two integers with the same sign. The result is negative when multiplying or dividing two integers with different signs.

• Use a number line to visualize and compare integers. A number line can also help us perform operations with integers, such as adding, subtracting, and finding absolute values.
• Use real-world examples to understand and apply integers. For example, we can use temperature, elevation, money, time, and more to represent and solve problems with integers.
• Practice, practice, practice! The more students practice with integers, the more confident and comfortable they will become with them. Encourage your 6^th Grade students to use worksheets, games, quizzes, puzzles, and more to practice their skills with integers.

If you want to test your 6^th grader's skills and knowledge on graphing and comparing integers, you can try Mathskills4kids’ Grade 6 integers worksheets that cover the topics we discussed in this article.

You can download and print them out for free or do them online with your students. Each worksheet has a set of questions, an answer key, and an explanation of how to solve each problem.

You can also check your student’s progress with a score report that shows how many questions they answered correctly and how long it took them to complete the worksheet.

• Understanding integers: This worksheet helps students review the basics of integers, such as what they are, how to write them, and how to identify them on a number line. They will also practice adding and subtracting integers using the rules of signs.
• Integers on number lines: This worksheet will help 6^th graders to practice graphing integers on horizontal and vertical number lines. They will also learn how to use arrows to show the direction and magnitude of an integer.
• Graph integers on horizontal and vertical number lines: This worksheet will help learners practice graphing integers on horizontal and vertical number lines. They will also learn how to label the points with their coordinates and how to find the coordinates of a point given its graph.
• Understand absolute value: This worksheet will help students understand the concept of absolute value, which is the distance of an integer from zero on a number line. They will also learn how to find the absolute value of an integer using brackets or a vertical bar symbol.
• Absolute value and opposite integers: This worksheet will help 6^th Grade students practice finding the absolute value and the opposite of an integer. They will also learn how to use the properties of absolute value and opposite integers to simplify expressions and solve equations.
• Compare integers: This worksheet will help learners practice comparing integers using greater than, less than, or equal to symbols. They will also learn how to use a number line to compare integers visually and how to order integers from least to greatest or vice versa.
• Put integers in order: This worksheet will help 6^th graders practice putting integers from least to greatest or from greatest to least. They will also learn how to use a number line to check their answers and arrange integers in ascending or descending order.
• Integers inequalities with absolute values: This worksheet will help students practice solving inequalities that involve integers and absolute values. They will also learn how to graph the solutions of inequalities on a number line and write the solutions using interval or set notation.
• Integers and absolute values word problems: This worksheet will help children practice solving real-world problems that involve integers and absolute values. They will also learn how to translate words into mathematical expressions and equations and how to use different strategies to solve word problems.