Integers and their operations are an important concept in mathematics, typically introduced in the middle or early high school grades. While integers are often used in everyday life, this concept can be challenging for students. The introduction of negative numbers, numbers that are less than zero, is new to students and it can be confusing.
Integers are one of the basic sets of numbers students encounter, including natural numbers, whole numbers, and rational numbers. A solid grasp of integers is essential for understanding these more complex number systems.
Below are some steps and tips for teaching integers effectively:
Start by explaining what integers are: Integers include all positive whole numbers, all negative whole numbers, and zero. Use visual aids like a number line to illustrate this concept. They are used to represent quantities that can increase or decrease in value.
Provide real-life examples and word problems that involve integers to make the concept more relatable to students. This can help them see the practical applications of integer operations. Integers are used in describing temperature, credit, and elevations.
Positive and Negative Numbers
Differentiate between positive and negative numbers: Positive numbers are greater than zero. Negative numbers are less than zero. Zero is neither positive nor negative.
Number lines are great for representing integers and gaining conceptual understanding. Place zero in the middle and show positive integers to the right and negative integers to the left. Ask students to order integers using the number line. This helps students visualize the concept of positive and negative numbers.
Teach students about the absolute value of integers: The absolute value of a positive integer is itself. The absolute value of a negative integer is its positive counterpart.
Show students how to compare integers: Use the greater than (>) and less than (<) symbols. Explain that the number farther to the right on the number line is greater, while the number farther to the left is smaller.
Addition and Subtraction:
Teach students how to add and subtract integers: Guide the students to figure out the “rules” with practice on the number line. Encourage them to identify patterns when adding and subtracting integers. When adding integers with the same sign, add their absolute values and keep the sign. When adding integers with different signs, subtract the smaller absolute value from the larger one and use the sign of the number with the larger absolute value. Similar rules apply to subtraction. Talk about the addition properties that allow us to rearrange the numbers and simplify problems.
Multiplication and Division:
Introduce multiplication and division of integers: Utilize the number line to show how the multiplication of integers corresponds to movement on the number line. For example, multiplying by a positive integer means moving to the right (toward positive numbers), while multiplying by a negative integer means moving to the left (toward negative numbers). The product of two integers with the same sign is positive. The product of two integers with different signs is negative.
Encourage students to identify patterns when multiplying integers. For instance, multiplying or dividing two numbers with the same sign (positive or negative) results in a positive number, while multiplying two numbers with different signs (positive or negative) results in a positive number.
Games and Activities
Use games and interactive activities to make learning integers fun and engaging. Here are some games for practicing integer operations.
Below you will find two collections of activity and explanation cards for teaching the concept of integers.
Introducing, Adding and, Subtracting Integers
The first collection includes the introduction of integers as well as adding and subtracting integers. The Google slides and print cards include explanations, practice on the number line, ordering, comparing, opposite integers, absolute value, rearranging, word problems, and challenge problems.
The second collection includes 35 slides and is all about understanding and practicing the multiplication and division of integers. Rules, opposite expressions, word problems, challenges, puzzles, opposite expressions, exponents, solutions, and more.