How to Identity & Inverse Properties of Algebra in Math for Middle School
The identity and inverse properties are the very essence of algebra. Middle school students need familiarity with the number line, negative numbers and fraction division before working with these concepts. Although inverses and identities seem simple, it is important for students to work with these concepts until they fully grasp their meanings and implications. As the pupil progresses through algebra, these properties will show up in word problems, problems of distribution and functions. Likewise, these properties will help with other more advanced subjects, such as geometry and statistics.
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Inverse for Addition
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The additive inverse is one of the more basic concepts in algebra. The website MathChamber defines this property as, "For every number a,
a + (-a) = 0"
This property is important for understanding algebra with negative numbers. Students should recognize the connection. Use a number line and have them identify a number on both sides of zero. Make sure they realize each number is the same distance from zero.
Inverse for Multiplication
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For first-year algebra students, the multiplicative inverse is more challenging than the other properties. West Texas A&M University defines the multiplicative inverse as "For each real number a, except 0, there is a unique real number 1/a such that
a * 1/a = 1/a * a = 1"
Make sure students realize they can write any number in this form. They need familiarity with the concept, as it will be important for all division in algebra.
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Identity Property for Addition
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The additive identity is a basic concept, but it is also an important one. MathChamber defines this property as, "For any number a,
a + 0 = 0 + a"
Make sure students are familiar with the idea and understand the difference between the additive identity and the multiplicative identity. This idea is important for all algebraic equations. Students should understand that they can use this property to balance any similar equation.
Identity Property for Multiplication
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The multiplicative identity uses the same concept as the additive identity, but through multiplication. West Texas A &M University describes the multiplicative identity as:
"a(1) = (1)a = a"
Students should be familiar with putting a parenthesized one in front of a number to symbolize multiplication. This concept is important for balancing equations with division, and the use of a one in front of numbers will help with visualization when the students start factoring and working with functions.
Learning the Properties
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Go through the concepts, one by one, until they are second nature. Although inverses and identities seem like basic concepts, they can prove difficult to anyone learning them for the first time. Practice is the best way for middle school students to learn the concepts. Make sure they know the definitions of each idea and recognize the differences. Students need to understand when to add by the number one and when to multiply. Make sure they do not mix up the use of zero with the number one.
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References
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