Algebra Vocabulary Algebra Vocabulary Vocabulary is important to successful mathematics. Without a good Vocabulary is important to successful mathematics. Without a good

understanding of the math vocabulary, you will struggle to understanding of the math vocabulary, you will struggle to understand the concepts. So, try this. Spend 15 minutes a day understand the concepts. So, try this. Spend 15 minutes a day

studying the material. It will help you understand what I’m talking studying the material. It will help you understand what I’m talking about. It will help you understand the questions you see on about. It will help you understand the questions you see on

standardized assessments. It will help you get a handle on why standardized assessments. It will help you get a handle on why you’re learning these concepts.you’re learning these concepts.

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13x + 5 = 75

AlgebraAlgebra Algebra is the branch of mathematics that uses letters and numbers. Algebra is the branch of mathematics that uses letters and numbers.

Algebraic concepts, that is, the concepts you learn in algebra, are used in Algebraic concepts, that is, the concepts you learn in algebra, are used in other branches of mathematics. You must understand these concepts to work other branches of mathematics. You must understand these concepts to work with geometry or calculus, for example. Algebra is an important foundation with geometry or calculus, for example. Algebra is an important foundation

in working with numbers. in working with numbers. Which of the following looks like an algebra problem?Which of the following looks like an algebra problem?

4 + 15 = 19

36 – 10 = 26

27 3 = 9

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x

EqualEqual Equal means the same in number, value, quantity or quality; having a one-Equal means the same in number, value, quantity or quality; having a one-to-one correspondence. You have been studying this concept for most of to-one correspondence. You have been studying this concept for most of

your life. Much of the time, a form of the word “equal” could replace a form your life. Much of the time, a form of the word “equal” could replace a form of the word “is”. It sounds funny, but try to see if you can trade “equal” for of the word “is”. It sounds funny, but try to see if you can trade “equal” for “is” sometime. I think you will find that your understanding of “equal” will “is” sometime. I think you will find that your understanding of “equal” will

broaden. broaden. Click on the equal sign.Click on the equal sign.

+

-

=

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14

VariableVariable A letter that represents one or more numbers.A letter that represents one or more numbers.

In algebra, letters are used to represent one or more number. One In algebra, letters are used to represent one or more number. One of the main goals of algebra is to make complicated number expressions of the main goals of algebra is to make complicated number expressions

simple. We do that by finding out what the variable equals. simple. We do that by finding out what the variable equals. Which of the following is a variable?Which of the following is a variable?

x

25

π

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x = 14

ExpressionExpression A statement in mathematics that usually includes numbers, variables, and A statement in mathematics that usually includes numbers, variables, and symbols. This word has a lot of meanings, not just a mathematical one.symbols. This word has a lot of meanings, not just a mathematical one.

Which of the following is NOT an expression?Which of the following is NOT an expression?

17x + 10x

314,781

πr2

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D = st

FormulaFormula A combination of symbols used to state a rule. One of the first formulas you A combination of symbols used to state a rule. One of the first formulas you will use in algebra is will use in algebra is A= lw, or A= lw, or area equals length times width. The rule is area equals length times width. The rule is

that if you multiply the length of a rectangle by its width, you get the that if you multiply the length of a rectangle by its width, you get the number of square units it would take to cover the rectangle. We use this number of square units it would take to cover the rectangle. We use this formula for covering everything from floors to yards, roofs to walls, and formula for covering everything from floors to yards, roofs to walls, and

parking lots to cornfields. parking lots to cornfields. Click on the one that is NOT a formula.Click on the one that is NOT a formula.

Acircle = πr2 17 + 4 = 21

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Vsphere = πr3 4

3

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5(5) + 7 = 25 + 7 = 32

EvaluateEvaluate To find the value of an expression. One step along the way to becoming To find the value of an expression. One step along the way to becoming

good with algebra is evaluating expressions. This is just good practice with good with algebra is evaluating expressions. This is just good practice with the concepts of “equal” and “substitution.” When a variable is equal to a the concepts of “equal” and “substitution.” When a variable is equal to a

number, replace the variable with the number, perform the operations, and number, replace the variable with the number, perform the operations, and you get another number. you get another number.

Which one shows the correct evaluation? (Remember, a number Which one shows the correct evaluation? (Remember, a number followed by a variable means the number followed by a variable means the number timestimes the variable.) the variable.)

5(5) + 7 = 55 + 7 = 62

5 x 3 + 7 = 8 + 7 = 15

5(3) + 7 = 15 + 7 = 22

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Evaluate 5x + 7 for x = 5

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14x

Algebraic ExpressionAlgebraic Expression A statement in mathematics that uses at least one operation and a variable. A statement in mathematics that uses at least one operation and a variable.

Remember the definition of “expression”. Any expression with an operation Remember the definition of “expression”. Any expression with an operation and a variable is an algebraic expression. To help with remembering the and a variable is an algebraic expression. To help with remembering the

difference between an “expression” and an “algebraic expression”, difference between an “expression” and an “algebraic expression”, remember that all algebraic expressions are expressions, but not all remember that all algebraic expressions are expressions, but not all

expressions are algebraic. The difference is the variable. expressions are algebraic. The difference is the variable. Which of the following is NOT an algebraic expression?Which of the following is NOT an algebraic expression?

17 + 10 = 27

12q + 11

x2 + 2xy + 5

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35 + 70 = 105

Open StatementOpen Statement A sentence that is neither true nor false. These statements are easy A sentence that is neither true nor false. These statements are easy

to spot. An open statement has an undefined variable, a true or false to spot. An open statement has an undefined variable, a true or false statement does not. “Undefined variable” means that the value of statement does not. “Undefined variable” means that the value of

the variable is not given.the variable is not given.Which of the following is an open statement?Which of the following is an open statement?

3x + 7 = 52 whenx = 15

12(5) + 70 = 130

3 + y = 5

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35 + 70 = 105

EquationEquation A number statement with an equal sign. This is another simple one. A number statement with an equal sign. This is another simple one.

If it has an equal sign, it is an equation. If it has an equal sign, it is an equation.

Which of the following is NOT an equation?Which of the following is NOT an equation?

48q

12(5) + 70 = 130

3x + 7 = 52 whenx = 15

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ReciprocalReciprocal A number that when multiplied with another number has a product A number that when multiplied with another number has a product

of 1. Use reciprocals to apply the identity principle of of 1. Use reciprocals to apply the identity principle of multiplication. Reciprocals are factors that equal 1. multiplication. Reciprocals are factors that equal 1. 1/2 X 2 = 1, 1/2 X 2 = 1,

1/2 and 2 are reciprocals.1/2 and 2 are reciprocals.

Which of the following are NOT reciprocals?Which of the following are NOT reciprocals?

25 = 1 = 123

32

125

= 34

34

916 = 17

887

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8

PatternPattern A pattern is a group of numbers, shapes, colors, and so on that A pattern is a group of numbers, shapes, colors, and so on that repeats in such a way that the next item can be guessed. For repeats in such a way that the next item can be guessed. For

thousands of years, people have used numbers to explore patterns, thousands of years, people have used numbers to explore patterns, and mathematics has been called the science of patterns. and mathematics has been called the science of patterns.

Which is next in the pattern?Which is next in the pattern?

10

9

7

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1, 0, 3, 2, 5, 4, 7, 6, ___

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n + 1

Algebraic ModelAlgebraic Model The formula for a pattern. Sometimes patterns can be turned into The formula for a pattern. Sometimes patterns can be turned into

formulas, like formulas, like A= lwA= lw. There are many of these formulas . There are many of these formulas representing relationships that stay the same among different parts representing relationships that stay the same among different parts

of a pattern. . of a pattern. . Which is the algebraic model for the pattern?Which is the algebraic model for the pattern?

2n - 1

n2 - 1

5n - 6

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1, 3, 5, 7, 9, 11, 13, 15, …

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Vocabulary Lesson 1Vocabulary Lesson 1 This concludes vocabulary lesson 1.This concludes vocabulary lesson 1.

I hope you enjoyed going through these little I hope you enjoyed going through these little drills. As your math vocabulary continues to grow, drills. As your math vocabulary continues to grow, so will your success with math. Try to have some so will your success with math. Try to have some fun with math. Life is, after all, a story problem.fun with math. Life is, after all, a story problem.

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