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Variables and Expressions

This lesson focuses on the appropriate use of variables in algebra to represent unknown values. Students will learn how to translate words into algebraic expressions and vice versa. Key concepts include understanding variables, algebraic expressions, and mathematical operations such as sum, difference, product, and quotient. Through practice, students will master how to express various numerical phrases as algebraic expressions, enhancing their understanding of algebra and preparing them for more advanced mathematical concepts.

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Variables and Expressions

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  1. Variables and Expressions

  2. Standards and Objectives GLE 0506.3.2 – Use variables appropriately to represent numbers whose values are not yet known. Objectives: The students will translate words into algebraic expressions and algebraic expressions into words.

  3. Variable: A letter or symbol that represents an unknown amount that can vary or change. Example: 5+n In 5+ n, “n” is the variable.

  4. Algebraic Expression: A mathematical phrase involving variables, numbers, and operations. 3+n=7 is an Algebraic Expression 3+4=7 is NOT an Algebraic Expression

  5. Math Words to Review… • Difference: The number that results from subtracting one number from another. • Product: The number that is the result of multiplying two or more factors. • Quotient: The number other than the remainder that is the result of dividing. • Sum: The number that is the result of adding two or more addends.

  6. What are some ways we can say this numerical expression? 3 + 4

  7. What are some ways we can say this numerical expression? 3 + 4 Three plus Four Four more than Three The sum of Three and Four

  8. What are some ways we can say this numerical expression? 7 - 2

  9. What are some ways we can say this numerical expression? 7 - 2 The difference of Seven and Two Two less than Seven Seven minus Two

  10. But how can we say this...

  11. 5 + 5 +

  12. How do you read this expression? 5 + • This ALGEBRAIC EXPRESSIONcan be read as: • The sum of five and a number • Five more than a number

  13. What about this one? How do we read this ALGEBRAIC EXPRESSION? 4 X • The product of four and a number • Four times a number

  14. In order to write a mathematical expression for the word phrase “5 plus a number” you must use a VARIABLE. • A variable is a letter or symbol that you use to represent unknown values that can vary or change. • When an expression includes a variable, it is called and ALGEBRAIC EXPRESSION. LET’S PRACTICE…

  15. Translate these Algebraic Expressions into Words… n + 9 A NUMBER plus nine.

  16. Translate these Algebraic Expressions into Words… n ÷ 12 A NUMBER divided by twelve.

  17. Translate these Algebraic Expressions into Words… 4 - n Four minus a NUMBER. Or A NUMBER less than 4.

  18. Translate these Algebraic Expressions into Words… 8 X n Eight multiplied by a NUMBER. Or The product of eight and a NUMBER.

  19. Now, let’s try writing each word phrase as an ALGEBRAIC EXPRESSION. Add six to a number. n + 6 Subtract a number from ten. 10 – n

  20. Write each word phrase as an ALGEBRAIC EXPRESSION. The product of nine and a number. 9 X n OR n X 9 Fifteen divided by a number. 15 ÷ n

  21. Write each word phrase as an ALGEBRAIC EXPRESSION. Twelve less than a number. n - 12 A number added to nine. 9 + n

  22. Time for some TEAM WORK!

  23. NOW IT’S YOUR TURN! Page 146 of your Math text book. Problems 1-20.

  24. Standards and Objectives GLE 0506.3.2 – Use variables appropriately to represent numbers whose values are not yet known. Objectives: The students will translate words into algebraic expressions and algebraic expressions into words.

  25. EXIT TICKET • Complete the following problems on your index card and turn in… • Translate this word phrase into an algebraic expression: • The product of a number and nine. • Translate this algebraic expression into a word phrase: • 10 - n

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