Grade-7-Quarter4 Translating Algebraic expression and phrase

Math 7

1. Translating Verbal Phrases into Algebraic Expressions with Quiz

2. COMPETENCY translate verbal phrases into algebraic expressions.

3. Agenda Introduction to Algebraic Expressions Basic Components of Algebraic Expressions Common Verbal Phrases and Their Algebraic Translations Translating Addition Phrases Translating Subtraction Phrases Translating Multiplication Phrases Translating Division Phrases Combining Operations in Verbal Phrases Practice Problems: Addition and Subtraction Practice Problems: Multiplication and Division Practice Problems: Mixed Operations Quiz Instructions Quiz: Addition and Subtraction Quiz: Multiplication and Division Quiz: Mixed Operations Quiz Answers: Addition and Subtraction Quiz Answers: Multiplication and Division Quiz Answers: Mixed Operations Common Mistakes and How to Avoid Them Additional Resources Conclusion and Next Steps

4. Introduction to Algebraic Expressions An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It represents a value that can change depending on the values of the variables. Algebraic expressions are fundamental in mathematics because they allow us to generalize arithmetic operations and solve problems involving unknown quantities. For example, the algebraic expression 3x + 5 represents a value that changes as the variable x changes.

5. 3 2 1 Variables: Symbols that represent unknown values, e.g., x, y, z. Constants: Fixed values that do not change, e.g., 3, -5, 7. Coefficients: Numbers multiplying a variable, e.g., in 4x, 4 is the coefficient. Basic Components of Algebraic Expressions

6. The phrase 'sum of' indicates addition. For example, 'the sum of a number and 5' translates to 'x + 5'. Sum of Common Verbal Phrases and Their Algebraic Translations The phrase 'difference between' indicates subtraction. For example, 'the difference between a number and 7' translates to 'x - 7'. Difference Between The phrase 'product of' indicates multiplication. For example, 'the product of a number and 4' translates to '4x'. Product Of The phrase 'quotient of' indicates division. For example, 'the quotient of a number and 3' translates to 'x / 3'. Quotient Of

7. Translating Addition Phrases Addition phrases involve combining two quantities. Common keywords: sum, plus, more than, increased by. Example: 'sum of a number and 5' translates to 'x + 5'. 'A number plus 8' translates to 'x + 8'. '3 more than a number' translates to 'x + 3'. 'A number increased by 12' translates to 'x + 12'. Understanding Addition Phrases Examples and Practice

8. Translating Subtraction Phrases Subtraction phrases indicate removing a quantity from another. Key terms include 'difference', 'less than', 'decreased by'. Identify the minuend (what you start with) and the subtrahend (what you subtract). 'The difference between a number and 7' translates to x - 7. '5 less than a number' translates to x - 5. 'A number decreased by 2' translates to x - 2. Understanding Subtraction Phrases Examples of Translation

9. Translating Multiplication Phrases Multiplication in verbal phrases often uses 'product of' or 'times'. These phrases indicate the need to multiply variables or numbers. Example: 'Twice a number' means 2 times the number, written as 2x. 'The product of a number and 4' translates to 4x. 'Three times a number' translates to 3x. 'Half of a number' translates to 0.5x or x/2. 'Five times the sum of a number and 2' translates to 5(x + 2). Understanding Multiplication Phrases Examples and Translations

10. Translating Division Phrases Division is represented by a fraction or division symbol (÷) The phrase 'the quotient of a number and 3' translates to x ÷ 3 or x/3 Always place the first number (dividend) before the division symbol or as the numerator 'The quotient of a number and 5' translates to x ÷ 5 or x/5 'Half of a number' translates to x ÷ 2 or x/2 'A number divided by 10' translates to x ÷ 10 or x/10 Understanding Division in Expressions Examples of Division Phrases

11. Combining Operations in Verbal Phrases Identify each operation in the phrase. Translate each operation step-by-step. Combine the translations into a single expression. Twice the sum of a number and 3: 2(x + 3) The difference between 5 times a number and 7: 5x - 7 The quotient of the sum of a number and 4 by 2: (x + 4) / 2 Translating Complex Phrases Examples

12. Practice Problems: Addition and Subtraction The sum of a number and 8: x + 8 Five more than a number: x + 5 A number increased by 12: x + 12 The total of a number and 3: x + 3 The difference between a number and 6: x - 6 Nine less than a number: x - 9 A number decreased by 4: x - 4 The result of subtracting 7 from a number: x - 7 Addition Phrases Subtraction Phrases

13. Practice Problems: Multiplication and Division The product of a number and 6: 6x Twice a number: 2x Triple a number increased by 5: 3x + 5 The quotient of a number and 8: x/8 Half of a number: x/2 A number divided by 4, then increased by 3: x/4 + 3 Multiplication Phrases Division Phrases

14. Practice Problems: Mixed Operations Twice the sum of a number and 3, subtracted from 10 The product of 4 and a number, added to 7 The difference of 8 and twice a number, divided by 5 7 added to the quotient of a number and 2 Triple a number, then subtract 5 and add 6 10 - 2(x + 3) 4x + 7 (8 - 2x) / 5 7 + (x / 2) 3x - 5 + 6 Verbal Phrases Algebraic Expressions

15. Quiz Instructions The quiz consists of three sections: Addition and Subtraction, Multiplication and Division, and Mixed Operations. Each section contains 5 questions, making a total of 15 questions. You will have 20 minutes to complete the quiz, which averages to about 1 minute and 20 seconds per question. Questions will ask you to translate verbal phrases into algebraic expressions, similar to the practice problems. Ensure you read each question carefully and double-check your answers before submission.

16. Quiz: Addition and Subtraction Translate: 'the sum of a number and 8' Translate: 'a number increased by 5' Translate: '8 more than a number' Translate: 'the difference between a number and 3' Translate: 'a number decreased by 2' Translate: '7 less than a number' Addition Phrases Subtraction Phrases

17. Quiz: Multiplication and Division Translate: The product of 5 and a number. Translate: Twice a number. Translate: Three times a number decreased by 2. Translate: The product of a number and 7 increased by 4. Translate: The quotient of a number and 6. Translate: A number divided by 8. Translate: The quotient of a number and 4 decreased by 3. Translate: Half of a number. Multiplication Questions Division Questions

18. Quiz: Mixed Operations 1. Five more than twice a number is decreased by three. 2. The product of a number and four, increased by seven. 3. The quotient of a number and six, minus five. 4. Three times a number, plus the difference between the number and two. For each question, let the unknown number be represented by 'x'. Translate the verbal phrase into an algebraic expression using 'x'. Write your answers clearly and check for any simplifications necessary. Example: 'Three more than twice a number' translates to '2x + 3'. Quiz Questions Answer Format

19. Quiz Answers: Addition and Subtraction 1. The sum of a number and 8: x + 8 2. The difference between a number and 6: x - 6 3. 5 more than a number: x + 5 4. 12 less than a number: x - 12 5. The sum of twice a number and 3: 2x + 3

20. Quiz Answers: Multiplication and Division The product of a number and 6: 6x The quotient of a number and 8: x/8 Four times a number decreased by 3: 4x - 3 Twice a number divided by 5: 2x / 5 The product of 7 and a number increased by 2: 7x + 2

21. Quiz Answers: Mixed Operations 1. Three times the sum of a number and five: 3(x + 5) 2. The difference between twice a number and nine: 2x - 9 3. The product of a number and the difference between seven and the number: x(7 - x) 4. The quotient of the sum of a number and four by the number itself: (x + 4) / x 5. Five less than the product of eight and a number: 8x - 5

22. Common Mistakes and How to Avoid Them Confusing addition and multiplication: Remember, 'sum of' means addition, while 'product of' means multiplication. Double-check each phrase. Misplacing terms in subtraction: 'Difference between' implies the order matters. Ensure you subtract the second term from the first. Incorrectly interpreting division: 'Quotient of' phrases can be tricky. Note the order in which to divide, paying close attention to the phrasing.

23. Khan Academy (www.khanacademy.org): Extensive video tutorials and practice exercises on algebraic expressions. Purplemath (www.purplemath.com): Clear explanations and examples for understanding and translating algebraic expressions. Algebra for Dummies by Mary Jane Sterling: A comprehensive book covering basic to advanced algebra topics. Additional Resources YouTube Channel 'Math Antics': Engaging video lessons on various algebra topics, including translating verbal phrases.

24. Conclusion and Next Steps Throughout this presentation, we explored how to translate various verbal phrases into algebraic expressions, covering key operations such as addition, subtraction, multiplication, and division. We also engaged in practice problems and a quiz to reinforce these concepts. Moving forward, continue practicing with more complex sentences and mixed operations. Utilize additional resources such as online tutorials, math workbooks, and educational videos to deepen your understanding and proficiency in translating verbal phrases into algebraic expressions.