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Mastering Variables and Equations: Open Sentences Explained

In this lesson, you'll learn how to identify and solve open sentences and translate verbal sentences into equations. An open sentence is an equation that contains a variable, with a solution being the value that makes it true. We explore properties of equality, including balance, symmetry, and transitivity through various examples. You will work on guided practice and homework assignments designed to solidify your understanding. Master these concepts to enhance your problem-solving skills in mathematics!

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Mastering Variables and Equations: Open Sentences Explained

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  1. Lesson 1-5 Pages 28-32 Variables and Equations

  2. What you will learn! • How to identify and solve open sentences. • How to translate verbal sentences into equations.

  3. Vocabulary

  4. What you really need to know! An equation that contains a variable is called an open sentence. A value that makes the sentence true is called a solution.

  5. Properties of Equality:

  6. Balance Example!

  7. Example 1: Find the solution of: 44 + p = 53. Is it 11, 9, or 7? p is 9 ; p = 9

  8. Example 2: Which value is the solution of 4x – 1 = 11? A 5 B 4 C 3 D 2 C 3

  9. Example 3: Solve the equation mentally. 7x = 56 x = 8

  10. Example 4: Solve the equation mentally. x – 15 = 40 x = 55

  11. Example 5: Name the property shown by the statement. If 3x + 1 = 10, then 10 = 3x + 1. Symmetric

  12. Example 6: Name the property shown by the statement. If z + 6 = 8 and 8 = 2 + 6, the z + 6 = 2 + 6. Transitive

  13. Example 7: Define a variable. Then write an equation and solve. The quotient of a number and four is nine. n ÷ 4 = 9 n = 36

  14. Page 30 Guided Practice #’s 3-13 Link to Pre-Made Lesson

  15. Read: Pages 28-30 with someone at home and study examples!

  16. Homework: Pages 31-32 14-46 even 48-51, 54-55, 58-59, 61-73 Lesson Check 1-5

  17. Page 725 Lesson 1-5

  18. Lesson Check 1-5

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