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Explore mathematical properties, algebraic expressions, and equations. Learn properties of equality, solve equations, and translate verbal expressions. Practice identifying properties, simplifying expressions, and mastering mathematical processes.

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  1. Five-Minute Check Mathematical Practices Then/Now New Vocabulary Example 1: Verbal to Algebraic Expression Example 2: Algebraic to Verbal Sentence Key Concept: Properties of Equality Example 3: Identify Properties of Equality Key Concept: Properties of Equality Example 4: Solve One-Step Equations Example 5: Solve a Multi-Step Equation Example 6: Solve for a Variable Example 7: Use Properties of Equality Lesson Menu

  2. A. naturals (N), wholes (W), integers (Z) B. wholes (W), integers (Z), reals (R) C. naturals (N), wholes (W), rationals (Q), reals (R) D. naturals (N), wholes (W), integers (Z), rationals (Q), reals (R) 5-Minute Check 1

  3. A. naturals (N), wholes (W), integers (Z) B. wholes (W), integers (Z), reals (R) C. naturals (N), wholes (W), rationals (Q), reals (R) D. naturals (N), wholes (W), integers (Z), rationals (Q), reals (R) 5-Minute Check 1

  4. A. naturals (N), wholes (W) B. reals (R) C. rationals (Q), reals (R) D. integers (Z), reals (R) 5-Minute Check 2

  5. A. naturals (N), wholes (W) B. reals (R) C. rationals (Q), reals (R) D. integers (Z), reals (R) 5-Minute Check 2

  6. Name the property illustrated by a + (7 + c) = (a + 7) + c. A. Associative Property of Addition B. Distributive Property C. Substitution Property D. Commutative Property of Addition 5-Minute Check 3

  7. Name the property illustrated by a + (7 + c) = (a + 7) + c. A. Associative Property of Addition B. Distributive Property C. Substitution Property D. Commutative Property of Addition 5-Minute Check 3

  8. Name the property illustrated by3(4 + 0.2) = 3(4) + 3(.02). A. Associative Property of Addition B. Identity Property C. Distributive Property D. Substitution Property 5-Minute Check 4

  9. Name the property illustrated by3(4 + 0.2) = 3(4) + 3(.02). A. Associative Property of Addition B. Identity Property C. Distributive Property D. Substitution Property 5-Minute Check 4

  10. Simplify (2c)(3d) + c + 5cd + 3c2. A. 3c2 + 5cd + c B. 3c2 + 11cd + c C. 3c2 + 10cd D. 3c2 + c 5-Minute Check 5

  11. Simplify (2c)(3d) + c + 5cd + 3c2. A. 3c2 + 5cd + c B. 3c2 + 11cd + c C. 3c2 + 10cd D. 3c2 + c 5-Minute Check 5

  12. A.5 + 0 = 5 B.5(1) = 5 C.5 + (–5) = 0 D. Which equation illustrates the Additive Identity Property? 5-Minute Check 6

  13. A.5 + 0 = 5 B.5(1) = 5 C.5 + (–5) = 0 D. Which equation illustrates the Additive Identity Property? 5-Minute Check 6

  14. Mathematical Processes A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 8 Look for and express regularity in repeated reasoning. MP

  15. You used properties of real numbers to evaluate expressions. • Translate verbal expressions into algebraic expressions and equations, and vice versa. • Solve equations using the properties of equality. Then/Now

  16. open sentence • equation • solution Vocabulary

  17. Example 1 Verbal to Algebraic Expression A. Write an algebraic expression to represent the verbal expression 7 less than a number. Answer:

  18. Verbal to Algebraic Expression A. Write an algebraic expression to represent the verbal expression 7 less than a number. Answer:n – 7 Example 1

  19. Verbal to Algebraic Expression B. Write an algebraic expression to represent the verbal expression the square of a number decreased by the product of 5 and the number. Answer: Example 1

  20. Verbal to Algebraic Expression B. Write an algebraic expression to represent the verbal expression the square of a number decreased by the product of 5 and the number. Answer:x2 – 5x Example 1

  21. A. Write an algebraic expression to represent the verbal expression 6 more than a number. A. 6x B.x + 6 C.x6 D.x – 6 Example 1a

  22. A. Write an algebraic expression to represent the verbal expression 6 more than a number. A. 6x B.x + 6 C.x6 D.x – 6 Example 1a

  23. B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number. A.x3 – 2 B. 2x3 C.x2 – 2 D. 2 + x3 Example 1b

  24. B. Write an algebraic expression to represent the verbal expression 2 less than the cube of a number. A.x3 – 2 B. 2x3 C.x2 – 2 D. 2 + x3 Example 1b

  25. Example 2 Algebraic to Verbal Sentence A. Write a verbal sentence to represent 6 = –5 + x. Answer:

  26. Algebraic to Verbal Sentence A. Write a verbal sentence to represent 6 = –5 + x. Answer: Six is equal to –5 plus a number. Example 2

  27. Algebraic to Verbal Sentence B. Write a verbal sentence to represent 7y – 2 = 19. Answer: Example 2

  28. Algebraic to Verbal Sentence B. Write a verbal sentence to represent 7y – 2 = 19. Answer: Seven times a number minus 2 is 19. Example 2

  29. A. What is a verbal sentence that represents the equation n – 3 = 7? A. The difference of a number and 3 is 7. B. The sum of a number and 3 is 7. C. The difference of 3 and a number is 7. D. The difference of a number and 7 is 3. Example 2a

  30. A. What is a verbal sentence that represents the equation n – 3 = 7? A. The difference of a number and 3 is 7. B. The sum of a number and 3 is 7. C. The difference of 3 and a number is 7. D. The difference of a number and 7 is 3. Example 2a

  31. B. What is a verbal sentence that represents the equation 5 = 2 + x? A. Five is equal to the difference of 2 and a number. B. Five is equal to twice a number. C. Five is equal to the quotient of 2 and a number. D. Five is equal to the sum of 2 and a number. Example 2b

  32. B. What is a verbal sentence that represents the equation 5 = 2 + x? A. Five is equal to the difference of 2 and a number. B. Five is equal to twice a number. C. Five is equal to the quotient of 2 and a number. D. Five is equal to the sum of 2 and a number. Example 2b

  33. Key concept

  34. Identify Properties of Equality A. Name the property illustrated by the statement. a – 2.03 = a – 2.03 Answer: Example 3

  35. Identify Properties of Equality A. Name the property illustrated by the statement. a – 2.03 = a – 2.03 Answer: Reflexive Property of Equality Example 3

  36. Identify Properties of Equality B. Name the property illustrated by the statement. If 9 = x, then x = 9. Answer: Example 3

  37. Identify Properties of Equality B. Name the property illustrated by the statement. If 9 = x, then x = 9. Answer: Symmetric Property of Equality Example 3

  38. A. What property is illustrated by the statement? If x + 4 = 3, then 3 = x + 4. A. Reflexive Property of Equality B. Symmetric Property of Equality C. Transitive Property of Equality D. Substitution Property of Equality Example 3a

  39. A. What property is illustrated by the statement? If x + 4 = 3, then 3 = x + 4. A. Reflexive Property of Equality B. Symmetric Property of Equality C. Transitive Property of Equality D. Substitution Property of Equality Example 3a

  40. B. What property is illustrated by the statement? If 3 = x and x = y, then 3 = y. A. Reflexive Property of Equality B. Symmetric Property of Equality C. Transitive Property of Equality D. Substitution Property of Equality Example 3b

  41. B. What property is illustrated by the statement? If 3 = x and x = y, then 3 = y. A. Reflexive Property of Equality B. Symmetric Property of Equality C. Transitive Property of Equality D. Substitution Property of Equality Example 3b

  42. Key Concept

  43. Example 4 ? 5.5 – 5.48 = 0.02 Substitute 5.5 for m. Solve One-Step Equations A.Solve m – 5.48 = 0.02. Check your solution. m – 5.48 = 0.02 Original equation m – 5.48 + 5.48 = 0.02 + 5.48 Add 5.48 to each side. m = 5.5 Simplify. Check m – 5.48 = 0.02 Original equation 0.02 = 0.02 Simplify.  Answer:

  44. ? 5.5 – 5.48 = 0.02 Substitute 5.5 for m. Solve One-Step Equations A.Solve m – 5.48 = 0.02. Check your solution. m – 5.48 = 0.02 Original equation m – 5.48 + 5.48 = 0.02 + 5.48 Add 5.48 to each side. m = 5.5 Simplify. Check m – 5.48 = 0.02 Original equation 0.02 = 0.02 Simplify.  Answer: The solution is 5.5. Example 4

  45. Solve One-Step Equations Original equation Simplify. Example 4

  46. Check Original equation ? Solve One-Step Equations Substitute 36 for t. Simplify.  Answer: Example 4

  47. Check Original equation ? Solve One-Step Equations Substitute 36 for t. Simplify.  Answer: The solution is 36. Example 4

  48. A. What is the solution to the equation x + 5 = 3? A. –8 B. –2 C. 2 D. 8 Example 4a

  49. A. What is the solution to the equation x + 5 = 3? A. –8 B. –2 C. 2 D. 8 Example 4a

  50. B. What is the solution to the equation A.5 B. C.15 D.30 Example 4b

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