MATH 8 Q1 LESSON 2_TRANSLATING ALGEBRAIC EXPRESSION

Lesson on Mean, Median, Mode

1. Sharpen your minds —it’s math time!

2. MATH 8, QUARTER 1, LESSON 2 x+y 2a-b Translation of real-life situations into algebraic expressions Addition and subtraction of monomials, binomials and multinomials

3. LESSON OBJECTIVES Translate Real-life Situations into Algebraic Expressions Add and Subtract Monomials Add and Subtract binomials and Trinomials

4. 01 DAY

5. SHORT REVIEW

6. ACTIVITY 1: WORD HUNT Draw a line or shade the words that illustrate addition, subtraction, multiplication, or division .

7. ACTIVITY 1: WORD HUNT ANSWER KEY SUBTRACTED SUM PRODUCT TWICE DIFFERENCE LESS DIMINISHED RATIO TOTAL INCREASED MORE ADDED QUOTIENT

8. Questions: Which of the words represent addition? Which of the words represent subtraction? Which of the words represent multiplication? Which of the words represent division? Can you think of other words that represent addition, subtraction, multiplication, or division? SUBTRACTED SUM PRODUCT TWICE DIFFERENCE LESS DIMINISHED RATIO TOTAL INCREASED MORE ADDED QUOTIENT

9. LESSON PURPOSE

10. 01 How much will you pay if you travel for a seven-kilometer trip? Jeepney Fare 2024 The minimum jeepney fare is Php 13 for the first 4 kilometers and Php 3 increase for each subsequent kilometer. 02 If you let x be the number of kilometers traveled beyond the first four-kilometer trip, what mathematical expression can you create to represent the jeepney fare? 03 Considering your answer in #2, what do you call an expression which consists of numbers, variables and operations? QUESTIONS

11. UNLOCKING CONTENT VOCABULARY

12. INSTRUCTION Rearrange the jumbled letters to form the correct term that matches the given definition.

13. CEAIRGALB SXEPEROSIN ALGEBRAIC EXPRESSION an expression consisting of variables and constants along with algebraic operations (addition, subtraction, multiplication or division).

14. CBEARGILA METR ALGEBRAIC TERM either a single number or letter, or the product of several numbers or letters. Terms are separated by the operations addition and subtraction.

15. ERBAVILA VARIABLE any letter or symbol that represents a number.

16. SCNATTON CONSTANT a number that has a fixed value that does not change.

17. AMSRILI STREM SIMILAR TERMS terms that have the same variable raised to the same power.

18. AOLOMINM MONOMIAL an algebraic expression having one term.

19. AIOLBINM BINOMIAL an algebraic expression having two terms.

20. IUNLMAMTLIO MULTINOMIAL an algebraic expression that contains at least two terms.

21. GOOD JO B

22. 01 DAY SUB-TOPIC 1: Translation of Real-life Situations into Algebraic Expressions

23. EXPLICITATION

24. In the activity about “Jeepney Fare 2024”, since x represents the number of kilometers traveled beyond the first four-kilometer trip, then the fare for every passenger if they exceed the first four-kilometer trip is represented by 3x + 13 with Php 3 increase for each subsequent kilometer. “Jeepney Fare 2024”

25. To easily translate real-life situations into algebraic expressions, here is the list of the keywords for each operation. ADDITION SUBTRACTION MULTIPLICATON DIVISION Sum Subtract times quotient more than take away multiply divided by Plus diminish by product divided into increased by diminish from twice ratio increased from less thrice added by less than added to difference total decreased by Decreased from

26. when “to” or “from” is added to the keyword, the order of the terms is interchanged. Example: x diminished by 2 is “x – 2”. x diminished from 2 is “2 – x”. “to” VS “from”

27. WORKED EXAMPLES

28. Write an agenda here. TRANSLATE ME! The sum of a number and seven A. x - 7 B. x - 4 C. 4 + x D. 8 + x E. x + 6 F. x - 2 G. 2 - x H. 5x - 2 I. 3x - 2 J. x + 7 1

29. Write an agenda here. TRANSLATE ME! Three times a certain number decreased by two A. x - 7 B. x - 4 C. 4 + x D. 8 + x E. x + 6 F. x - 2 G. 2 - x H. 5x - 2 I. 3x - 2 J. x + 7 2

30. Write an agenda here. TRANSLATE ME! Two subtracted from five times a number A. x - 7 B. x - 4 C. 4 + x D. 8 + x E. x + 6 F. x - 2 G. 2 - x H. 5x - 2 I. 3x - 2 J. x + 7 3

31. Write an agenda here. TRANSLATE ME! A certain number decreased by two A. x - 7 B. x - 4 C. 4 + x D. 8 + x E. x + 6 F. x - 2 G. 2 - x H. 5x - 2 I. 3x - 2 J. x + 7 4

32. Write an agenda here. TRANSLATE ME! Four increased by a certain number A. x - 7 B. x - 4 C. 4 + x D. 8 + x E. x + 6 F. x - 2 G. 2 - x H. 5x - 2 I. 3x - 2 J. x + 7 5

33. Write an agenda here. TRANSLATE ME! A certain number decreased by 4 A. x - 7 B. x - 4 C. 4 + x D. 8 + x E. x + 6 F. x - 2 G. 2 - x H. 5x - 2 I. 3x - 2 J. x + 7 6

34. Write an agenda here. TRANSLATE ME! Seven subtracted from a number A. x - 7 B. x - 4 C. 4 + x D. 8 + x E. x + 6 F. x - 2 G. 2 - x H. 5x - 2 I. 3x - 2 J. x + 7 7

35. Write an agenda here. TRANSLATE ME! A number added to six A. x - 7 B. x - 4 C. 4 + x D. 8 + x E. x + 6 F. x - 2 G. 2 - x H. 5x - 2 I. 3x - 2 J. x + 7 8

36. Write an agenda here. TRANSLATE ME! The sum of eight and a number A. x - 7 B. x - 4 C. 4 + x D. 8 + x E. x + 6 F. x - 2 G. 2 - x H. 5x - 2 I. 3x - 2 J. x + 7 9

37. Write an agenda here. TRANSLATE ME! The difference of two and a number A. x - 7 B. x - 4 C. 4 + x D. 8 + x E. x + 6 F. x - 2 G. 2 - x H. 5x - 2 I. 3x - 2 J. x + 7 10

38. LESSON ACTIVITY

39. 1. two more than y ballpens. 2. thirteen pesos added to x pesos. 3. eight subtracted from b marbles. 4. v increased by five candies. 5. twice a number m bacteria. 6. six less than m passengers. 7. z chocolates divided by seven persons. 8. half of n kilograms of meat. 9. twelve chocolates decreased by w chocolates. 10. twice a number c books. Translate the following statements into algebraic expressions. y + 2 x + 13 b - 8 v + 5 2m m - 6 z ÷ 7 or z/7 n ÷ 2 or n/2 12 - w 2c ANSWER KEY

40. ASSESSMENT

41. ACTIVITY : MAZE TO AMAZE Directions: Translate each statement into algebraic expression. Begin at the “start” and continue to follow the path until you hit the finish line. x+30

42. ANSWER KEY

43. 02 DAY

44. SHORT REVIEW

45. ACTIVITY 2: ADDITION AND SUBTRACTION SQUARES Complete the squares by adding or subtracting the integers. Examples are given as your guide to fill in the missing boxes. + 5 -7 -3 8 2 -3 + 5 = 2 1

46. ACTIVITY 2: ADDITION AND SUBTRACTION SQUARES Complete the squares by adding or subtracting the integers. Examples are given as your guide to fill in the missing boxes. + 5 -7 -3 8 2 13 8 + 5 = 13 1

47. ACTIVITY 2: ADDITION AND SUBTRACTION SQUARES Complete the squares by adding or subtracting the integers. Examples are given as your guide to fill in the missing boxes. + 5 -7 -3 8 2 13 -3 + (-7) = -10 -10 1

48. ACTIVITY 2: ADDITION AND SUBTRACTION SQUARES Complete the squares by adding or subtracting the integers. Examples are given as your guide to fill in the missing boxes. + 5 -7 -3 8 2 -10 13 1 8 + (-7) = 1 1

49. ACTIVITY 2: ADDITION AND SUBTRACTION SQUARES Complete the squares by adding or subtracting the integers. Examples are given as your guide to fill in the missing boxes. + 5 -7 -3 8 2 -10 13 1 1

50. ACTIVITY 2: ADDITION AND SUBTRACTION SQUARES Complete the squares by adding or subtracting the integers. Examples are given as your guide to fill in the missing boxes. - 9 -11 6 -5 -3 17 -14 -6 2 6 - 9 = 6 + (-9) = -3 -5 – 9 = -5 + (-9) = -14 6 – (-11) = 6 + 11 = 17 -5 – (-11) = -5 + 11 = -6

51. ACTIVITY 2: ADDITION AND SUBTRACTION SQUARES Complete the squares by adding or subtracting the integers. Examples are given as your guide to fill in the missing boxes. + 8 -3 4 -2 + -6 -9 7 -5 - 11 -8 3 -4 - 12 -10 7

52. ACTIVITY 2: ADDITION AND SUBTRACTION SQUARES Complete the squares by adding or subtracting the integers. Examples are given as your guide to fill in the missing boxes. + 8 -3 4 12 1 -2 6 -5 + -6 -9 7 1 -2 -5 -11 -14 - 11 -8 3 -8 11 -4 -15 4 - 12 -10 -12 10 7 -5 17 ANSWER KEY

53. 02 DAY SUB-TOPIC 2: Addition and subtraction of monomials

54. EXPLICITATION

55. + + + 1 tile x tile x 2 tile - - - -1 tile -x tile -x 2 tile Tiles can be used to model algebraic expression.

56. a) 3 . + + + b) - 4x - - - - c) 2x 2 + + 3, -4x, and 2x 2 are algebraic expressions consisting of 1 term . These are examples of MONOMIALS. Using the tiles, make a model for

57. - - + What about if you use the tiles to model x-2, how will it look like? Observe that there are two kinds of tiles used. x – 2 is an example of BINOMIAL . It consists of two terms. Note: Terms are separated by a plus sign or a minus sign.

58. + + - This time make a model for x 2 -3x + 4. + - - + + How about -2x 2 + 4x - 5. - - + - + + - - - + - 1. How many kinds of tiles are used? 2. What kind of algebraic expression is x 2 -3x + 4 and -2x 2 + 4x - 5? 3 kinds trinomial

59. Monomial, binomial, and trinomial are kinds of polynomials . Polynomials are algebraic expressions that consist of non-negative exponents.

60. Use algebra tiles to model 3x + 4x, then find its sum. ADDITION OF MONOMIALS + + + + + + + for 3x for 4x +

61. Use algebra tiles to model 3x + 4x, then find its sum. ADDITION OF MONOMIALS + + + + + + + for 3x for 4x = = 7x +

62. 2. Use algebra tiles to model -5x 2 + 3x 2 and then find its sum. ADDITION OF MONOMIALS for -5x 2 for 3x 2 + - - - - - + + +

63. 2. Use algebra tiles to model -5x 2 + 3x 2 and then find its sum. ADDITION OF MONOMIALS = = -2x 2 - - - - - + + + = for -5x 2 for 3x 2 +

64. Questions: 1. What can you say about the monomials 3x and 4x? 5x 2 and 3x 2 ? 2. What have you noticed about the sum of the monomials? They have the same literal coefficients. Only the numerical coefficients are added.

65. 3x + 4x = 3 4 + = 7 x x -5x 2 + 3x 2 = -5 3 + = -2 x 2 x 2 6x + (-4x) = 2x ? -10x 2 + x 2 = -9x 2 ? Only the numerical coefficients are added.

66. 3x + 4x 7 x -5x 2 + 3x 2 -2 x 2 6x + - 4x 2 x -10x 2 + x 2 -9 x 2 1 OTHER WAY

67. Since in addition of monomials, only the numerical coefficients of similar terms are added, the same rule applies in subtraction of monomials that only the numerical coefficients are to be subtracted. SUBTRACTION OF MONOMIALS

68. 4x 2 – 6x 2 SUBTRACTION OF MONOMIALS = 4x 2 + (–6x 2 ) = –7x + (–10x) = –2x 2 = –17x Find the difference of the given monomials. Observe the rules in subtracting integers. 2. –7x – (10x) 4x 2 + -6x 2 -2x 2 -7x + -10x -17x

69. WORKED EXAMPLES

70. 1. 4a + 6a + (-8a) A. FIND THE SUM OF THE FOLLOWING MONOMIALS. 2. -11xy + 7xy + (-15xy) 4a 6a + -8a 2a -11xy 7xy + -15xy -19xy 3. -10b 3 c + (-9b 3 c) + b 3 c -10b 3 c -9b 3 c + b 3 c -18b 3 c

71. 1. 9x 2 – 4x 2 B. FIND THE DIFFERENCE OF THE FOLLOWING MONOMIALS. 2. –10ab – 15ab 9x 2 + -4x 2 5x 2 3. –12c 2 d 2 – (-8c 2 d 2 ) = 9x 2 + (-4x 2 ) = –10ab + (-15ab) = –12c 2 d 2 + 8c 2 d 2 -10ab + -15ab -25ab -12c 2 d 2 + 8c 2 d 2 -4c 2 d 2

72. LESSON ACTIVITY

73. Success in math starts with effort —believe in yourself!

74. 1. 2x + (-5x) 9. –8m 2 n 2 + 7m 2 n 2 – 15m 2 n 2 2. –2a 2 – (–6a 2 ) 10. –b 2 c 3 + (–b 2 c 3 ) – (–b 2 c 3 ) 3. y + (–y) 11. 15m 2 n 3 – 12m 2 n 3 + 8m 2 n 3 4. –9x 2 y 3 – (-9x 2 y 3 ) 12. a 2 b 4 + 2a 2 b 4 – 9a 2 b 4 5. 12ab 2 – ab 2 13. –18xyz + (–5xyz) – (–12xyz) 6. –16mn 3 + (–12mn 3 ) 14. 11ab – 6ab – 15ab 7. 10a 2 b 3 – (–8a 2 b 3 ) + a 2 b 3 15. –21x 4 + 17x 4 – 12x 4 8. 7xy + 4xy – (–21xy) Activity 4: Find the sum or difference of the following monomials. –3x 4a² 11ab² –28mn³ 19a²b³ 32xy 9. –16m²n² 10. –b²c³ 11. 11m²n³ 12. –6a²b⁴ 13. –11xyz 14. –10ab 15. –16x⁴ ANSWER KEY

75. 03 DAY

76. 03 DAY SUB-TOPIC 3: Addition and Subtraction of Binomials

77. EXPLICITATION

78. + + + 1 tile x tile x 2 tile - - - -1 tile -x tile -x 2 tile Tiles can be used to model algebraic expression.

79. + - Using the tiles, make a model for -5x + 3 and 2x + 2 then find its sum. - - - - + + + + + + -5x + 3 2x + 2 +

80. + - Using the tiles, make a model for -5x + 3 and 2x + 2 then find its sum. - - - - + + + + + + -5x + 3 2x + 2 + = -3x + 5 In adding binomials, similar terms are added. Same rule applies in the subtraction of binomials.

81. SOLUTION 1: (12x 2 + 4x) – (4x 2 – 7x) = (12x 2 + 4x) + (-4x 2 + 7x) Find the difference of 12x 2 + 4x and 4x 2 – 7x. = 8x 2 + 11x SOLUTION 2: 12x 2 + 4x 4x 2 7x - - + - + 8x 2 + 11x

82. WORKED EXAMPLES

83. 1. (7b – 3) + (-19b + 8) A. FIND THE SUM OF THE FOLLOWING BINOMIALS. 2. (-21x 2 y 3 z + 12) + (-6x 2 y 3 z - 6) 3. (18 + 6mn) + ( -8 – 19mn) + (12 – mn) 1. 7b – 3 -19b + 8 + -12b + 5 2. -21x 2 y 3 z + 12 -6x 2 y 3 z - 6 + -27 x 2 y 3 z + 6 3. 18 + 6mn 12 - mn + 22 - 14mn -8 - 19mn

84. 1. (7x 2 + 3x) – (x 2 – 2x) A. FIND THE DIFFERENCE OF THE FOLLOWING BINOMIALS. 2. (-a 2 b 3 c – 17) – (8a 2 b 3 c – 7) 3. (m 2 – 8n) – (3m 2 + 5n) 1. 7x 2 + 3x -x 2 + 2x + 6x 2 + 5x 2. -a 2 b 3 c - 17 - 8a 2 b 3 c + 7 + -9 a 2 b 3 c -10 3. m 2 - 8n - 3m 2 - 5n + -2m 2 - 13n

85. LESSON ACTIVITY

86. Column A Column B ____ 1. (5a – 7b) – (2a – 5b) A. 2a + 11b ____ 2. (5a – 7b) + (2a – 5b) B. a – 12b ____ 3. (–9a + 3b) – (–11a – 8b) C. 7a – 4b ____ 4. (–9a + 3b) + (–11a – 8b) D. 7a – 12b ____ 5. (–3a – 8b) – (4a – 4b) E. –3a – 6b ____ 6. (–3a – 8b) + (4a – 4b) F. 3a – 2b ____ 7. (a – 5b) – (6a – 2b) + (2a – 3b) G. 3a + 6b ____ 8. (a + 5b) + (–6a + 2b) – (–2a – 3b) H. –20a – 5b ____ 9. (a – 5b) + (–6a–2b) – (–2a – 3b) I. –3a + 4b ____ 10. (a – 5b) + (6a – 2b) – (2a – 3b) J. 5a – 4b K. –3a – 4b Activity 5. Perfect Match Find the sum or difference of the given binomials in Column A and it with its corresponding answer in Column B F D A H C B E I K J ANSWER KEY

87. 04 DAY

88. 04 DAY SUB-TOPIC 4: Addition and Subtraction of Multinomials

89. EXPLICITATION

90. + + + 1 tile x tile x 2 tile - - - -1 tile -x tile -x 2 tile Tiles can be used to model algebraic expression.

91. - Using the tiles, make a model for 2x 2 + 4x – 3 and –3x 2 – x + 2 then find its sum + + + + - - 2x 2 + 4x - 3 -3x 2 - x + 2 + + + - - - + - +

92. Using the tiles, make a model for 2x 2 + 4x – 3 and –3x 2 – x + 2 then find its sum + + + - 2x 2 + 4x - 3 -3x 2 - x + 2 + = -x 2 + 3x -1 -

93. WORKED EXAMPLES

94. 1. (5a- 2b + 4c) + (-a – 3b + 8c) A. FIND THE SUM OF THE FOLLOWING TRINOMIALS. 2. (8x 2 + 2x – 9) + (-14x 2 - 2x – 11) 3. (-m - 9n + 16) + (-5m - 18n + 11) + (-3m + 13n - 21) 1. 5a - 2b + 4c -a - 3b + 8c + 4a - 5b 2. 8x 2 + 2x - 9 -14x 2 - 2x - 11 + -6x 2 + 0x 3. -m - 9n + 16 -3m + 13n - 21 + -9m - 14n -5m - 18n + 11 + 12c - 20 -6x 2 - 20 + 6

95. 1. (21w – 8x + 13) – (-11w – 12x + 17) B. FIND THE DIFFERENCE OF THE FOLLOWING TRINOMIALS. 2. (2a 2 + 14a – 4) – (a 2 – a – 4) 3. (5y 2 – 6y + 12) – (-11y 2 – 7y + 19) 1. 21w - 8x + 13 11w + 12x - 17 + 32w + 4x 2. 2a 2 + 14a - 4 -a 2 + a + 4 + a 2 + 15a 3. 5y 2 - 6y + 12 + 16y 2 + y 11y 2 + 7y - 19 - 4 + 0 a 2 + 15a - 7

96. LESSON ACTIVITY

97. Math: The only subject where you can count on it!

98. Directions: Find the sum or the difference of the multinomials in Box 1. Then write the letter on the blank for the multinomial that corresponds to your answer in Box 2 to decode the famous person who said the mentioned inspiring quote. Activity 6: Passage to Encourage “Keep away from people who try to belittle your ambitions. Small people always do that, but real great people make you feel that you too can become great.”

99. Activity 6: Passage to Encourage BOX 1 BOX 2 ANSWER KEY M A R K T W A I N

100. 05 DAY

101. Use the Frayer Diagram to show what you learned. LEARNERS’ TAKEAWAYS Are there any challenges or misconceptions you encountered while studying the lesson? If there are, what are those? REFLECTION ON LEARNING

102. FORMATIVE ASSESSMENT

103. 1. five times the price of x ballpens. 2. the amount to be paid for x kilos of meat if each kilo costs y pesos. 3. the sum of the points gained by Axl and Gelo in a basketball game if Axl got nine more than the score of Gelo. 4. each student’s share of marbles if there are x marbles and y students. 5. John’s score in a game is 4 increased by b points. 6. the average of Ben’s grade in the first and second quarter if he got m and n in the two quarters respectively. 7. twelve pesos less a discount of d. 8. Tim’s tokens in an arcade game is x less than twenty. 9. the perimeter of a triangle if the sides of a triangle are three consecutive numbers. 10. 3 hours less than the time traveled t. A. Translate the following into mathematical expressions.

104. 1. (–x 4 y 2 – 3) + (–14x 4 y 2 + 9) 2. (9 – 5ab + 6a) – (-12 – 3ab – 3a) 3. (-10a 2 b 2 + 1) + (14a 2 b 2 + 8) 4. (b 2 c 3 - 17) - (-4b 2 c 3 - 6) 5. (-17x 2 y + 11xy – 2) + (-7x 2 y – 11xy – 8) 6. (-abc + 2b + 6c) – (7abc – 9b – 13c) 7. (m 2 – 3m - 5) + (m 2 + 10m - 8) 8. (11mn + 11) – (12mn – 8) 9. (18p 2 q – pq 2 ) + (-8p 2 q + 2pq 2 ) 10. (5x 3 y 2 – 7) - (–4x 3 y 2 +11) B. Find the sum or difference of the following polynomials.

105. A garment factory produces two sizes of shirts, large and small. If x represents the number of large shirts and y represents the number of small shirts, then the polynomial 230x + 170y + 100 describes the revenue from the sale of the shirts. The polynomial 170x + 140y + 55 describes the cost of producing the shirts. Write an expression in simplest form for net profit from the sale of the shirts of the garments factory. Find the perimeter of a triangle whose lengths of the sides are x – 3, x + 6 and x. C. Solve the problems.

106. ANSWER KEY

107. THANK YOU! Have a great day ahead.

108. RESOURCE PAGE This presentation template uses the following free fonts: Titles: ITC Motter Corpus Regular Headers: Kollektif Body Copy: Kollektif You can find these fonts online too. Happy designing! Don't forget to delete this page before presenting. Use these design resources in your Canva Presentation.