DLL in Math 7 Week 3.docx
- 1. Republic of the Philippines Department of Education Region VIII Division of Samar DISTRICT OF MARABUT Marabut, Samar GRADES 1 to 12 DAILY LESSON LOG School Osmeña National High School Grade Level Grade 7 Teacher Angelina S. Tabugoca Learning Area Mathematics Inclusive Dates November 21-25, 2022 Section Week No. 3 Scheduled Time I. OBJECTIVES TUESDAY WEDNESDAY THURSDAY FRIDAY A. Content Standard The learner demonstrates understanding of key concepts of algebraic expression, the properties of real numbers as applied in linear equations and inequalities in one variable. B. Performance Standards The learner is able to model situations using oral, written, graphical, and algebraic methods in solving problems involving algebraic expressions, linear equations, and inequalities in one variable. C. Learning Competencies / Objectives (Write the LC Code) Translates English phrases to mathematical phrases and English sentences to mathematics sentences, and vice versa. (No MELC Code given) (K to 12 MELCs with CG Codes DepEd Commons p. 288 Illustrates and differentiates related terms in algebra: a. 𝑎𝑛 where 𝑛 is a positive integer b. constants and variables c. literal coefficients and numerical coefficients d. algebraic expressions, terms, and polynomials e. number of terms, degree of the term and degree of the polynomial. D. Specific Learning Objectives Knowing Remembering Identify the words / phrases that are used to indicate mathematical operations. Identify the constants and variables in a given algebraic expression. Under- standing Understanding Applying Translate verbal phrases to mathematical phrases and vice versa. Analyzing Interpret the meaning of an where n is a positive integer. Differentiate between constants and variables in a given algebraic
- 2. expression Evaluating Evaluate an. Evaluate algebraic expressions for given values of the variables. Doing Creating Integration Value accumulated knowledge as means of new understanding. Value accumulated knowledge as means of new understanding. Value constant love of God. Value accumulated knowledge as means of new understanding II. CONTENT Verbal Phrases and Mathematical Phrases Laws of Exponents Constants, Variables and Algebraic Expressions Evaluation of Algebraic Expressions III. LEARNING RESOURCES A. References 1. Teacher’s Guide pages 2. Learners’ Materials pages pp. 117 – 121 pp.126 - 129 pp.112 - 116 pp.112 - 116 3. Textbook pages G8 Math Module pages 66 – 67; Gladys C. Nivera, Ph.D.,Grade 7 Mathematics Patterns and Practicalities, pp.184-188 Gladys C. Nivera, Making Connections in Mathematics I pp. 99 – 104 Grade 7Our World of Math Kto12 pp. 133-135, Gladys Niverra Patterns and Practicalities on G7- Math pp. 172-175 Ricardo M. Crisostomo et.al, Grade 7Our World of Math Kto12 pp. 153-155, Orlando A.Oronce and Marilyn O.Mendoza e-math, Worktext in Mathematics 7 pp. 164-168 4. Additional Materials from Learning Resources Portals B. Other Learning Resources IV. PROCEDURES A. Revisiting previous lesson or presenting the new lesson Ask two students to draw the following sets on the board using Venn Diagram. Group the class into three. Let a member of each group score a point by naming the following logos. Remind each group about the following: will have to answer by level respectively. logos to be named. Pre-Assessment Give the product of each of the following as fast as you can. a) 3 x 3 = ________ b) 4 x 4 x 4 = ________ c) 5 x 5 x 5 = ________ d) 2 x 2 x 2 = ________ e) 2 x 2 x 2 x 2 = _______ f) 2 x 2 x 2 x 2 x 2 =______ Suppose numbers are assigned to some letters as follows; O=1, C=3, I=2, P=7, D=5, L=6, R=4 and E=8; Name the picture which is one of the Cavite’s prides and find the numbers that corresponds to each
- 3. will score 1 point; level 2 (2points) and so on. highest score will be the winner. letter given the sum. First two letters are given as your clues. B. Establishing a purpose for the lesson In mathematics, what do these symbols mean? + – x ÷ Share your insights about the game. What is the importance of interpreting or translating symbols into words and vice versa correctly? Guide Questions: Can you give a short way of finding the product of the given? Explain your answer. Guide Questions 1. What is the difference of changing and unchanging? 2. In Mathematics, what idea or concept can we consider us changing and unchanging? Guide Questions 1. How did you find the activity? 2. What is Substitution Method? C. Presenting examples/ instances of the new lesson In translating verbal phrases into algebraic expressions, it is important to know the words that are used to indicate mathematical operations. Some of these words are shown in the chart that follows: Solution: Given Mang Nonito is a barbecue stick maker. He makes 10 to 12 bundles of sticks daily. Each bundle contains twenty sticks. Complete the table: Question: Without the table, how many Given: Mark is 8 years old. On Sunday, his parents are planning to watch movie after attending mass. The prices of movie tickets are Php 200 for adults and Php150 for children 10 years old and below. If x= the number of adults and y= the number of children; Compute how much will they pay for movie tickets if a. only Mark and his parents will watch the movie b. Mark, his parents and his
- 4. Example1.1: Translate the verbal phrases into algebraic expressions. a. the sum of x and y b. 6 more than a c. Twice m d. The difference of b and 10 e. 9 less than z Solutions: a. x + y d. b - 10 b. a + 6 e. z – 9 c. 2m Example 1.2: Express the algebraic expressions into verbal phrases. a. 7p c. r + 5 b. 2x – 3 d. x + (x+2) + (x+4) Solutions: a. 7 times p b. The difference of twice a number and three c. r increased by 5 d. the sum of three consecutive odd integers an = a x a x a x a .....(n times) In an, a is called the base and n is called the exponent. sticks could Mang Nonito make in every 10 bundles? In 12 bundles? To find the number of sticks in all bundles, multiply the number of bundles by 20,that is, Number of bundles X 20, thus if we let s=number of sticks. The total number of sticks is s x 20 or 20s or n=20s So 10 bundles= 20 (10) or 200 and 12 bundles = 20 (12) or 240 sticks in all. s can take on many different values, we say that s is a variable. Its value varies. On the other hand, 20 is a constant since the number of sticks in every bundle has fixed value. An expression 20s, where s represents the number of bundles, is an example of algebraic expression. An algebraic expression is any combination of one or more constants and variables along with at least one mathematical operation. A variable is any symbol representing possible value of a quantity. 5-year old cousin will watch the movie c. Mark, his parents and his uncle Joey will watch the movie Solution: To compute for the amount of tickets needed is to substitute the values of x and y In the expression 200 x + 150y,where x= number of adults and y= number of children a. x=2, y=1 (two adults,one child) 200x+150y= 200(2)+ 150 (1) = 400 + 150 =Php 550 b. x=2,y=2( two adults,two children) 200x+150Y=200(2) + 150 (2) =400 + 300 = Php 700 c. x=3, y=1( three adults,one child) 200x+150Y =200(3)+150(1) =600 + 150 = Php750 Example: Evaluate the following expressions if a=2, b= -1 and c=3 1) a2 + 3c 2) 4b2c + 2a
- 5. A constant is any symbol representing one fixed value. A term is a constant or a variable or constants and variables multiplied together. Examples: Identify the constants and variables in the given expressions: a. 5x-1 b. 2 c. a+ 3 b constants: 5 and 1 constants: 2 and constant: 3 variable: x variable: r variables: a and b 3) b2-2a +c D. Discussing new concepts and practicing new skills #1 Guide Questions: a. What words serve as clues to what operation symbol is to be used? b. What must be considered in translating verbal phrases to mathematical phrases and vice versa? c. In translating a verbal phrase to an algebraic expression, a single word can make a difference. Thus, every word in the Guide Questions: a. What do you observe as you answer column B? What do you observe as you answer column C? b. What happens to its value when the exponent decreases? c. What do you mean by an? Guide Questions: (Developmental Activity) a. In your own words, describe how to find the number of sticks if you know the number of bundles? b. What operation is involved? Why? c. Which has a fixed value? Which varies? d. Can you give your own example similar to this relationship? Guide Questions: (Developmental Activity) a. How did you find the amount to be paid for the movie tickets? b. What operation did you perform? c. Why is there a need to substitute the assigned values of x and y? d. What are the constants and variables in the given situation?
- 6. statement must be interpreted correctly. In what way does it affect our dealings with others? E. Discussing concepts and practicing new skills #2 The teacher gives a set of verbal phrases then the students will select the corresponding mathematical phrase written on each picture and they will paste it on the board. a. Twice a number increased by four. b. The difference of five and a number. c. Eight diminished by thrice of a number. d. Ten added to a number. e. The quotient of a number and two. Which of the following is/are correct? If correct, do the THUMBS UP. Otherwise, THUMBS DOWN and give the correct value. a) 52 = 5 x 5 = 25 b) 64 = 6 x 6 x 6 x 6 = 216 c) 25 = 2 x 5 = 10 d) 103 = 10 x 10 x 10 = 300 Identify the constant(s) and the Variable(s) in each expression. Complete the table. A magic square is a puzzle in which the sum of the numbers in any row, column, and along the diagonal are the same. When 5, 3 and 7 are substituted in place of a, b, and c respectively for the expressions in the left square, the result is the square at the right. Complete the square at the right by evaluating the given algebraic expressions at the left. Examine the sum of the numbers in any rows, columns and along the diagonals. What did you notice? F. Developing mastery (Leads to Formative Assessment 3) A. Translate the verbal phrases into algebraic expressions. a. The ratio of x and 4. b. 3 less than thrice a number c. The sum of twice a number and 8 B. Express the algebraic Rewrite each of these in exponential form. (an) a) 5∙5∙5∙5∙5 = ______ b) (a)(a)(a)(a) = ______ c) 6∙x∙x∙x∙x∙x∙x= ______ d) 7∙7∙y∙y = ______ e) 10 = ______ I. Determine whether each quantity is fixed or varied a. the electric bill each month b. the number of months in a year c. the number of hours of daylight in a day Evaluate the following algebraic expressions using the given values for the variables a.5x + 2, when x= 2 b. x2 – 3x, when x= 3 c. 2x + 3y, when x=1 and y= -2 d. 4x2 +6y, when x=-2 and y= -1 e. If x=4,find the numerical
- 7. expressions into verbal phrases. d. 8x – 6 e. 5(x + y) II. Identify the constants and variables in the given algebraic expressions d. 2xy + z e. ½ bh f. 3a-b g. a+ b value of 3x +4 G. Finding practical applications of concepts and skills in daily living Each group must answer the following tasks. The first group to answer correctly will get the score for each task. a. Write the mathematical translation of the following: 1. The difference of four times a number and one.___________ 2. z less than 3. ________ b. Suppose you have a 120 cm stick and you cut off x centimeters from it. How will you represent the length of the remaining part? c. Translate the mathematical expression 2(x – 3) in at least two ways. Group Activity A local chocolate candy costs Php 2.00 a. How much will Bryan pay if she buys 15 of these chocolates? b. Fill up the table of values. c. Write the pattern in symbols d. Identify the constant and variables. THINK-PAIR-SHARE. The following mathematical statements describe cost and revenue in pesos from the production and sale of x unit of cell phones. Cost C of manufacturing: C=900x + 15 Cost M of marketing : M= 20 x2-5x+8 Revenue R from sales: R= 20x2+6x 1.What is the cost of manufacturing; a. 10 units of cell phones b. 25 units of cell phones 2. What is the cost of marketing 30 units of cell phones? 3. What is the revenue from selling 50 units of cell phones? 4. What is the total cost of manufacturing and marketing 30 units of cell phones? H. Making generalizations and abstractions about the lesson In translating verbal phrases into mathematical phrases, consider the following terms: Addition would indicate an increase, a putting The exponent tells us how many times the base is multiplied by itself. The base is the factor which is to be multiplied by itself n times to obtain the product. The power To evaluating algebraic expressions, replace the variable with a number and perform the operation(s) in the expression. Example : Evaluate x + 7, for x = 12
- 8. together, or combining. Thus, phrases like increased by and added to are addition phrases. Subtraction would indicate a lessening, diminishing action. Thus, phrases like decreased by, less, diminished by are subtraction phrases. Multiplication would indicate a multiplying action. Phrases like multiplied by or times are multiplication phrases. Division would indicate partitioning, a quotient, and a ratio. Phrases such as divided by, ratio of and quotient of are common for division. refers to the product of equal factors. To interpret an where n is a positive integer: an= a x a x a x a ….. (n times) *a is called the base *n is called the exponent Ex. 53 = 5x5x5 = 125 X+7 replace the x with the given value, 12 12+7 perform the operation 19 I. Evaluating learning Directions: Translate the given verbal phrases into mathematical expressions or vice versa. a) The sum of a number and three b) Four times a certain number decreased by one c) The ratio of a number x and six increased by two d) A certain number decreased by two Identify the base and the exponent. Then evaluate the expression. a) 28 b) 82 c) 51 d) 32 e) 182 I. Tell whether each of the following expressions describes a constant or a variable. a. the life span of humans b. the number of hours in a day c. the amount of rainfall in a month d. the Philippine population e. the minimum salary of a labourer per hour as prescribed by law II. Identify the constants and variables in each algebraic expressions. f. a – 10 g. 2m + 3n h. y2 – 4y Evaluate the following algebraic expression using a=2, b= 3 and c= -4 1. 5a + 3b 2. 2c2 -1 3. c2 –b2 4. 4a – 2b 5. a2 + 3b +c
- 9. e) The product of p and q divided by three f) 9m g) 4x– 7 h) 5(x+1) i) 4 + x j) 2a + 3 i. 2π r j. 4π r3h k. 3 J. Additional activities for application or remediation 1. Follow-up: Write your own pair of mathematical phrase and its verbal translation. 2. Study: Polynomials 1. Follow-up Activity: Rewrite in exponential form: a)(xyz)(xyz)(xyz) b)3∙3∙3∙x∙x∙y∙y∙y 2. Study: Laws of Exponent pages 126-129 (Learner’s Material) Math Journal Read, analyze, and answer. 1. If |a| = -5, what are the possible values of a? Justify your answer. 2. Explain what is meant by absolute value of a number? 1.Evaluate the polynomial 2x3-x-4 when; a. x= -1 b. x=1 c. x= 3 d. x= 4 e. x= -2 2. Study Polynomials and their classifications V. REMARKS REFLECTION VI. No. of learners who earned 80% in the evaluation. A. No. of learners who require additional activities for remediation B. Did the remedial lessons work? No. of learners who have caught up with the lesson. C. No. of learners who continue to require remediation. D. Which of my teaching strategies worked well? Why did it work? E. Which of my teaching strategies worked well? Why did it work? F. What difficulties did I encounter which my principal or supervisor can help me solve?
- 10. G. What innovation or localized materials did I used/discover which I wish to share with other learners? Prepared by: ANGELINA S. TABUGOCA Teacher III Reviewed by: GLENDA G. SEBANDAL. MT-I, Department Head - Designate