Contents

**1 **Elementary Mathematics Resource Materials**2 **Giving the Meaning of Expression**3 **Give the Meaning of Equation, Exponent and Base.**4 **Giving the Meaning of Exponent and Base, Evaluating Expressions Involving Exponents**5 **Evaluating an Expression with Two Different Operations with Exponents and Parenthesis/Grouping Symbols**6 **Evaluating an Expression with Two Different Operations Without Exponents and Parenthesis/Grouping Symbols**7 **Evaluating an Expression With More Than Two Operations With or Without Exponents and Parenthesis/Grouping Symbols

Contents

**1**Elementary Mathematics Resource Materials**2**Giving the Meaning of Expression**3**Give the Meaning of Equation, Exponent and Base.**4**Giving the Meaning of Exponent and Base, Evaluating Expressions Involving Exponents**5**Evaluating an Expression with Two Different Operations with Exponents and Parenthesis/Grouping Symbols**6**Evaluating an Expression with Two Different Operations Without Exponents and Parenthesis/Grouping Symbols**7**Evaluating an Expression With More Than Two Operations With or Without Exponents and Parenthesis/Grouping Symbols

**Giving the Meaning of Expression**

**I. Learning Objectives**

### Cognitive: Define expressions. Translate word phrases to numerical expressions

Psychomotor: Write the correct numerical expressions

Affective: Appreciate good deeds of past presidents

**II. Learning Content**

References: BEC PELC A. 1.1.1Materials: chart, stopwatch, pictures of Philippine Presidents

Value: Nationalism

**Ill. Learning Experiences**

*A. Preparatory Activities*

**Game: "Name-the-Baby"**

b) Teacher gives an operation, say "addition."

d) Within 2 minutes, each group has to write as many terms or phrases as they can. Afterwards, teacher checks and counts the correct answers.

e) Repeat the same process with subtraction, multiplication and division.

f) The group with the most number of correct answers wins.

**2. Motivation**

(The President of the First Philippine Republic)

What expression describes Manuel L. Quezon?

(President of the Philippine Commonwealth) etc.

Ask the same questions with other Presidents.

c) Why should we remember our past Presidents?

d) If we use expressions to describe the Presidents, we also use expressions in Mathematics, to describe relationships between numbers and the operations being use.

**B. Developmental Activities**

**1. Presentation**

**a. Activity I — Use of Chart**

WORD PHRASES | NUMERICAL EXPRESSIONS |

(Four times ten) divided by five Twelve diminished by two (Six times three) added to seven Eight added to the product of five and three Twenty-five added to two Three times twenty -five less twenty Thirty-six divided by six; 36 has how many 6 (Thirty-nine added to three) divided by seven | (4 x 10) 5 12 — 2 7 + (6 x 3) 8 + (3 x 5) 25 + 2 (3x 25) — 20 36 + 6 (39 + 3) = 7 |

**b. Activity 2 -."Create Your Own" (By Pairs)**

3) Check answers.

**2. Practice Exercises**

5) your age plus your seatmate's age

**3. Generalization**

What is an expression? How do you translate word phrases into an expression?

**C. Application**

IV. Evaluation

IV. Evaluation

*Direction: Which expression is correct? Choose between A or B.*

2. Eight decreased by five. A. 8-5 B. 8x5

3. Twelve plus thirty-six. A. 12+36 B. 12x36

4. Five less than seven. A. 5x7 B.7-5

5. Four times the sum of two and five. A. 4x(2+5) B. 4x(5-2)

*Direction: Write the expression for the following.*

2. Fourteen divided by the sum of three and four

3. Triple the sum of eleven and six

4. One more than the product of six and eight

5. Twenty plus five less than eighty

*Direction: Write an expression for each problem/situation.*

2. Edna is 155 cm. tall. Lilia's height is ten cm. less then twice Edna's height.

3. Roman weighs 25 kg. His father weighs five kg. less than three times Roman's weight.

4. Francis is ten years old. Ben is twice as old as Francis.

5. Aning is five years old. I am six years more than thrice her age.

**V. Assignment**

## Give the Meaning of Equation, Exponent and Base.

**I. Learning Objectives**

**II. Learning Content**

Reference: Math Textbook, BEC PELC A.1.1.1

Materials: chart, roulette

Value: 1. Appreciation for beauty 2. Be clean and orderly

**Ill. Learning Experiences**

**A. Preparatory Activities**

*1. Review/Drill*

2) Teacher gives an operation, say "addition."

3) Each member of the group simultaneously goes to the board and writes a term or phrase that refers to the given operation

Ex. more than, increased by, plus, added to

4) Within 2 minutes, each group has to write as many terms or phrases as they can. The teacher checks and counts the correct answer.

5) Repeat the same process with subtraction, multiplication and division.

6) The group with the most number of correct answers wins.

**2. Motivation**

b) The Philippines is in the Southeast Asia.

c) Every Filipino celebrates Christmas in the 12th month of the year.

**B. Developmental Activities**

**1. Presentation**

**Activity 1**

b) What is the shape of their table?

c) Where will she use the tablecloth?

d) Where is the table placed?

e) Why does Rhoda need to sew a tablecloth for their table?

f) If you were Rhoda, will you also have to sew a table cloth? Why?

b) What number sentence best fits to the problem? 9 x 9 = N

c) What makes your sentence true? What sign is used to show that your sentence is true?

d) If the sentence is true, what is its other name? (equation) Are the two quantities equal?

e) Write the equation about the problem. (9 x 9 = 81)

f) Rename the 81 as a product of 9 x 9.

^{2}?. 2 in 9

^{2}?

What does exponent mean? base?

h) Write the exponential notation about the problem.

**Activity 2 - Use of Proving**

16 [ =,≠ ] 9

16 ≠ 9

**Yes, 3 is a solution of 3 x 3 = 9.**Why did you say so?What do you call this number sentence having two equal quantities?

Rename 9 as a product of 3 x 3.

What do you call 3 in 3

^{2}? 2 in 3

^{2}?

What is the number multiplied by itself twice? What number tells you that 3 is multiplied by itself twice?

What is exponent? base?

**Activity 3- Use of Illustration**

Rename 25 as a product of 5 x 5.

What is meant by 5

^{2}? What is 5 in 5

^{2}?

What is 2 in 5

^{2}? What is exponent? base?

**2. Fixing Skills**

a) 18 - ___ = 5 + 6 d) 96 - ___ = ___ + 24

___ = 11 72 = 72

b) ___

^{2 }= 10x ___ e) 1+ ___ + ___ = ___ x 1

100 = 100 6 = 6

c) ___ 3 = 8 --

64 = 64

**3. Generalization**

**C. Application**

1) Mang Sixto plans to have a rectangular terrace 3 m by 4 m. After a while, he changes his plan. He thinks of having the maximum perimeter possible.

2) A germ splits into 2 at a certain size with such situation the germ will have 6 splittings.

3) An order from a certain food chain for value meal costs P60 with P3 VAT and a delivery fee of P10 each. The five friends made an order.

**IV. Evaluation**

*A. Complete the equation to make a true statement.*

2) ___

^{3 }= 3 x 9 5) 91 ÷ ___ = 6 + ___

27 =___ 13 = 13

3)9 x ___ =___ x 27

54 = 54

*B. Write Yes or No. Explain why you answer No.*

2. If A is 4, then 12 = A = 3 + 2

3. If Z is 5, then 20 - 2Z = 10 - Z

4. If L is 6, then 2L - 4 = 8

*C. Write the equation for the following. Then make the equation true.*

2) The least perimeter possible for a rectangular garden having an area of 24

m

^{2}.

3) The cost of a girl's underwear when a dozen of it is P180.

4) A meter of cloth is P75 and another cloth costs 6 metres at P468. Which is a

good buy?

**V Homework**

___

^{2}= 36 ÷ ___

___ x 6 = 294 ÷ ___

## Giving the Meaning of Exponent and Base, Evaluating Expressions Involving Exponents

**I. Learning Objectives**

**II. Learning Content**

Reference: BEC PELC- A.1.1.1.2, A.1.1.1.3

Materials: Flashcards, charts, activity cards

Value: Awareness of dreaded diseases

**III. Learning Experiences**

**A. Preparatory Activities**

**1. Drill**

Example:2+2=2x2=4

Expected Answers: 3 + 1.5 = 3 x 1.5 = 4.5

11 + 1.1 = 11 x1.1 = 12.1

**2. Motivation**

**B. Developmental Activities**

**1. Presentation**

*Read the selection below (written on the chart)*

DAY NUMBER | NUMBER OF CANCER CELLS |

1 2 3 4 5 6 7 8 9 10 | 2 (2) (2) = 4 (4) (2) = 8 (8) (2) = 16 (16) (2) = 32 (32) (2) = 64 (64) (2) = 128 (128) (2) = 256 (256) (2) = 512 (512) (2) = 1024 |

- How is this obtained?

(The number of cancer cells in a given day is obtained by multiplying the number of cancer cells present on the preceding day by 2 since the cancer cells double daily.)

- If we try to rewrite this product in terms of the number of cancer cells . present on the first day, we will have the following table.

DAY NUMBER | EXPRESSION IN TERMS OF THE NUMBER OF CELLS | NUMBER OF CELLS PRESENT |

1 2 3 4 5 6 7 8 9 10 | 2 2 (2) 2 (2) (2) 2 (2) (2) (2) 2 (2) (2) (2) (2) 2 (2) (2) (2) (2) (2) 2 (2) (2) (2) (2) (2) (2) 2 (2) (2) (2) (2) (2) (2) (2) 2 (2) (2) (2) (2) (2) (2) (2) (2) 2 (2) (2) (2) (2) (2) (2) (2) (2) (2) | 2 4 8 16 32 64 128 256 512 1024 |

- Let us focus our attention on the expression that describes the

number of cancer cells in a given day in terms of cancer cells present

on the first day. This is seen in the second column of table 2.

- What can you say about the writing of the expression? Why?

(It becomes tedious because we write the number repeatedly.)

- It is for this reason that in 1637, Rene Descartes, a French

mathematician, introduced a system of writing numbers indicating

repeated multiplication.

What can you say about Rene Descartes? Do you want to be like him someday? Why?

**2. Fixing Skills**

1.16 = 4 x 4 = ____ = ____

16 = 2 x 2 x 2 x 2 = ____ = ____

2. 81 = 9 x 9 = ____ = ____

81 = 3 x 3 x 3 x 3 = ____ = ____

3.100 = 10 x 10 = ____ = ____

100 = 2 x 5 x 2 x 5 = ____ = ____

4.125 = 5 x 5 x 5 = ____ = ____

5.144 = 12 x 12 = ____ = ____

144 = 3 x 4 x 3 x 4 = ____ = ____

**3. Generalization**

**exponent**tells the number of times the base is used as a factor.

The

**base**is the number used as the factor.

**C. Application**

I**V. Evaluation**

**A. Formative Test**

1. In 5

^{3}, __________ is the base and __________ is the exponent.

2. 6

^{2}is the exponent form of 6 x ____.

3. 144 is the _______ power of 12.

4. 2

^{4}means 2 multiplied by itself ________ times.

5. 7

^{4}means _________ is multiplied by itself four times.

**B. Give the value of the following.**

^{3 }2. 4

^{5}

3. 2

^{7}

4. 9

^{2}

5. 7

^{4}

**V. Assignment**

2.16= ____ x ____ = ____

^{2}

3. 8 = 2 x 2 x 2 = 2-

4.10

^{2}= 10 x 10 = ____

5.10

^{3}= ____ x ____ x ____ = _____

Complete the pattern. 3^{1} 3^{2} 3^{3} 3^{4} 3^{5} 3^{6} 3^{7} 3^{8}

## Evaluating an Expression with Two Different Operations with Exponents and Parenthesis/Grouping Symbols

### I. Learning Objectives

### Cognitive: Evaluate an expression with two different operations with exponents and parenthesis/grouping symbols

### II. Learning Content

### Ill. Learning Experiences

#### A. Preparatory Activities

#### 1. Mental Computation: Drill on Giving an Expression

**a. Activity I**

*Mechanics*:

2) The leader having drawn number 1 opens the problem and reads aloud.

3) Each group decides within 60 seconds.

4) One member of each group simultaneously goes to the board and writes the numerical expression.

5) The teacher together with the class check the answer.

6) The other leaders follow one at a time according to the number drawn.

7) The group having the highest number of correct answer wins.

#### a. Activity 1

*Mechanics:*

#### b. Activity 2

*Mechanics:*

^{2}) + 8

^{2}) + 8

2 x 9 + 8

18 + 8

26

*(Make your illustration here.)*

1) Have the pairs of pupils answer the following questions?

^{2}) + 5

48 + 5

53

a. (2 x 5

^{2}) + 3 d. (8

^{2 }÷ 4) + 2

^{3}

b. (8 ÷ 2) + 2

^{3}e. 92 ÷ (3

^{2}+ 18)

c. (18 + 6) ÷ 2

^{3}

b) What operations must be used? Which operation comes first? last? Which operation should be used first? 'Why? Next? ' Why? Last? Why?

^{2}) + 3 b. (8 ÷ 2)+2

^{3}c. (18 + 6)÷ 2

^{3}(2 x 25) ± 3 4 + 8 24 ÷ 8

50 + 3 13 3

53

d. (8

^{2}-4)+2

^{3}e. 9

^{2}÷ 3

^{2 }+ 18)

(64 ÷ 4) + 8 81 ÷ (9 + 18)

16 + 8 81 ÷ 27

24 3

Evaluate the expressions.

^{2}x 4

^{3}

^{3}

c. (16 - 7)

^{2}- 2

^{3}d. (8 + 8

^{2}) ÷ 24

e. (36 - 9) + 5

^{2}

a. Write an expression about the problem. Then evaluate the expression.

^{3}+ 243

100

500

### IV. Evaluation

Evaluate the following expressions.

^{2}6) 10

^{2}- ( 3

^{2}+ 4

^{2 })

2) ( 2+ 3

^{2}) x 5 7) ( 8

^{2}+ 6

^{2 }) - 4

^{3}3) ( 25 - 15 )

^{3}+ 4

^{2}8) ( 3

^{2}- 2

^{3}) + 8

4) 8 + (5 - 3)

^{5}9) ( 7 - 5 )

^{2 }x 5

^{2}

5) (8 x 3

^{3}) - 4

^{2}10) ( 3 + 4 )

^{2}+ 51

1. Evaluate the following expressions.

^{2}- 20

b. 100

^{2}- (3

^{2}x 5)

^{2}

c. (42 ÷ 7) x 2

^{3}d. (3 + 4)

^{3}+ 6

e. (7 - 3)

^{3}x 5

^{2}

2. Write a problem. Make an expression about it. Then evaluate.

## Evaluating an Expression with Two Different Operations Without Exponents and Parenthesis/Grouping Symbols

### 1. Learning Objectives

### II. Learning Content

### III. Learning Experiences

*b. Activity 2— Game on Naming the Word Expression Mechanics:*

#### 2. Review

#### a. Activity 1 — Naming the Baby

Example: For the next 7 years Minerva turns 27 years old. How old is she now?

Possible Answers: N = 27 — 7

b) The teacher flashes the situation.

c) Each group thinks aloud and decides within 60 seconds for their answers.

d) The teacher checks the answer.

e) The group with the most number of correct answers wins.

### B. Developmental Activities

1) Ask the following questions:

b) Who delivers dozens of eggs?

c) How many dozens of eggs are delivered to them ?

d) If you were Jethro:

• will you keep the change given by the delivery man? Why?

2) Have each pair of pupils act it out using play money and ask them to answer the following:

b) What are the operations to be used?

3) Lead each 'pair of pupils to think of an expression related to the problem.

4) Let them evaluate the expression they have formulated?

P160 + P840

5) Require them to analyze which operation they use before arriving at the exact change.

1) Ask the following questions:

b) How many items does the test have?

c) How many points does each item have?

d) If you were Dangdang will you also study hard? Why? Can you help your family when you study hard? Why?

2) Have each pair of pupils use counters to visualize the problem. Let them answer the following questions.

b) What are the processes to be used?

3) Guide each pair of pupils think of an expression in relation to the problem.

4) Let them think: Why must Dangdang be wrong? Ask them to evaluate the expression.

10 - 8

2

5) Oblige each pair of pupils analyze which operation they use before arriving at the missed points.

b. 7 x 9 - 3 e. 3 x 2 + 4

c. 18 - 12 ÷ 2 f. 48 ÷ 12 + 8

Can you answer these? Let us try to answer the items.

a. 2 x 3 + 4 = b. 7x 9 - 3 c. 18 - 12 ÷ 2

6 + 4 63 - 3 18 - 6

10 60 12

d. 35 - 6 x 3 e. 3 x 2 + 4 f. 48 ÷ 12 + 8

35 - 18 6 + 4 4 + 8

17 10 12

3) Lead each pair of pupils analyze how to arrive at the answer.

Evaluate the expression.

b. 5 x 8 ÷ 4

c. 65 - 91 ÷ 7

d. 72 ÷ 3 x 8

e. 67 + 33 ÷ 25

Write an expression about the problems. Then evaluate the expression.

a) In a certain eatery, there are 5 glass racks having 24 glasses and 8 left over. The answer says she has 130 glasses in all. Is she right? Why?

b) Use the number less than 7 once to make the expression right.

____ - ____

c) Write the operation in the blank to make the expression right.

81 ___ 63

Evaluate the following expressions.

2. 84 ÷ 3 x 4

3. 76 - 8 + 5

4. 53 + 7 - 20

5. 3 x 5 ÷ 25

6. 7 x 8 + 130

7. 195 ÷ 3 x 5

8. 3 + 83 - 73

9. 76 - 8 x 9

10. 90 x 5 ÷ 75

Write the operations to make the expression right.

1. Evaluate the following expressions.

2) 44 + 56 ÷ 7

3) 67 + 3 x 9

4) 27 - 8 ÷ 4

5) 3 x 8 ÷ 6

2. Write a problem. Make an expression about it. Then evaluate.

## Evaluating an Expression With More Than Two Operations With or Without Exponents and Parenthesis/Grouping Symbols

### I. Learning Objectives

### Cognitive: Evaluate an expression with more than two operations with or without exponents and parenthesis/grouping symbol

### Psychomotor: Work in teams

### II. Learning Concepts

Materials: charts, flashcards, cross number puzzles

Value: Cooperation, honesty

### Ill. Learning Experiences

A. Preparatory Activities

### 1. Review

2) 3 x 5 - 4 = 3

3) 18 ÷ 6 x 3 = 1

4) 16 - 7 + 8 = 17

5) 12 ÷ 2 + 4 = 2

2) _____ x _____ ÷ ( _____x_____ ) = 1

3) _____ x ( _____ x _____ ) ÷ ______ = 18

4) _____ ÷ ( _____ - _____ ) + _____ = 14

### 2. Motivation

D | I | F | F | E | R | E | N | C | E |

T | S | T | A | D | D | E | N | D | S |

W | U | H | L | E | S | S | S | R | M |

I | M | R | U | T | I | M | E | S | A |

C | R | I | S | D | I | V | I | D | E |

E | M | I | N | U | S | E | O | U | A |

Q | U | O | T | I | E | N | T | R | E |

A | D | E | X | F | O | N | E | N | T |

### 1. Presentation

4) Fourth, perform addition and subtraction as they occur from left to right.

4 + 4 - 5 Rule 3

^{2}= 3 x 2 + 5 - 1

12 x 2 + 5 - 1 Rule3

24 + 5 - 1 Rule3

29 - 1 Rule4 28

3 x [ 4 - 2 x 2 + 12 ÷ 6 x 1] Rule 1

3 x [ 4 - 4 + 12 -÷ 6 x 1] Rule 3

3 x [4 - 4 + 2 x 1] Rule 3

3 x [4 - 4 + 2] Rule 3

3 x [ 0 + 2 ] Rule 4

3 x 2 Rule 1

6

#### b. Ask:

2) What are the rules for the order of operation when parenthesis, exponent, addition, subtraction, multiplication and division are involved?

3) What should you remember in answering some exercises in mathematics? What" character traits does it require?(patience and perseverance)

### 2. Fixing Skills

#### Simplify the expressions below and solve.

^{2}

2) 6 ÷ 2 + 1 x 4

3) ( 15 - 6 ) + ( 4 - 1 ) x 23

4) 3 x [ 3 + 2 x ( 10 - 3 ) ]

5) 12 + 3 x { 3 x [ 4 + ( 9 - 8 ) - 2 ] - 3 }

### 3. Generalization

### C. Application

### IV. Evaluation Simplify and solve

^{2}- 6 + 3

2. 6 + ( 2 x 7 + 52 )

3. 3 x ( 4 + 8

^{2}) - 8

4. 37 + 3 x 2 ÷ 6

5. 14 ÷ 2 - 3 + 2 x 2

### V. Assignment

^{127}is one followed by how many zeros?

2. Find (x

^{2})

^{2}if x= 3

3. If your calculator does not have an exponent key, can you use the definition of the exponent in 23 + 3 = 2 x 2 x 2 + 3? How?