BASIC EDUCATION ASSISTANCE FOR MINDANAO LEARNING GUIDE

FIRST YEAR - MATHEMATICS

REAL NUMBER SYSTEM

Basic Education Assistance for Mindanao (BEAM) project. Prior approval must be

given by the author(s) or the BEAM Project Management Unit and the source must

be clearly acknowledged.

Mind Map

The Mind Map displays the organization and relationship between the concepts and activities in this Learning Guide in a visual form. It is included to provide visual clues on the structure of the guide and to provide an opportunity for you, the teacher, to reorganize the guide to suit your particular context.

Stages of Learning

The following stages have been identified as optimal in this unit. It should be noted that the stages do not represent individual lessons. Rather, they are a series of stages over one or more lessons and indicate the suggested steps in the development of the targeted competencies and in the achievement of the stated objectives.

Assessment

All six Stages of Learning in this Learning Guide may include some advice on possible formative assessment ideas to assist you in determining the effectiveness of that stage on student learning. It can also provide information about whether the learning goals set for that stage have been achieved. Where possible, and if needed, teachers can use the formative assessment tasks for summative assessment purposes i.e as measures of student performance. It is important that your students know what they will be assessed on.

1. Activating Prior Learning

This stage aims to engage or focus the learners by asking them to call to mind what they know about the topic and connect it with their past learning. Activities could involve making personal connections.

Background or purpose

In this stage, the students will determine the fractions, lowest terms and decimals of the given figures.

Strategy

BUZZ SESSION. This strategy aims to maximize students' engagement and to tap their verbal/linguistic and mathematical intelligences through answering questions or solving problems and come up to some kind of conclusion.

Materials

• strips (refer to Teacher Resource Sheet 1 on page 18) • activity sheet (refer to Student Activity 1 on page 19)

Activity 1: “Me and My Figure”

Instructions:

1. Prior to the activity, prepare the strip cards and put them inside the envelope. 2. Organize the class into 10 groups or as desired and distribute the materials needed. 3. Instruct the students to paste the strips in the indicated column found in the

Student Activity 1 and match the figures with their equivalent fractions and decimals.

4. Set a time allotment for them to work for the activity.

5. Call 2 volunteers to present their outputs in the class for comparison.

Formative Assessment

Ensure the participation of the students in the activity by monitoring their performance. Check their outputs. Refer to page 19 for the answers.

Roundup

The students would have determined the fractions, lowest terms and decimals of the given figures.

2. Setting the Context

This stage introduces the students to what will happen in the lessons. The teacher sets the objectives/expectations for the learning experience and an overview how the learning experience will fit into the larger scheme.

Background or purpose

The students in this stage will add and subtract similar fractions. This will lead them to have an overview on operations involving fractions and decimals.

Strategy

PAIRED-STRIPS. This strategy allows students to use their knowledge and skills in performing the task with accuracy in order to get the exact detail of the activity. This motivates them to work in their group with a sense of cooperation and responsibility. The activity aims to develop their logical/mathematical and visual/spatial intelligences.

Material

• pair cards (refer to Teacher Resource Sheet 2 on page 20)

Activity 2: “It's You!”

Instructions:

1. Prior to the activity, prepare the pair cards.

4. Set a sufficient time allotment for the activity. Explain to them that side B of the paired cards contain also the equivalent expressions.

Question:

● How will you perform operations involving dissimilar fractions? decimals?

Formative Assessment

Ensure the participation of the students in the activity by monitoring their performance and progress.

Check their paired cards. Refer to the answer key on page 20.

Roundup

The students would have added and subtracted similar fractions.

3. Learning Activity Sequence

This stage provides the information about the topic and the activities for the students. Students should be encouraged to discover their own information.

Background or purpose

At the end of this stage, the students are expected to:

• perform the operations on dissimilar fractions and mixed forms; • perform the operations on decimals; and

• solve problems involving fractions and decimals.

Strategies

 INTERACTIVE LECTURE. This strategy provides students with a general outline to give

them a framework for thinking about a subject and to structure their note-taking. This type of lecture involves the students by focusing their attention on key words and emphasizes information transfer at the knowledge, recall, and comprehension levels of learning.

 TRIVIA. This strategy requires an accurate response that will enable the students to

learn and develop their mathematical skills. It is a fun and interesting way of activating the students' comprehension through visuals. This aims to enhance their logical/mathematical and visual/spatial intelligences.

 BUZZ SESSION. This strategy aims to maximize students' engagement and to tap their

verbal/linguistic and mathematical intelligences through answering questions or solving problems and come up to some kind of conclusion.

 DECODING. A strategy used to translate data or message from a code into the original

language or form. In the context of this activity, the students will solve problems

involving the operations on rational algebraic expressions. After which, they will look for the corresponding answers on the decoder that will satisfy the given challenge.

Materials

Activity 3: “It's Fantastic”

Activity 4: “Yes! I Can Fly...”

• activity sheet (refer to Student Activity 4 on page 23-24)

Activity 5: “Building a House”

• strips (refer to Teacher Resource Sheet 5 on page 26) • manila paper

• Masking tape • envelopes (4 pieces)

Activity 6: “This is Real”

• strips (refer to Teacher Resource Sheet 6 on page 27)

LECTURETTE 1

Begin the lesson by asking the students to perform the following operations of fractions below. 1. 2 7



Encourage them to solve the next problems.

1. 1 3  1 4 2. 1 2 − 2 5

If they could not recall their learning about the topic the previous years, then show them the solutions.

1. 2 3 

1 4

Find the least common denominator (LCD).

Divide the LCD by the denominator of each fraction, then multiply the quotient to its numerator.

8 12 

3

12 Add the numerators and keep the LCD as the denominator.

11

12 Simplify the resulting expression if possible.

2. 1 2 −

2 8

Find the least common denominator (LCD).

Divide the LCD by the denominator of each fraction, then multiply the quotient to its numerator.

8 16 −

4 16

Subtract the numerators and keep the LCD as the denominator.

4

Present some problems of fractions in mixed forms. Ask the students to solve on the board.

1. 31 2



2

5 2. 12

2 3 − 5 16

Solutions:

1. 31 2



2 5

= 3₁₀5  4 4 10

= 7 9 10

2. 122 3 − 5 16

= 124 6 − 5 16

= 73

6 or 7 12

Introduce the positive and the negative signs in performing addition or subtraction of fractions.

a) 1

2





−

6



−

3 4

−

2





−



Find the least common denominator (LCD).

Divide the LCD by the denominator of each fraction, then multiply the quotient to its numerator.

= 3 6



1 6



Follow the rules of adding unlike integers in combining the numerators and keep the LCD as the denominator.

= 2 6 or

1 3

Simplify

b)

−

4

−

Find the least common denominator (LCD).

Divide the LCD by the denominator of each fraction, then multiply the quotient to its numerator.

= −15 20



8 20



Follow the rules of subtracting integers in combining the numerators and keep the LCD as the denominator.

= −23

20 or −1 320

Simplify

Let them give their own rules in adding or subtracting fractions. Consolidate their ideas by presenting these rules.

Give more exercises for them to practice.

1.

−

7





−

6



3 4



2

3



5 6−



1

3



1 5−



4 7



Solutions:

1.

−

7





−



= −12 42



14 42



= −26 42 or−

13 21

2. −33 4



2 3



= −3 9 12



8 12



= −1 1 12

3. −5 6−



1 3



= −5 6−



2 6



= −5 6

2 6

= −3 6 or −

1 2

4. 31 5−



4 7



= 3 7 35−



20 35



= 3₃₅7 1 20 35

= 427₃₅

Activity 3: “It's Fantastic”

Instructions:

1. Organize the class into 10 groups and distribute the activity sheet. Refer to Student Activity 3 on page 21.

2. Set a sufficient time allotment to work for the activity. 3. Check their outputs. Refer to page 22 for the answers.

LECTURETTE 2

Review the students on what they had learned about multiplication of fractions. Let them answer some problems below.

1. 3₅ x 1

6 2. 2

1 2 x 3 23

Solutions:

= ₁₀1 = 55₆

= 91 6

Now, introduce the multiplication of fractions involving their signs. Guide them to solve the problems relating to multiplication of integers. Ask them to answer the following:

1. −1 2 x −

2

3 2. −3 56 x 1 13

Solutions:

1. −1 2 x −

2 3 or

= 2₆

= 1₃

=

= 1 3

2. −3 5 6 x 1 13

= −23 6 x 43

= −92

18 or − 46

9

= −5 1 9

Practice:

a. 9

10 x 9 b. 8

4 9 x −

5 6

Let the students generalize their learning by asking them the rules for multiplying two fractions having like or unlike signs. Then, synthesize their answer by presenting these rules below.

After which, show problems about division of fractions. Call somebody from the class to answer.

−1 2 x−

2 3 1

1. 1₂

÷

5

÷

2 4

Solutions:

1. 1₂

÷

= 1₂ x 6₁

= 6₂ or 3

2. −2

5

÷

2 4

= −2 5 x

4 2

= −8

10 or − 4 5

You may give seat works or board works.

1. −9

11

÷

3

6 2. 6

1

5

÷

5 7

Solutions:

1. −9

11

÷

3 6

= −9 11 x −

6 3

= −9 11 x −

6 3

= 54₃₃

= 18₁₁

= 1 7 11

2. 61₅

÷

= 31₅ x −7 5

= −217 25

= −8 17 25

You can tell the students to use the short method of solving if possible.

Activity 4: “Yes! I Can Fly...”

Instructions:

1. Organize the class into 10 groups and distribute the activity sheet. Refer to Student Activity 4 on pages 23-24.

2. Set a sufficient time allotment to work for the activity. 3. Check their outputs. Refer to page 25 for the answers.

LECTURETTE 3

As a recall to students' learning, let them change the given fractions below into decimals.

1. 1

2 2.

3 5

Answers:

1. 1

2 = 0.5 2.

3 5 = 0.6

Then, ask them to perform the given operations. Let them answer one at a time.

1) 1.8 + 5.2 2) 1.5 + 1.116 3) 2.6 – 1.7 4) 1.6 – 1.13

Solutions:

Give another problems that involve the positive and the negative signs.

1) 39.1 + (-81.2) 2) (-15.74) + (-24.954) 3) 16 − (-9.07) 4) - 61.3 − 31.345

Solutions: 1.8 1.8 5.2 7.0 +

1) 1.5

1.16 2.66 +

2) 2.6

1.7 0.9

-3) 1.6

Let the students formulate the rules for adding and subtracting decimals. Then, present the one below.

Exercises:

1) - 99.326 + 24.8 2) 20.4 - 100.8

Solutions:

Thereafter, ask the students to solve some problems about multiplication of decimals.

1) 2 x 1.7 2) -0.3 x 0.2 3) -7.2 × -2.8

Solutions:

Give them board work for practice.

1) 3.6 x 8.1 2) 1.5 x - 9.12

39.1 - 81.2 - 42.1 +

1) - 15.74

- 24.954 - 40.694 +

2) - 61.3

31.345 -4) - 61.3 - 31.345 + - 92.645 16

- 9.07 -3) 16.00 9.07 25.07 +

- 99. 326 24.8 - 74.526 + 1) 20.4 100.8 -2) 20.4 - 100.8 + - 80.4 1.7 2 3.4 x 1) -0.3 0.2 - 0.06 x

2) - 7.2

Solutions:

Allow the students to give their rules in multiplying decimals based on their understanding and process their ideas to generate a common rules.

After which, introduce the division of decimals.

1) 7.4 ÷ 2 2) -3.2 ÷ 0.4

Solutions:

Remind the students that in dividing decimals involving their signs, divide the decimals naturally and prefix the positive sign if they are like decimals and negative sign, if unlike. Show more examples for further emphasis.

1) 1.68 ÷ -4 2) -1.47 ÷ -0.07

2) 0.4 -3.2

- 8

0 4 -32

32 3.6

8.1 36 x 1)

288 29.16

1.5 - 9.12

4560 x 2)

912 13.680

7.4 3.7 2

Let them answer this question:

● How do you divide a decimal by a whole number with like signs? unlike signs?

Then, present a concise rules.

● How do you divide a decimal by a decimal number with like signs? unlike signs?

Activity 5: “Building a House”

Instructions:

1. Prior to the activity, prepare the strips and put them inside the envelope. 2. Reorganize the class into 4 groups and distribute the materials needed. Refer to

Teacher Resource Sheet 5 on page 26.

3. Ask the students to pair the two strips correctly to form a house and paste them on a manila paper, and post on the board.

4. Check their outputs. Refer to page 26 for the answers.

Activity 6: “This is Real”

Instructions:

1. Prepare the strips which is found in Teacher Resource Sheet 6 on page 27.

2. Reorganize the class into 8 groups and distribute the strips. Ensure that two groups will answer the same problem.

3. After which, let the group with the same problem join together for comparison and discussion and to reach consensus.

4. Let them write their outputs on the manila paper and post on the board. 5. Check their outputs. Refer to page 28 for the answers.

Formative Assessment

Ensure the participation of the students in the activity by monitoring their performance and checking their progress.

Roundup

The students would have performed the operations on dissimilar fractions and mixed forms, operations on decimals, and solved problems involving fractions and decimals.

4. Check for Understanding of the Topic or Skill

This stage is for teachers to find out how much students have understood before they apply it to other learning experiences.

Background or purpose

In this stage, the students will demonstrate their knowledge and skill in performing the operations on fractions and decimals.

Strategy

PUZZLE. This strategy is structured for small group work that encourages participation, cooperative learning and group responsibilities. It caters students whose comprehensions are activated using visuals. This enhances their interpersonal and verbal/linguistic intelligences.

Materials

Activity 7: “I'm Puzzled”

Instructions:

1. Divide the class into 10 learning groups and distribute the activity sheet. 2. Set a time allotment for them to perform the activity.

3. Ask 2 volunteers to present their outputs in the class for comparison and discussion.

Formative Assessment

Ensure the participation of the students in the activity by checking their progress and monitoring their performance.

Check their outputs. Refer to the answer key on page 30.

Roundup

The students would have demonstrated their knowledge and skill in performing the operations on fractions and decimals.

5. Practice and Application

In this stage, students consolidate their learning through independent or guided practice and transfer their learning to new or different situations.

Background or purpose

The students will solve problems involving fractions and decimals in real life situations.

Strategy

TASK CARDS. These specify a task or activity for students to complete individually, in pair or as a small group. Making tasks “real life” tasks make them more meaningful. Task can be issued to practice a newly developed skill. This strategy aims to develop their

logical/mathematical, spatial/visual and interpersonal intelligences.

Materials

• task cards (refer to Teacher Resource Sheet 9 on pages 31) • marking pen

• manila paper • masking tape

Activity 8: 'Life in Action”

Instructions:

1. Prior to the activity, prepare the task cards.

2. Divide the class into 8 learning groups and distribute the materials needed. Ensure that two groups will have the same task.

Roundup

The students would have solved problems involving fractions and decimals in real life situations.

6. Closure

This stage brings the series of lessons to a formal conclusion. Teachers may refocus the objectives and summarize the learning gained. Teachers can also foreshadow the next set of learning experiences and make the relevant links.

Background or purpose

In this stage, students will consolidate their learning about the topic.

Strategy

GAME. This strategy asserts students' interest in performing the operations on radical expressions and solving radical equations while having fun doing the activity. This enhances their logical/mathematical, visual/spatial and interpersonal intelligences.

Materials

• chip boards - 10 pieces (refer to Teacher Resource Sheet 11 on page 34) • chalk

Activity 9: “Have Fun”

Instructions:

1. Prior to the activity, prepare the questions.

2. Reorganize the class into 10 groups and give the necessary materials.

3. Post the mechanics of the game. Refer to Teacher Resource Sheet 12 on page 35.

Formative Assessment

Ensure the participation of the students in the game by monitoring their performance. Check their answers using the answer key on page 34 and 36.

Roundup

The students would have consolidated their learning about the topic.

Teacher Evaluation

(To be completed by the teacher using this Teacher’s Guide) The ways I will evaluate the success of my teaching this unit are: 1.

TEACHER RESOURCE SHEET 1

Me and My Figure

STUDENT ACTIVITY 1

Me and My Figure

Objective: Determine the fractions of the shaded parts of the figures, their lowest terms and equivalent decimals.

Directions: 1. Paste all the figures on the first column.

TEACHER RESOURCE SHEET 2

It's You!

Directions:

1. Prepare 32 pieces of 5 in x 5 in cards.

STUDENT ACTIVITY 3

It's Fantastic!

What living organism can be 30 times the size of a blue whale?

http://www.triviaplaying.com/107_nature_Q_.htm

To answer this trivia, perform first the addition and subtraction of fractions in the

table and look for their answers in the DECODER. Then, write each letter in the

empty box that corresponds with the correct answer.

A

6

7

−

1

2



1

4

O

7

15



2

5

−

11

10

E



−

2

1

6



−



−

3

8



Q

19

13

−

6

7

G

3

4

5



3

3

4

S

11

1

12

−

5

1

8

I

−

4

4

5





−

2

1

8



T

9

17



8

6

N

−

13

7

−

1

4

U

1

7

−



−

13

17



7 11

20 −6 3740 17

28 −

59

28 1 4451 5 2324 −1 1924 55 91

108

119 −

7

TEACHER RESOURCE SHEET 3

It's Fantastic!

Answer Key

They are the only animals that can fly backwards. What are they?

http://www.triviaplaying.com/04_bird.htm

A

6

7

−

1

2



1

4

O

7

15



2

5

−

11

10

E



−

2

1

6



−



−

3

8



Q

19

13

−

6

7

G

3

4

5



3

3

4

S

11

1

12

−

5

1

8

I

−

4

4

5





−

2

1

8



T

9

17



8

6

N

−

13

7

−

1

4

U

1

7

−



−

13

17



STUDENT ACTIVITY 4

Yes! I Can Fly...

Directions:

1. Multiply or divide each expression that is seen in every pot.

3. Write each letter inside the flower below that corresponds to the answer of the expression in the pot to answer the question.

TEACHER RESOURCE SHEET 4

Yes! I Can Fly...

Teacher Resource Sheet 5

Building a House

Directions:

1. Reproduce 4 enlarged copies of this sheet and cut the strips as shown in

the example below.

TEACHER RESOURCE SHEET 6

This is Real

Directions: Reproduce the strips and cut.

A large chocolate cake is served in a table. Gilbert gets 2

12 of it while Nante,

1 8. a) Who gets more? Justify your answer.

b) What part of the cake do they get? c) How much is left?

e) If Rey receives 3

4 of Gilbert's share, then what part of the whole cake is taken by Rey?

Romel and friends rode a taxi going to SM Mall. The flag down rate in the first 200 meters was P27.00 and an additional of P2.50 for every 100 meters covered thereafter.

a. How much did Romel pay in 1.5-km ride?

b. If Romel gave P100, then how much was the change?

c. How far in kilometers would Romel and friends be from their post if the driver charged them P120?

World Record shows that the lowest temperature happened in the earth was -89.2 o_{C on July 21, 1983 at}

Vostok, Russia. In Manila, Philippines, it was on December 19, 2008 where it reached to 18.2 o_C.

a. Based on the two recorded temperatures, how much warmer was Manila compare to Vostok? b. On May 28, 2009, Manila has a temperature of 30.56 o_{C. Find the temperature rate of increase in}

Manila between the two dates.

Teacher Agnes brought 10 boxes of jelly roll to school during her birthday. She sliced them in such a way that everyone could have a share. She gave 33₈ her co-teachers, 51₄ to her pupils and the rest to the utility.

TEACHER RESOURCE SHEET 7

This is Real

Answer Key

A large chocolate cake weighs 4.8 kg. Gilbert gets 2 12 of it while Nante, 1

8.

a) Who gets more? Justify your answer.

Solution: Gilbert  2

12 = 1 6 =

4 24

Nante 1

8 = 1 8 =

3 24 Therefore, Gilbert gets more.

b) What part of the cake do they get?

Solution: = 2 12 1 8 = 1 6 1 8 = 4 24 3 24 = 7 24

Therefore, they get 7

24 of the cake. c) How much is left?

Solution: 1− 7

24 = 24 24− 7 24 = 17 24

d) If Rey receives 3

4 of Gilbert's, then what part of the whole cake is taken by Rey?

Solution: 2

12 3 4= =

1 8

Therefore, Rey takes 1

8 of the whole cake.

Romel and friends rode a taxi going to SM Mall. The flag down rate in the first 200 meters was P27.00 and an additional of P2.50 for every 100 meters covered thereafter.

a. How much did Romel pay in 1.5-km ride?

Solution: 1.5 km = 1,500 m; 200 m + 1300 m = 1,500 m

Formula: Initial fare + additional charge

= 27+





= 27 + 32.50 = 59.50

Therefore, Romel paid P59.50 in 1.5-km ride.

b. If Romel gave P100, then how much was the change?

Solution: 100 – 59.50 = 40.50

Therefore, Romel's change was P40.50.

c. How far would Romel and friends be in kilometer from their post if the driver charged them of P120?

Given: n = total distance

Solution: total distance = initial distance+ additional distance

n = 200 m +





n = 200 m + (37.20) (100 m) n = 200 m + 3,720 m n = 3,920 m

Therefore, the distance traveled by the taxi was 3.92 km.

World Record shows that the lowest temperature happened in the earth was -89.2 o_{C on July 21, 1983 at Vostok, Russia. In}

Manila, Philippines, it was on December 19, 2008 where it reached to 18.2 o_C.

a. Based on the two recorded temperatures, how much warmer was Manila compared to Vostok?

Solution: 18.2 O_{C - (-89.20} O_{C) = 107.4} O_C

b. On May 28, 2009, Manila has a temperature of 30.56 o_{C. Find}

the temperature rate of increase in Manila between the two dates.

Solution: 30.56 – 18.2 = 12.36

÷

Teacher Agnes brought 10 boxes of jelly roll to school during her birthday. She sliced them in such a way that everyone could

have a share. She gave 3 38 her co-teachers, 5 14 to her pupils and the rest to the utility.

a) Altogether, what portion was being given to her co-teachers and pupils?

Solution: 3 3

85 14=3 9245 624=8 1524 b) How much was shared to the utility?

Solution: 10−8 15

STUDENT ACTIVITY 7

I'm Puzzled

1

3

+

2

8 =

÷

_

1 = 13

_

+

= −1

24 x −2 36 = 0.81

0.8 = =

_

- 20 x 1

2 = - 10 −

1 5

= = =

105 27

3

10 x =

7

10

÷

2

15 =

=

+

+

÷

1

5 =

TEACHER RESOURCE SHEET 8

I'm Puzzled

Answer Key

1

3

+

2

8 =

7

12 - 0.09

1.8

÷

_

3 - 0.9

1 5.49 = 13

_

+

= −1

24 x −2 36 =

5

48 0.81

0.8 = 4

5 =

_

6

- 20 x 1

2 = - 10 −

1

5 −

1 3

= = =

105 27

3

10 x

7

3 =

7

10

÷

2

15 = −5 14

=

+

+

3 8

9

÷

25

9 = 1 25 −

9

10 −

1

TEACHER RESOURCE SHEET 9

Life in Action

Task Cards

TEACHER RESOURCE SHEET 10

Life in Action - Task Cards-

Answer Key

TASK 1

1. At my birthday, the girls ate 31

2 pies and the

boys, 71

2. How pieces of pies were eaten?

Solution: 31 2 + 7

1

2 = 10 2

2 = 11

Therefore, there are 11 cakes which were eaten? 2. Susan has 4.5 times as much money as her brother. If Susan has P24.75, how much money does her brother have?

Solution: 24.75

÷

Therefore, Susan's brother has P5.50.

TASK 2

1. Nestor bought 21

2 gallons of paint but he only

used 3

4 of it. How much paint was left?

Solution: 2 1 2− 3 4 = 5 2 − 3 4 = 10 4 − 3 4 = 7

4 = 1 34

Therefore, 13

4 gallons of paint was left. 2. Monaliza and her classmates bought slices of banana cakes from the canteen. If P 38.50 were paid for 11 slices, then how much was a slice of banana cake?

Solution: 38.50

÷

Therefore, a slice of banana cake was P3.50.

TASK 3

1. To make a panel of curtain, Mary needs 13 4

meters of cloth. How many meters of cloth should she buy to make 10 panels of curtains?

Solution: 1 3

4 x 10= 7

4 x 10= 70

4 = 35

2 =17 12 2. The grades of Arnold in mathematics from first grading to third are 85.6%, 89.45% and 92%

respectively. What should be his grade in the fourth grading so that he can have an average of 90.5%?

Solution: 85.6







4

=

267.05n=362 n=362−267.05 n=94.95

Therefore, Arnold's grade in 4th _{grading should be}

94.95%.

TASK 4

1. Peter's truck can travel 101

2 km per liter of

gasoline. How many liters can the truck consume in

56 7 10 km?

Solution: 56 7

10÷10 12= 567 10 ÷ 21 2 567 10 × 2 21= 1,134 210 = 567

105=5 42105

5 42

105 =5 1435=5 25

Therefore, the truck can consume 52₅ liters in

56 7

10 kilometers.

2. Ellen bought 2 boxes of milk worth P28.75 each and 1 pack of sugar worth P18.95. How much change did she receive after paying P100? Solution: 28.75 x 2 = 57.5 + 18.95 = 76.45

100 – 76.45 = 42.5

TEACHER RESOURCE SHEET 11

Have Fun!

5 12 

2

3=1 112 2 −

2

3=1 13 12.35 + 5.287 = 17.637 12.3 x 3.54 = 43.542

3 5 



1 2



1 10

2 9 −



2 3



8

9 45.12 + 3.71 = 48.83 -4.23 x -2.7 = 11.421

1 2 

6

10=1 110

7 4 −

10 7 =

9

28 -8.28 + (-32.6) = -40.88 -0.18 x 0.06 = -0.0108

−10 7 

1 2= −

13

14 −

2 3 −

4

8 = −1 16 47.4 + (–9.6) = 37.8 4.05 x -22 = -89.1

2 5 

5 6=1 730

1

4 − 1= − 3

4 63.1 + 4.02 = 67.12 64.5 x 4 = 258

−42 3 



5 6



1

2 2 14 − 1

8=2 18 8.5 - (-8.19) = 16.69 9.2

÷

3 1 2 

2

3=4 16 −2 7

8 −





3

8 93.04 – 18.17 = 74.87 -2.73

÷

2 1

7  3 45 =5 3335 1 56 − 1 34= 1

12 1.15 - 3.2= -2.05 3.84

÷

4 1

2  3 56=8 13 2 14 − 1

8=2 18 14.793 – 8.95 = 5.843 13.169

÷

1 1

2  4 34 =6 14

1

6 − 1 35= −1 1330 1.387 - 12.17 = -10.783 0.2334

÷

1. Juliana stopped her car to get something to eat. She bought a cheeseburger for P32.95, french fries for P31.75 and a soft drink for P12.50. How much did Juliana spend?

2. The mother of Justin wanted to buy him a bag to be used in school. In the shopping mall, she found a bag with a regular price of P890 at 35 % less. She also found another one that was regularly priced at P665 with 15 % discount. Which bag is cheaper? by how much?

3. Rod walks 41

2 km from home to school. Five-eighths of his way is the house of his English

teacher, Nor. How far is teacher Nor's house from Rod's?

4. Rose Marie has P 75. She spends half of it for snacks and 2

5 for fare. How much does she spend

TEACHER RESOURCE SHEET 12

Have Fun!

Mechanics of the Game

1. You will solve problems involving operations on fractions and decimals. 2. The teacher will read each

question twice and you can immediately solve it. 3. As soon as you are through,

write your answer on the illustration board and stand. 4. Thereafter, the teacher will

count from 1 to 10. After counting, you will stop solving and stand to show your answers. The following are the corresponding points for the game.

5 points – first who answers correctly 3 points – correct answers but not the first 1 point – wrong answer

0 point – no answer

TEACHER RESOURCE SHEET 13

Have Fun!

Answer Key

1. Juliana stopped her car to get something to eat. She bought a cheese burger for P32.95, french fries for P31.75 and a soft drink for P12.50. How much did Juliana spend?

Solution: P32.95 + P31.75 + P12.50 = P77.20

2. The mother of Justin wanted to buy him a bag to be used in school. In the shopping mall, she found a bag with a regular price of P890 at 35 % less. She also found another one that was regularly priced at P665 with 15 % discount. Which bag is cheaper? by how much?

Solution:

6. P890 x 0.35 = P311.50 7. P890 – P311.50 = 578.50 8. P578.50 – P565.25 = 9. P13.25

P665 x 0.15 = P99.75 P665 – P99.75 = P565.25

Therefore, the bag with 35 % discount is cheaper by P13.25.

3. Rod walks 41

2km from home to school. Five-eighths of his way is the house of his English teacher, Nor. How far is teacher Nor's house from Rod's?

Solution: 4 1 2 x

5 8

= 9 2x 58

= 45 16

= 213 16

Therefore, teacher Nor's house is 213

16km from Rod's.

4. Rose Marie has P75. She spends half of it for snacks and 2 5 for fare. How much does she spend in all ?

Solution: 1 2 2 5 = 5 10 4 10 = 9 10

= P75 x 9 10

= P75 x 9 10

= 675 10

= P67.50

Therefore, Rose Marie spends P67.50.

5. The electrical men replace their old post along the highway with a concrete one which length measures 50 feet. How high is the post from the ground, if they dig 1

8 of the length of the post?

Solution: 50x1

8

= 50 8 or

25 4

= 61 4

= 50-6 1 4

= 494 4-6 14

= 433 4

Therefore, the length of the post from the ground is 43 3

For the Teacher: Translate the information in this Learning Guide into the following matrix to help you prepare your lesson

plans.

Stage

_1.

Activating Prior

Learning

2.

Setting the

Context

3.

Learning Activity

Sequence

4.

Check for

Understanding

5.

Practice and

Application

6.

Closure

Strategies

Activities from the Learning Guide

Extra activities you may wish to include

Materials and planning needed

Estimated time for this Stage