BEAM Learning Guide - DepEd Manilamgaraullo.depedmanila.com/wp-content/uploads/2019/... · MODULE 9: WITH POWERS Information about this Learning Guide Recommended number of lessons

BASIC EDUCATION ASSISTANCE FOR MINDANAOLEARNING GUIDE

SECOND YEAR - MATHEMATICSINTEGRAL EXPONENTSModule 9: With Powers

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Written, edited and produced by Basic Education Assistance for Mindanao, April 2009

BASIC EDUCATION ASSISTANCE FOR MINDANAO

SECOND YEAR - MATHEMATICS

INTEGRAL EXPONENTS

MODULE 9: WITH POWERS

Information about this Learning GuideRecommended number of lessons for this Learning Guide: 6

Basic Education Curriculum CompetenciesYear 2 Mathematics: With Powers

• Demonstrate knowledge and skill in simplifying expressions with integral exponents and apply these in the solution of problems.

• Demonstrate understanding of expressions with:

• positive exponents

• negative exponents

• zero exponents

• Evaluate numerical expressions involving integral exponents.

• Rewrite algebraic expressions with zero and negative exponents.

• Solve problems involving expressions with exponents.

Objectives• Identify prime factors of a number.

• Demonstrate understanding of expressions with positive, negative and zero exponents.

• Evaluate numerical expressions involving integral exponents.

• Rewrite algebraic expressions with zero and negative exponents.

• Solve problems involving expressions with exponents.

Essential concepts, knowledge and understandings targeted• Exponential Notation. If a is a real number and n is a positive integer, then the symbol an

represents the product of n factors of a. That is, an = a•a•a•...a•a. In an, a is called the base and n is the exponent.

• Rules for integral exponents:

Let m and n are integers, and a and b are nonzero real numbers.

➢ Product rule: am•an = am+n

➢ Quotient rule: am

an = am−n

➢ Power of a power rule: (am)n = amn

➢ Power of a product rule: (ab)n = anbn

➢ Power of a quotient rule: ab

n

= an

bn

➢ Definition of zero exponent: a0 = 1

Basic Education Assistance for MindanaoLearning Guide, April 2009 3



INTEGRAL EXPONENTS


➢ Definition of negative exponent: a−n = 1an

• Exponential expressions are said to be in simplest form if:

1. the exponents are positive,

2. there are no powers of powers,

3. each base appears only once, and

4. all fractions are in simplest form.

Specific vocabulary introduced• Exponent – a number used to tell how many times a number is used as a factor

• Power – a product represented by the number and its exponent

• Integral exponent – power of a number in the form of an integer

Suggested organizational strategies• Have the classroom ready to accommodate groups of students to learn and explore the

activities where they will be at ease and comfortable to move and explore the activities in every stage of learning.

• Assign roles to students within the groups.

• Be prepared with the complete materials to be used by students in performing the tasks.

• Prepare enough and clear copies of the activity sheets prior to the lessons.

Opportunities for IntegrationPEACE EDUCATION

• The activities encourage the students to work harmoniously with others to achieve accuracy and considerable outputs.

VALUES EDUCATION

• Students working in a group develop their sense of being sensitive to the needs and feelings of others especially in doing group tasks.

GENDER INCLUSIVITY

• Mutual responsibility and conscious participation of both boys and girls are considered.

MULTICULTURALISM

• The activities in this Learning Guide are suited to different tribes and cultures.

ENGLISH

• Some of the suggested activities in this Learning Guide require students to express their ideas.

GENERAL INFORMATION

• Student Activities 4 and 5 encourage them to discover the hidden messages that will give them useful information.

HISTORY




INTEGRAL EXPONENTS


• Student Activity 4, “Task B: Pyramid Passage”, acquaint students about pyramids of the ancient Egyptians.

Activities in this Learning GuideActivity 1: Get Intersected

Multiple Intelligences

• Logical/Mathematical

• Interpersonal

Skills

• Use information

• Observation and recall of information

Activity 2: Starts With...



• Interpersonal

Skills

• Predict consequences

• Use information


Activity 3: What Power?



• Interpersonal

Skills

• Identification of components

• Understanding information

• Use information

Activity 4: “More Powers”



• Interpersonal

Skills

• Knowledge of major ideas




INTEGRAL EXPONENTS


• Solve problems using required skills or knowledge


Activity 5: Inbox Message



• Interpersonal

Skills

• Mastery of subject matter



Activity 6: Find Out


• Body/Kinaesthetic


• Interpersonal

Skills




Activity 7: Go around the Stations


• Body/Kinaesthetic


• Interpersonal

Skills



• Use methods, concepts, theories in new situations

Activity 8: Check It Out






INTEGRAL EXPONENTS


Skills

• Use information


Key Assessment Strategies• Self and Peer Assessments

• Observing students

• Trivia

• Puzzle




INTEGRAL EXPONENTS


Mind MapThe 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 LearningThe 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.

AssessmentAll 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 LearningThis 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 purposeIn this stage, students will identify the prime factors of a number. The activity will lead them to realize a more convenient way of writing repeated multiplication or very large numbers.

StrategyTHINK PAIR SHARE. This strategy allows groups to reach consensus or check understanding. This can be used in an introductory activity. This also encourages students to think about an issue, question or problem and record response. Students will discuss ideas with a partner and record what they have shared and finally, share with the whole group or join another pair to reach consensus.




INTEGRAL EXPONENTS


Materials• activity sheet (refer to Student Activity 1, “Get Intersected” on page 15)

• ruler

Activity 1: “Get Intersected”Instructions:

1. Let each student look for a partner and distribute to each pair the sheet of Student Activity 1.

2. Instruct them to answer individually the problems. After which, let them compare answers with their partner to reach consensus.

3. Assign pairs to present to the class their outputs for discussion. Refer to page 16 for the answer key.

Formative AssessmentSee to it that each pair of students are working cooperatively.

Check their outputs.

RoundupThe students would have identified prime factors of a number. It is hoped that they realized a more convenient way of writing repeated multiplication or very large number.

2. Setting the ContextThis 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 purposeStudents at this stage will identify what they already know and want to know more about the integral exponents by completing the chart.

StrategyKWL. A chart to ascertain what students KNOW about a topic, what they WANT to know and what they have LEARNED. This strategy helps the students identify prior knowledge and experience as a bridge to a new concept, lesson, or unit of work.

Materials

• KWL chart • manila paper • pentel pen

Activity 2: “Starts with...”Instructions:

1. Prior to the activity, prepare and post the chart found on page 17.

2. Organize the class into groups of 10 or as desired.

3. Let them complete the first and second columns of the KWL chart. Ask them to write their consolidated output on a manila paper to be presented to the class. The last column will be revisited in the Closure.

4. Facilitate the presentation of outputs.




INTEGRAL EXPONENTS


Formative AssessmentMonitor the involvement of all the students in the activity.

RoundupThe students would have identified what they already knew and want to know more about integral exponents by completing the chart.

3. Learning Activity SequenceThis stage provides the information about the topic and the activities for the students. Students should be encouraged to discover their own information.

Background or purposeIn this stage, the students will be able to:

• demonstrate understanding of expressions with positive, negative and zero exponents;

• evaluate numerical expressions involving integral exponents;

• rewrite algebraic expressions with zero and negative exponents; and

• solve problems involving expressions with exponents.

StrategiesINTERACTIVE 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 students by focusing their attention on key words. This emphasizes information transfer at the knowledge, recall, and comprehension levels of learning.

DECODING. A strategy used to translate data or a message from a code into the original language or form. In the context of this activity, students will perform certain expressions. After which, students will look for the corresponding answers on the choices to decode the words that will satisfy the given challenge/puzzle.

Materials

• activity sheet 3 (refer to Student Activity 3, What Power?, on page 18)

• activity sheet 4 (refer to Student Activity 4, “Lettered Number Line”, on page 24)

• activity sheets 5 (refer to Student Activity 5, “Inbox Message”, on pages 25-26)

Activity 3: “What Power?”Instructions:

1. Organize the class into groups of 5 or as desired.

2. Provide them the materials and let them perform the activity at a given time.

3. After which, ask them to compare outputs with the other groups for discussion. Refer to Teacher Resource Sheet 3 on page 19 for the answer key.

4. Conduct a brief interactive lecture for clarification of the concepts presented in the activity. Refer to Teacher Resource Sheet 4 on pages 20-.




INTEGRAL EXPONENTS


Activity 4: More PowerInstructions:

1. Organize the class into groups of 8 or as desired and distribute to them the Student Activity 4 on page 24.

2. Allow them to finish the activity with the time you set.

3. After which, let them compare outputs with the other groups to reach consensus.

4. Ask volunteers to present their outputs to the class for comparison and discussion.

Activity 5: “Inbox Message”

Pre-ActivityConduct a brief interactive discussion on Rewriting and Simplifying Algebraic Expressions with Zero and Negative Exponents. Then, let the students try to rewrite and simplify the following algebraic expressions: (Note: Assume that no denominators are zero.)

a) x-5 b) (2x)-4

c)4x7 y3

28x 9 y 3

d)75r2 s−6

5q−4 r5 s−2

e) 4a3b0(20a-5b)-1

f)212⋅518

1012

Expected solution:

a)

x−5 = 1x5

b)

(2x)-4 = 2-4 • x-4

= 124 1

x 4 = 1

16⋅ 1

x 4= 1

16x4

c)

4x7 y3

28x 9 y 3 = 428 x 7

x 9 y 3

y 3 = 1

7x−2 y 0 = 1

7 1x 21= 1

7x 2

d)

75r2 s−6

5q−4 r5 s−2 = 755 1

q−4 r2

r5 s−6

s−2 = 15q4 r−3 s−4 = 15q4

r3 s 4

e)

4a3 b0 20a−5 b−1 = 4a31 120a−5 b

= 420 a3⋅a5 1

b = 4a8

20b= a8

5b

f)

212⋅518

1012 = 212⋅518

2⋅512

= 212⋅518

212⋅512 = 212

212 518

512= 20•56 = (1)(15625)

= 15,625

From the exercise given, when do we say that an exponential expression is in the simplest form?

Exponential expressions are in simplest forms if:

• the exponents are positive,

• each base appears only once, and

• there are no powers of powers,

• all fractions are in simplest form.




INTEGRAL EXPONENTS


Activity ProperInstructions:

1. Reorganize the class into groups of 5 or as desired.

2. Distribute to them the activity sheet. Refer to Student Activity 5 on pages 25-26.

3. Let them perform the task at a sufficient time.

4. After which, ask a representative from a group to present their output for comparison and discussion. Refer to the answer key on page 27.

Formative AssessmentEnsure the involvement of all students in their group activities.

Check their outputs using the answer key provided in each task.

RoundupThe students would have:

• demonstrated understanding of expressions with positive, negative and zero exponents;

• evaluated numerical expressions involving integral exponents;

• rewritten algebraic expressions with zero and negative exponents; and

• solved problems involving expressions with exponents.

4. Check for Understanding of the Topic or SkillThis stage is for teachers to find out how much students have understood before they apply it to other learning experiences.

Background or purposeStudents at this stage will simplify expressions with integral exponents.

StrategyGAME. This strategy enables the students to learn and develop their mathematical skills in a fun and interesting way. It caters students whose comprehensions are activated using visuals. This enhances their logical/mathematical, kinesthetic and spatial intelligences.

Materials• expression strips (refer to Teacher Resource Sheet 6A on pages 29-30)

• masking tape

Activity 6: “Find Out”Instructions:

1. Prior to the activity, prepare the expression strips and table of answers on page 31).

2. Organize the class into 4 groups and distribute the materials.

3. Explain to them the mechanics of the game.

a) Each group will be given 1 set of expression strips.




INTEGRAL EXPONENTS


b) Form 4 words out of the strips containing letters and algebraic expressions involving integral exponents.

a) Simplify each given expression. Then, look for the answer on the board and paste its corresponding strip below it.

b) The game starts upon the GO-signal of the teacher and when all the groups are ready.

c) The score depends on your rank in completing the activity (first, second, third, or fourth).

4. Set a time allotment for the activity. Refer to page 31 for the answers.

Formative AssessmentRoam around to ensure the active participation of all the students in the activity.

RoundupThe students should have simplified expressions with integral exponents.

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

Background or purposeStudents' learning on the integral exponents will be applied in solving problems involving real-life situations.

StrategyLEARNING STATIONS. This strategy allows each group to perform the task in each station. The teacher needs to post the tasks in 4 different stations or distinct parts of the classroom. Each group will move from one station to another in any order.

Material

• station cards (refer to Teacher Resource Sheet 7 on page 32-34)

Activity 7: “Go Around the Stations”Instructions:

1. Prior to the activity, prepare the station cards. Arrange each set in a designated corner of the classroom.

2. Organize the class into 8 groups. Assign each group to a specific station.

3. Then, let them move to another station until they have visited all the stations. Set a time allotment for them to perform each task.

4. After which, ask volunteers to present their outputs for comparison and discussion.

Formative AssessmentSee to it that all students are actively involved in the group activity.

Check their outputs. You may refer to the answer key on page 35.




INTEGRAL EXPONENTS


RoundupStudents would have applied their learning on integral exponents in solving problems involving real-life situations.

6. ClosureThis 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 purposeIn this stage, students will consolidate their learning on integral exponents.

StrategyKWL. A chart to ascertain what students KNOW about a topic, what they WANT to know and what they have LEARNED. This strategy helps students identify prior knowledge and experience as a bridge to a new concept, lesson, or unit of work and record as well their learning.

Material

• activity sheet (refer to Student Activity 8 on page 36)

Activity 8: “Check It Out”Instructions:

1. Use the same grouping as in Activity 2.

2. Distribute the activity sheets and let them complete it at a set time.

3. After which, collect and consolidate their outputs.

Formative AssessmentSee to it that all students are working collaboratively in their group.

RoundupThe students would have consolidated their learning on integral exponents.

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.

2.

3.




INTEGRAL EXPONENTS


STUDENT ACTIVITY 1Get Intersected

Directions:

1. Match each number in the first column to its equivalent prime factors in the last column of the table below by connecting them with a straight line.

2. Write each intersected letter below the corresponding number to reveal the word.

ITEM 8 12 25 27 32 90 100 180 324 468

LETTER


8

12

25

27

32

90

100

180

324

468

(5)(5)

(2)(2)(2)(2)(2)

(2)(2)(3)

(2)(2)(3)(3)(5)

(2)(2)(2)

(2)(2)(3)(3)(13)

(2)(3)(3)(5)

(3)(3)(3)

(2)(2)(3)(3)(3)(3)

(2)(2)(5)(5)

P

X

AN E

O

E

S

T

N

L

C



INTEGRAL EXPONENTS


Teacher Resource Sheet 1Get Intersected – Answer Key

ITEM 8 12 25 27 32 90 100 180 324 468

LETTER E X P O N E N T S


P

X

N E

TO

E

N

S

A

L

C8

12

25

27

32

90

100

180

324

468

(5)(5)

(2)(2)(2)(2)(2)

(2)(2)(3)

(2)(2)(3)(3)(5)

(2)(2)(2)

(2)(2)(3)(3)(13)

(2)(3)(3)(5)

(3)(3)(3)

(2)(2)(3)(3)(3)(3)

(2)(2)(5)(5)



INTEGRAL EXPONENTS


Teacher Resource Sheet 2KWL Chart

Directions: Enlarge this chart on a manila paper.

Topic What you KNOW WANT to know Have LEARNED

Positive Integral Exponents

Negative Integral Exponents

Zero Exponent

Solve problems involving

expressions with exponents




INTEGRAL EXPONENTS


STUDENT ACTIVITY 3What Power?

Objective: Define exponential expression.

Directions:

1. Fold the paper according to the number of times indicated in the table.

2. Determine the number of regions formed in each fold and express it as a product of its prime factors. Record the results in the second and third rows respectively.

3. Then, write the factors in exponential form to complete the table.

Number of Folds 1 2 3 4 5

Number of Regions

● Prime Factors

● Exponential form

4. Write an exponential expression that describes the number of regions formed when the paper is folded n times. Then, name/label and describe its parts.

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

5. How many region/s is/are formed when the paper is NOT folded? Express this in exponential form based on the pattern observed in the table.

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

6. What conclusion can you make when the exponent of a number is zero. ______________________________________________________________________________________________________________________________________________________________________________________________________




INTEGRAL EXPONENTS


Teacher Resource Sheet 3What Power?Answer Key

Number of Folds 1 2 3 4 5

Number of Regions 2 4 8 16 32

● Prime Factors 2 (2)(2) (2)(2)(2) (2)(2)(2)(2) (2)(2)(2)(2)(2)

● Exponential form 21 22 23 24 25

4. Write an exponential expression that describes the number of regions formed when the paper is folded n times. Then, name and describe its parts.

2 n , where 2 is the base and n is the exponent.

5. How many regions are formed when the paper is NOT folded? Express this in exponential form based on the pattern observed in the table.

There is only 1 region when the paper is not folded. This can be expressed in exponential form as 1 0 , where 1 is the base and 0 is the exponent.

6. What conclusion can you make when the exponent of a number is zero?

When the exponent is 0, the expression is equal to 1.




INTEGRAL EXPONENTS


Teacher Resource Sheet 4Interactive Lecture

(Positive Integral Exponent)In the paper-folding activity, we learned that for any positive integer n and real number a,

where a is called the base and n is the exponent of a, and n is any positive integer. The exponent indicates the number of times the base is taken as a factor. an is read as “a to the nth power” or simply “a raised to n”. The expression an is also referred to as an exponential expression.

Let the students recall the laws of exponent by simplifying the following expressions:

53 (-2)4 -82 34

5

Expected answer:

53 = (5)(5)(5) = 125

(-2)4 = (-2)(-2)(-2)(-2) = 16

-82 = -(8)(8) = -64

34

5

= 34 3

4 34 34 3

4 = 2431024

Again, by applying the laws of exponents, let them simplify the following expressions:

1. (a3b4)(a2b2) 4. (-2p•2q3)3

2. (c5)2

3. c4 d 6

c2 d

5. 7x3

9y 2 3

Solutions:

1. (a3b4)(a2b2) = (a3•a2)(b4•b2)

= a3 + 2b4 + 2

= a5b6

2. (c5)2 = c5(2) = c10

3.c4 d 6

c2 d= c4 – 2 • d6 – 1

= c2d5, where c ≠ 0 and d ≠ 0


an = a•a•a•...a

n factors

When multiplying like bases, we add their exponents.( The Product Rule for Exponents)

When we raise a base to two exponents, we multiply those exponents together.( The Power Rule for Exponents)

When dividing like bases, we subtract their exponents.( The Quotient Rule for Exponents)

CALCULATOR TIP When using a scientific or graphing calculator, there are multiple ways to evaluate exponents. To square a number, or raise it to a power of 2, use the button. To evaluate exponents other than 2, use the power key which looks likey x or x y

x 2

For example to calculate the value of press the key sequence

53

y x5 3The answer is 125. If your particular calculator has the button

^34

to raise a number to an exponent, use it in the same manner. For example, would be entered

4^3The result is 81.



INTEGRAL EXPONENTS


4. (-2p•2q3)3 = (-2)3p3 • 23q3(3)

= (-8p3)(8q9)

= -64p3q9

5. 7x 3

9y 2 3

= 733x 33

93y23= 343x9

729y6

Post the following problem on the board and let the students perform it by pair.

a. 103•102 b. (32)3 c. 1112

1110 d. (2x3)4 e. 3x7

x 3 2

Solution:

103•102 = 105 = 100 000 (32)3 = 36 = 7291112

1110 = 112 = 121 (2x3)4 = 24x12 = 16x12 3x7

x 3 2

= 9x8

(Zero and Negative Exponents)You have learned the Law of Exponents for division of powers to the same base. It is said

that when m > n, mn, xm

xn = xm−n . We will apply this law when m = n.


REMEMBERam •an = amn1. Product of two powers

amn = amn2. Power of a power

3. aman

= Quotient of two powersam−n , if mn

1, if m=n1a n−m

, if mn

ab m

= am

bm, b≠05. Power of a quotient

4. a• bm = ambm Power of a product

Let a and b be any real numbers and m and n be any positive integers.

When we have a PRODUCT raised to an exponent, we can simplify by raising each base in the product to that exponent.( The Power of a Product Rule)

When we have a QUOTIENT raised to an exponent, we can simplify by raising each base in the numerator and denominator of the quotient to that exponent.( The Power of a Quotient Rule)



INTEGRAL EXPONENTS


Simplify 35

35 and27

27 .

Solution:

35

35 = 35−5 = 30 and 27

27 = 27−7 = 20

You also learned that any number (other than zero) divided by itself is one. Thus,35

35 = 1 and27

27 = 1.

From the illustrative examples, what can you conclude about the definition of zero exponent?

From the above, we can see that it is reasonable to conclude that 30 = 1 and 20 = 1. These examples suggest a definition for zero exponents.

Let the students simplify the following on the board and the other on their seats.

50 22 9

(5 - 2)0 (x + 3)0 2x2 3x − 4

0

Solution:

50 = 1 22 9

= 1 (5 – 2)0 = 1 (x + 3)0 = 1 2x2 3x − 4

0

= 1

In addition to the law of exponents stated above for m > n, you learned that when m < n,

mn, xm

xn = 1x n−m . We will apply these two laws for division of exponents.

Applying the two laws for the expressions42

45 and37

39 .

Solution:

mn, xm

xn = xm−n mn, xm

xn = 1x n−m

42

45 = 42−5 = 4−3 42

45 =1

45−2 =143


If x is any nonzero number, then

Remember

x0 = 1.

THINK ABOUT THISWhat happens when the exponent of the numerator is less than the exponent of the denominator?



INTEGRAL EXPONENTS


37

39 = 37−9 = 3−2 37

39 = 139−7 =

132

From the illustrative examples, what can you conclude?

We can see from the examples that 4−3 = 143 and 3−2 = 1

32. This leads to the definition

of negative exponents.

Let the students do on the these expressions: (2)-1, (-3)-2, and -5-2

Solution:

2−1 = 12

−3−2 = 1−32

= 19

−5−2 =− 152

=− 125

From the definition and the examples given, we can say that x-n is the reciprocal of xn.

Try this another example, 23 −2

.

Solution: 23 −2

= 1

23

2= 1÷ 2

3 2

= 1÷ 49= 1 x 9

4= 3

22


If x is any nonzero number, then

Remember

x−n =1x n

.



INTEGRAL EXPONENTS: MODULE 9: WITH POWERS

STUDENT ACTIVITY 4Task A: Lettered Number Line

Objective: Evaluate numerical expressions involving integral exponents.

Directions:

1. Evaluate each numerical expression in the first row of the table below.

20

−2−3

23 31•3−118

117 105

2 −3−2

36−1 90 17−1 −2 20

3 0

422

3

93

81− 604

−9−55⋅29

54⋅28 (1-4)(-6) −52

511− 102

5 −5−1−45

70+(6-1•

24)−62

6

2. Write the letter of the expression inside the box that corresponds to your answer to reveal the message.


E R A H L N B W H A T A F U V I G E

!

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10




STUDENT ACTIVITY 5Inbox Message

Objective: Rewrite and simplify algebraic expressions with zero and negative exponents.

Task: A message is hidden in the answer box. Follow the steps to decode it.

Step 1. Simplify each expression in the Question Box.

Step 2. Match your answer with those found in the Answer Box.

Step 3. Take note of the word/mark above each expression. Write this in the appropriate space

below its corresponding answer in the Answer Box.

Question Box

TO NOT PERSON PRAY FOR

(-2)0 (8)2(3)0 (2-3)2 (x-5)-4 (-3x2y-1)-4

; AN A BE STRONG

(3y-3)-2 x2 y4

3z −3

2x3 y2

5z4 −1

(28)(2-7)(20)20 2−3

2−1 22

PRAY EASY INSTEAD • LIFE

33 3−2

3−4 − 30−4x2 y0

2xy 22x3 y23

3xy 2x y 0x y 2

x y −3x4y−3

x−3y7 3





Answer Box

−54920

64y4

81x827 z3

x6 y12

14 x2 y2

−27 x21

y30y6

989

x7 y4 x20 1

2 5z4

2x3 y2 14

164

x + y





Teacher Resource Sheet 5Inbox Message - Answer Key

Answer Box

−54920 64 y4

81x827 z3

x6 y12

14 x2 y2

PRAY NOT FOR AN EASY

−27 x21

y30y6

989

x7 y4 x20 1

LIFE ; INSTEAD PRAY TO

2 5z4

2x3 y 2 14

164 x + y

BE A STRONG PERSON •

You may check their solution using the following:

(-2)0 = 1 2x3y2

5z4 −1

= 5z4

2x3y 2(8)2(3)0 = 82•1 = 64 (28)(2-7)(20) = 28 1

27 1= 256 1128 1= 256

128 = 2

(2-3)2 = (2-3)2 = 2-3(2) = 2-6 =126 = 1

6420 2−3

2−1 22 =1 1

23

12 22

=

23 123

1 2 22 2

=

9892

= 98⋅ 2

9= 1

4





(x-5)-4 = (x-5)-4 = x-5(-4) = x20 33 3−2

3−4 − 30 =33 1

32

134 − 1

=27 1

9181

− 1=

2449

−8081

= 2449 −81

80= 54920

(-3x2y-1)-4 = (-3)-4(x2)-4(y-1)-4 = 1−34 1

x8y4 = 181

⋅ 1x8⋅y4 = y4

81x8

−4x2 y 0

2xy2=

122 x 2 y 2 =

14 x 2 y 2

3-2y-3(-2) =132 y6 = y 6

32 = y6

9x y 0 x y 2

x y = 1(x + y)2-1 = (x + y)1 = x + y

x 2 y 4

3z −3

= x 2 y 4−3

3z−3= 3z3

x2 y 43= 33 z3

x 6 y 12= 27 z3

x 6 y12

−33 x 43 y−3 3

x−33 y73= −33 x12 y−9

x−9 y 21= −33 x 21

y 30= −27x 21

y 30





Teacher Resource Sheet 6A: Expression StripsDirections: Reproduce 4 copies of these (2) sheets and cut each strip.


x32 I N

2x23

R

23

4

E

3x2 y44y5 x3

R

35

0

T

−52

E

−4x2−4x2

G

−35

E

−52•65

5 •64

P

x12 x10x5

O

x6 • x3

W

2x4 y5xy

2

4x 3 y5

x3 y2 4

E

427 − 40

X

33x0 y0

P

8 • −30




s


X

4x−2 y3

16x−6 y−5

P

−33−−32−22

O

25x6 y 15x3 y0−2

N

−2−1 2

E

12

−3

N

−5x−3 y0−1

T

x4

x0

R

−46x2 y30

E

304022

S

−5−2

S

2−3

I

5x−7

O

x−11 • x9

N

x−2

x−7x−3

x−7

E

13−1

12−1




Teacher Resource Sheet 6B: Table of AnswersCopy this table of answers on the board.

x6 8x6 -25 -64x4 -243 -30 1681

x17 x9 1024x6 y12

25 12x5y9 1

16 34 -8 -1 4

125

18

5x7

1x2 x5 + x4

5 x4 y8

4 -32 y 32 8 − x

3

5 x4

Expected answers:

x6 8x6 -25 -64x4 -243 -30 1681 x17 x9 1024x6 y12

25 12x5y9 1 16 34 -8 -1 4

125

18

5x7

1x2 x5 + x4 5 x4 y8

4 -32 y 32 8 − x

3

5 x4

I N T E G E R P O W E R E X P R E S S I O N E X P O N E N T




INTEGRAL EXPONENTS


Teacher Resource Sheet 7: Station CardsDirections: Reproduce two copies of each card and cut.


If the area of a rectangular garden is and its width is , what is the measure of its length?

STATION

1

2y216y8

The sun has a mass of about 2 000 000 000 000 000 000 000 000 000 000 kilograms. The Earth has a mass of about 5 980 000 000 000 000 000 000 000 kilograms. How many times heavier is the sun than the Earth?

STATION

2



INTEGRAL EXPONENTS



Allan Jay will celebrate his birthday on September 12. As a gift, he can choose one of the following options:

STATION

3

His parents will give him Php 7,000.00 on September 12.OPTION 1

His parents will give him Php 2.00 starting September 1. After each day, they will double the amount given until September 12.

OPTION 2

If you are Allan Jay, which of the options you will choose? Support your answer.



INTEGRAL EXPONENTS


n


The price of a bike is Php 2,500.00 now and it increases at a rate of 5% per year. What will be the cost of the bike in 4 years?

Hint: We can mathematically model this problem by using the following:

where = initial amount at time t=0 r = rate (as a decimal) t = time A = amount after the time t

STATION

4

A = A0 1 r t

A 0



INTEGRAL EXPONENTS


Teacher Resource Sheet 8Go Around the Stations – Answer Key

Station 1.

Solution:

Given: A = 16y8

w = 2y2

A = lw

16y8 = l(2y2)

= 162 y

8

y 2 = 8y6 = l

Therefore, the measure of the length of the rectangular garden is 8y6.

Station 2.

Solution:

Write both quantities in scientific notation since the numbers are very large.

Given: 2 x 1030 = mass of the sun

5.98 x 1024 = mass of the Earth

Divide the mass of the sun by the mass of the Earth.

2 x 1030

5.98 x 1024 = 25.981030

1024 1

2.99• 106 = 334 448.16

Thus, the sun is about 334 448 times heavier than the Earth.

Station 3.

Solution:

Option 1. Allan Jay will receive Php 7,000.00 on September 12.

Option 2. Allan Jay will receive a total of Php.8,190.00 on September 12.

Accounts

Sept. 1

21

Sept. 2

22

Sept. 3

23

Sept. 4

24

Sept. 5

25

Sept. 6

26

Sept. 7

27

Sept. 8

28

Sept. 9

29

Sept.10

210

Sept.11

211

Sept.12

212

Therefore, if I were Allan Jay, I will choose option 2 so that I can receive Php 8,190.00.

Station 4.

Solution:

Given: A0 = 2,500

r = 5% = 0.05

t = 4

Using the formula A = A0(1 + r)t,

we have, A = 2,500(1 + 0.05)4

= 2,500(1.05)4

= (2,500)(1.2155063)

= 3,038.7656 or 3,039 (rounded to the nearest whole number)

Therefore, the bike will cost Php 3,039.00 in 4 years.


16y 8 l(2y 2)2y2 2y2

=




STUDENT ACTIVITY 8 - Check It OutDirections: Complete the table below. In line with each topic, write U if you understood it well, NM if you need more explanation, or NU if you did not understand at all.

Group #:_______

TOPICS

GROUP MEMBERS

Expressions with:

• positive exponents

• zero exponents

• negative exponents

Evaluating numerical expressions involving integral exponents.

Rewriting algebraic expressions with zero and negative exponents.

Solving problems involving expressions with exponents.





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

Total time for the Learning Guide Total number of lessons needed for this Learning Guide


Documents

BEAM Learning Guide - DepEd Manilamgaraullo.depedmanila.com/wp-content/uploads/2019/... · MODULE 9: WITH POWERS Information about this Learning Guide Recommended number of lessons