Learning Plan - Integers

8/17/2019 Learning Plan - Integers

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LEARNING PLAN IN MATHEMATICS 7

Prepared by:

Awao, Orpha

Co, William Mhae

Donguiz, May Joy

Malaggay, Febie

Quarter: 1st Grading Topic: Integers Time Frame: 12 days (50minutes per session)

STAGE 1 – DESIRED RESULTS

Established Goal (s)

At the end of the lesson, the learners should be able to:

A.

demonstrates understanding of key concepts of sets and the real number system;

B.

solve word problems involving fundamental operations and properties of integers; C. visualize integer and their order on a number line; and

D. formulate challenging situations involving sets and real numbers and solve these in a

variety of strategies.

Content standard:

demonstrates understanding of keyconcepts of sets and the real numbersystem.

Performance Standard:

is able to formulate challenging situationsinvolving sets and real numbers and solvethese in a variety of strategies.

Essential Understanding (s):

Students will understand that…

Integers involve two concepts: size(magnitude) and sign (direction;

Integers are used to describe relativechanges between two or more items;

and

Integers are used to represent values liketemperatures, altitudes, stock price

changes, etc.

Essential Question (s):

1. How positive signs and negative signs

affect our daily life?

Students will know:

The representation of every integer in thenumber line;

The different properties of operation onthe set of integers;

The key concepts of integers; and

The representation of absolute value onthe number line as a distance of anumber from 0

Students will be able to:

Perform fundamental operations onintegers;

Illustrate the different properties ofoperations on the set of integers; and

Formulate challenging situations involving

integers and solve these in a variety ofstrategies.


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a. Angel Alden is floating on a cloud at zero. One balloonsupports one weight. If we gave him 100 balloons and 100

weights, what would happen to him? Explain why.

b. Now that Angel Alden has 100 balloons and 100

weights, let's make him move. We want him to go up 4

spaces but we do not have any balloons to give him.

How can we still make him move up 4 spaces?

STAGE 2 – ASSESSMENT EVIDENCE

Product or

Performance Task (s)

Business plan(Financial plan)

(see attachment)

Evidence at the Level of Understanding

Learners should be able to demonstrateunderstanding using in- depth discussionsin...

1. Explanation

Why is associative and commutativeproperties not applicable to all realworld and mathematicaloperations?

2. Interpretation

Can you interpret absolute value in

the context of distance using

thermometer?3. Application

How and when can we use integers

in our everyday life?4. Perspective

Does the properties of fundamentaloperations really make it easier for usto solve real life problems thatinvolve integers? Why and how?

5. Empathy

What would it be like to walk in abusinessman’s shoes having manydebts due to mismanagement of hisbusiness?

6. Self-knowledge What are your blind-spots inperforming the fundamental

operation of integers?

Evidence at the Level of

Performance

Goal: To recruitbusinessmen to invest in

the business proposed.

Role: Businessman

Audience: Businessmen

and entrepreneurs

Situation: The company

needs more investors

Performance: Business

plan presentation

Standard: Seeattachment

STAGE 3 – LEARNING PLAN

Teaching/Learning Sequence

A. EXPLORE

1. Preliminary Assessment: Assess the knowledge of the students about the next lessons by

giving challenging problems.


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Additional questions:

TAKING AWAY BALLOONS makesAngel Alden move_______.

TAKING AWAY WEIGHTS makes Angel Alden move _______.

Expected answer:

2. Motivation:

a. Group the students into two. Each group must have three presenters (actor/actresses).

b. Presenters will act the word given to them regarding the picture posted in the board.

c. Each group must guess the word with the help of the pictures and their presenters and

write it in a one fourth sheet of pad paper. The group will have one minute of guessing.

1 2 3 4 5

Expected answer:1.

thermometer

2.

speed3. weight4.

zero

5.

sign

3. Pose the following questions to the student:

a. What is the opposite of the opposite of a number?b. How are opposites and absolute value similar and different?

c. How can you recognize integers and their opposites with or without number line?

4. Ask the students if they have any questions to be clarified about the topic.

Example Misconceptions:

c. Again, Angel Alden is at zero with 100 balloons and 100

weights. If you want to make him drop down 28 steps but

do not have any weights to give him, how can you still

get the end result of 28 down?

a. Angel Alden will move upwards. When we gave him 100 balloons

and 100 weights, 100 added to 100 will be equal to 200 so he will move

200 ste s oin u .

a. When adding or subtracting integers these students ignore the signs,

carry out the operation, then decide on the sign of the answer.

b.

Zero is positive or zero is negative.


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5. Pose the following websites and let the students search and read the content of the given

websites:a. www.mathsdoctor.co.uk

b. www.mathgoodies.com c. www.mathguide.com

6. Ask the students the focus question: How do positive signs and negative signs affect our

daily life? Let them think and reflect for 2 minutes and ask for volunteers to share theirinsights.

7. Discuss to the students that at the end of the lesson they must be able to come up with a

business plan focused in the creation of the financial statement of the business that willapply all the concepts about integer that will be tackled. Tell them that they will present the

business plan that they created in a particular situation. The rubric will be provided.

B. FIRM – UP

1. Give the activity provided below to assess the student’s prior knowledge.

Directions: Answer the following items

using the mathematical operations.

1. Divide : 2448 by 68

2. Find the value of the expression:168 -

198 + ( -145 ) + 73 + ( -81 ) - ( -187 ) - ( -

172 )

3. I7I - I3I=______

4. I-8I + I6I=______

5. Find the predecessor of each of thefollowing integers:

a) -31 = ______b) -13 = ______c) -41 = ______

6. Find the sum of the following integers:a) -95901 and -21481 =_______b) -75792 and 89373 =_______

c) 66572 and 47566 =_______

7. While doing the science experiment

in the physics lab, Wilma had to take 5

measurements of the temperature and

write the average of those as an

answer. If the measurements of the

temperature are 2, 1, -3, 1, -2, what is

the final answer of her experiment?

8. An integer is divided by 7 giving a

remainder of 6. The resulting quotient

when divided by 4 gives a remainder of

2. The resulting quotient is then dividedby 8 giving a quotient of 1 and a

remainder of 2. What will the finale

remainder be if the order of the divisors

is reversed?

9. Find how many integers are therebetween:

a) -5 and 2b) -2 and 3

10. Rizza is in the process of making ice

cream. She has heated all the

ingredients to 50 °C and put them in

refrigerator to freeze. If the cooling rate

is 9 °C per hour, what will be the

temperature in freezer after 9 hours?

http://www.mathsdoctor.co.uk/http://www.mathsdoctor.co.uk/http://www.mathsdoctor.co.uk/http://www.mathgoodies.com/http://www.mathgoodies.com/http://www.mathgoodies.com/http://www.mathguide.com/http://www.mathguide.com/http://www.mathguide.com/http://www.mathgoodies.com/http://www.mathsdoctor.co.uk/


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Expected Answer:

2. a. Discuss opposites by asking the students to give examples. Use student’s responses tocome up with a definition of the opposite of a number.

b. Create cards with opposite integers written on them. Distribute these cards to the

students and have them locate and sit with their opposite, in zero pairs.c. Have students create a line, label it by the use of the cards given to them. Each

student must place his/her card on the line in its correct position and say the opposite

of the number that they got.d. After they have created the number line, present the following question and ask for

volunteer to answer it.

Expected answer:

e. Discuss to the students the Important Terms to Remember and Notations and Symbols

1) 36 6) a. -117382 10) -31°C2) 176 b. 13581

3) 4 c. 1141384) 14 7) -0.2

5) a. -32 8) 2

b. - 14 9) a. 6c. - 42 b. 4

1. Absolute Value – of a number is the distance between that number and zero onthe number line.

2. Number Line –is best described as a straight line which is extended in bothdirections as illustrated by arrowheads. A number line consists of three elements:

a. set of positive numbers, and is located to the right of zero;

b. set of negative numbers, and is located to the left of zero; andc. Zero.

*The absolute value of a number is denoted by two bars ││.

1. What does it mean for the same distance travelled but in opposite directions?

2. What can you say about the distance of opposite numbers say -5 and +5?3. How can we represent the distance of a number? What notation can we use?

1.

We can represent the distance by using the absolute value sign.2.

The distance are the same even though they have different sign.


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f. Give the student a short activity.

Expected answer:.

3. Pose the following questions to the students and let them share it in class.

4. Remind to the students of the business plan focused in the creation of its financial planthat they will be going to do and present in the class.

1.

Can you interpret absolute value in the context of distance using thermometer?2. Is it possible to remove any negative sign in front of a number, and to think of all

numbers as positive or zero in doing absolute value?

Activity 1

On the space provided before each item, write your answer that correspondsto what is being described.

_ _______1.) Jason’s spent way too much money and is now in the hole $50. ________2.) Tammy received her allowance of $10.00.

________3.) Jimbo went to the beach on a bright and sunny day. Thetemperature was 80 degrees outside.

________4.) Stan owes his brother $50.00. ________5.) Put the following temperatures in order from coldest to hottest.

1. – 50 5.2. +103. +80

4. - 50


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SUBTRACTIONRule in Subtracting Integers:

In subtracting integers, add the

negative of the subtrahend to the minuend,Subtract integers by reversing the

process of addition, and by convertingsubtraction to addition using the negative of

ADDITIONIf the integers have the same sign, just

add the positive equivalents of the integersand attach the common sign to the result.

If the integers have different signs, getthe difference of the positive equivalents ofthe integers and attach the sign of the larger

number to the result.

MULTIPLICATION

Rules in Multiplying Integers:In multiplying integers, find the product oftheir positive equivalents.

1. If the integers have the same signs, theirproduct is positive.

2. If the integers have different signs, theirproduct is negative.

1. the magnitude of a real number without regardto its sign.

2. used to represent integers3. a negative integer –n to m means moving

along the the real line a distance of n units tothe left from m.4. a representation of the absolute value

5. to separate into equal parts6. the set of whole numbers and their opposites

7. Whole numbers less than zero8. repeated addition9. addition, subtraction, multiplication, and

division10. 3 and -3

11. Whole numbers greater than zero12. either positive (+) or negative (-), except zero

5. By the terminologies discussed in the lesson, give the following activity:

6. a. Discuss to the students the concepts of operations in integers and its properties.b. Generalize the lesson about the concepts of operations in integers and its properties.

DIVISIONThe quotient of two integers with the

same signs is a positive integer, and thequotient of two integers having unlike signs isa negative integer. However, division by zero

is not possible.Division is the reverse operation ofmultiplication. Using this definition, it is easy to

see that the quotient of two integers with thesame signs is a positive integer, and the

quotient of two integers having unlike signs is

a negative integer.

Expected Answer:

1) ABSOLUTE 5) DIVIDE 9) OPERATION

2) NUMBER LINE 6) INTEGER 10) OPPOSITE3)

ADD 7) NEGATIVE 11) POSITIVE4)

DISTANCE 8) MULTIPLY 12) SIGN


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c. Let the students do activity 1 to check their understanding.

Important Terms to Remember

The following are terms that you mustremember from this point on.

1. Closure PropertyTwo integers that are added andmultiplied remain as integers. The set of

integers is closed under addition andmultiplication.

2. Commutative PropertyChanging the order of two numbers that

are either added or multiplied does notchange the value.

3. Associative PropertyChanging the grouping of numbers that

are either added or multiplied does notchange its value.

4. Distributive PropertyWhen two numbers are added /

subtracted and then multiplied by afactor, the result is the same when eachnumber is multiplied by the factor and

the products are then added /subtracted.

5. Identity PropertyAdditive Identity

- states that the sum of any number and

0 is the given number. Zero, “0” is theadditive identity.

Multiplicative Identity- states that the product of any number

and 1 is the given number, a • 1 = a. One, “1” is the multiplicative

identity.

6. Inverse Property

In Addition

- states that the sum of any number andits additive inverse, is zero.

The additive inverse of the number a is –a.In Multiplication

- states that the product of any numberand its multiplicative inverse or

reciprocal, is 1. The multiplicative inverseof the number a is 1/a.

Activity 1

I. Direction: Determine what kind of property of real numbers is illustrated in the

following images and fill in the blanks with the correct symbols

1. 2.


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Expected answer:

1. Commutative Property of Addition: a + b = b + a

2. Associative Property of Addition : (a + b) + c = a + (b + c)

3.

Distributive Property: a(b + c) = ab + ac

4. Identity Property for Addition: a + 0 = a

5. a. 14 cabbages

b. (+14) + (-14) = 0

c. Inverse Property for Addition

a + (-a) = 0

3. 4.

5. Guide Questions:

a. How many cabbages are there in the crate?

b. Using integers, represent “put in 14 cabbages”and “remove 14 cabbages”? What will be theresult if you add these representations?

c. Based on the previous activity, what property isapplied in the images presented?

II. Direction: Answer the following by using any graphic organizer and in 3-5

sentences explain the concept of your graphic organizer.

*Rubic: Content= 10 points

Neatness and Grammar= 5 pointsCreativity= 5 points

1. Why are associative and commutative properties not applicable to all real worldand mathematical operations?

2. How and when can we use integers in our everyday life?


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Going Down

In general, negative integers represent decreasing or downwards movement, orto the left (in relation to the number line). If we are describing a car slowing downfor a stop sign, its acceleration is represented with a negative value because its

speed is decreasing. If you were digging a hole, your depth could berepresented using negative integers.

The Thermometer

A common example of negative integer usage is the

thermometer. Thermometers are similar to number lines, but vertical. They havepositive integers above zero and negative integers below zero. Commonly,

people recognize a temperature of -25°C as cold. People use this number systemto measure and represent the temperature of the air. Also, if it -23°C outside, and

the temperature drops 3 degrees, what is temperature now? -26°C. If we picturethe thermometer, we know that as the temperature drops, we look downwards onthe thermometer.

Altitude

Geographically, we represent sea level with integers. Obviously, below sea level is

represented with negative integers. For example, Death Valley (pictured below)

in California is located at 86 m below sea level. This can be representednumerically as –86 m. Antarctica is 2,538 m below sea level(-2,538). When geography specialists study the difference between say the top ofMount Everest in Tibet, which is 8,848 m above sea level, and the bottom of the

Dead Sea (409 m below sea level), they use negative representations of integers.

d. Discuss to the students some applications of integers and their properties and operations.

7. a. Talk over with the students the problems in financial statements and taxes in business

and economic issues. And explain to them that integers are applicable to a proposal ofbusiness to the international companies that would like to invest in the Philippines bycoming up with a financial plan that is reliable and accurate. Integrate integers in the

context of money and temperature.b. Pose a question to the students. Let them write it on a one half sheet of pad paper. Pick

randomly at the paper of the students and let the owner of the paper read his/her

answer in the class.

8. a. Let the students search on the following websites in preparation to the activity that theywill be given to them.

a. www.mathmovesu.com/integers

b. http://goeurope.about.com/library/bl-europe-distance-maps.htm

b. Give the Activity Amazing Math Race to the students to check the progress of the

students about the lesson.

Does the properties of fundamental operations really make it easier for us tosolve real life roblems that involve inte ers? Wh and how?

http://www.mathmovesu.com/http://www.mathmovesu.com/http://goeurope.about.com/library/bl-europe-distance-maps.htmhttp://goeurope.about.com/library/bl-europe-distance-maps.htmhttp://goeurope.about.com/library/bl-europe-distance-maps.htmhttp://www.mathmovesu.com/


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Expected Answers:

9. Convey the students to reflect about the lesson for 1-3 minutes. After the given time, pose

the following question.a. What would it be like to walk in a businessman’s shoes having many debts due to

mismanagement of his business?b. What are your blind-spots in performing the fundamental operation of integers?

10. Let the student have a recitation to check for their understanding and provide themimmediately the feedback that they must know.

a. Trip Distance travelled (in kilometres)1. London to Paris 414 km

2. Paris to Hamburg 880 km3. Hamburg to Berlin 291 km

4. Berlin to Munich 604 km5. Munich to Rome 969 km6. Rome to Madrid 2099 km

b. 1. -190 2. -80 3. -1164 4. -176

Activity 1: Amazing Math Race!

a.

You and your team will be travelling around the world, gathering data you will

need to win the competition. You will be visiting Europe to gather data for

your group. You have been asked to keep track of the distances between the

cities you visit. Please use http://goeurope.about.com/library/bl-europe-

distance-maps.htm to find the distance of each trip

Trip Distance travelled (in kilometres)

1. London to Paris 2. Paris to Hamburg 3. Hamburg to Berlin

4. Berlin to Munich 5. Munich to Rome

6. Rome to Madrid

b. Use the above data to solve the following questions. For each one, write out theequation needed and the solution to the equation.

1. What is the difference between the distance from London to Paris and the

distance from Berlin to Munich?

2. What is half of the difference found in #1?

3. You need to take four trips the length of Hamburg to Berlin off of your itinerary.

4. You need to take away a trip a fifth the length of your trip from Paris to Hamburg.


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C. REFLECT AND UNDERSTAND / DEEPEN

1. Enrich the student’s understanding by providing additional activity and reading.

Expected Answer:

Additional Readings:

www.purplemath.com/in-te-gers

2. Raise again the focus question to the class. Give them two minutes to reflect and let them

share their answer to the class.

“How positive signs and negative signs affect our daily life?”

EXAMPLE QUESTIONS:

When you add two negative integers, you always get a negative sum.

When you subtract two negative integers, do you always get a negative

difference? Explain with the aid of examples.

a. Complete the table.

Given Property

1. 0 + (-3) = -3

2. 2(3 - 5) = Distributive Property

3. (- 6) + (-7) = Commutative Property

4. 1 x (-9) = -9 5. -4 x -1/4 = 1

6. 2 x (3 x 7) = (2 x 3) x 7

7. 10 + (-10) = Additive Inverse Property

8. 2(5) = 5(2)

9. 1 x (1/4 ) = ¼

10. (-3)(4 + 9) = (-3)(4) + (-3)(9)

Given Property1. 0 + (-3) = -3 Additive Identity Property

2. 2(3 - 5) = Distributive Property

3. (- 6) + (-7) = Commutative Property

4. 1 x (-9) = -9 Multiplicative Identity Property

5. -4 x -1/4 = 1 Multiplicative Inverse Property

6. 2 x (3 x 7) = (2 x 3) x 7 Associative Property

7. 10 + (-10) = Additive Inverse Property

8. 2(5) = 5(2) Commutative Property

9. 1 x (1/4 ) = ¼ Multiplicative Identity Property10. (-3)(4 + 9) = (-3)(4) + (-3)(9) Distributive Property

http://www.purplemath.com/in-te-gershttp://www.purplemath.com/in-te-gershttp://www.purplemath.com/in-te-gers


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3. Let the students do the activities to measure the student’s essential understanding.

Activity 1: Extended Constructed Response-

Use the following table of golf scores to answer the

following questions

Part AWhat is the mean golf score? ___________

Part B

Use what you know about finding mean and

performing operations on integers to justify

why your answer is correct. What if another

golfer’s score (who shot a 6) was added to

the table? Explain how this would change

the mean score.

Expected Answers:

Part A: -5

Part B:You take the total

score, which is –50and divide that by thenumber of players,

which is 10 to get –5.

Adding 6 to the

previous total of –50

would give us a newtotal of –44, whichwould be divided by

11, since you added

another golfer, to get

Activity 2: Use the following table of golf scores to

answer the following questions

a.

How much deeper can a Bottlenose Dolphin

dive than a Dall’s Porpoise?b.

How much deeper can a Beluga Whale divethan a Pacific White-Sided Dolphin?

Expected Answers:

a.

-330 – (-1640) = 1310 feet

b. -660 – (-990) = 330 feet


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4. Provide a website to the learners in order for them to read examples of word problems

involving integers. After that, ask them to formulate their own word problem. http://blog.ipracticemath.com/2013/11/25/integers-in-real-life/

http://mathcentral.uregina.ca/beyond/articles/Integers/integer1.html

http://www.kwiznet.com/p/takeQuiz.php?ChapterID&CurriculumID=40&Num=4.1

5. Encourage the students to rethink, reflect, and revise their understanding by posing the

following questions:

6. Let the students express their understanding by means of presenting a play, composing a

song, creating a video presentation, or whatever presentation they want to present.

7. a. Let the students have their recitation to check their mastery against the essentialUnderstanding and provide a feedback to the students.

Sample questions:

b. Let the students have a quiz to check their mastery against content standards.(see attachment)

8. Let the students make a story out of the concepts they learned about integers and share itto the class. They will be graded by the number of concepts they mentioned in their

stories.

D. TRANSFER

1. Give an overview or instructions that students are expected to come up with a businessplan that focuses in the creation of the financial statement applying all the concepts they

learned about integers. And at the given date of presentation, the student will proposetheir business to convince investors to invest on their own business company. The rubric will

be provided to the students.

2. Let the students to transfer his/her learning through the financial statement that should bepresent on their business proposal presentation as a group. As a start of formulating their

financial plans, let them brainstorm as a group and pass a draft of their plannedbusiness.

3. The teacher should discuss and provide the rubrics for the performance task:

A. From the Financial Plan Project, the teacher should see the following:a. Understands money managing skills - The student has an excellent understanding ofthe basic money managing skills needed to be financially successful and fully

comprehends how each are used towards achieving a financial goal.b. Financial Goals - Clearly Written; contains at least one financial goal and has

exceptional grammar.

a.

How do integers specifically the concept of positive and negative affect life?

b. Does the properties of fundamental operations really make it easier for us to

solve real life problems that involve integers? Why and how?

1.

The absolute value of an integer is greater than the integer.

2. The average of any four consecutive odd integers is always ___.

http://blog.ipracticemath.com/2013/11/25/integers-in-real-life/http://blog.ipracticemath.com/2013/11/25/integers-in-real-life/http://blog.ipracticemath.com/2013/11/25/integers-in-real-life/


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c. Budgeting & Saving Money - The student has an excellent understanding of what a

budget consist of and uses proper steps towards saving money before paying bills.d. Credit/Debit Cards - The student will be able to explain the difference between

credit cards and debit cards and can give clear examples of what they are useful for.e. Concepts of Integers - The student will be able to apply the concepts of integers

and can clearly show how it is applied.B. From the Business Proposal Presentation, the teacher should see the following:

a. Financial Plan - The student understands the importance of a financial plan anddelivers every step to achieving their goal clearly, without any grammatical errors.b. Collaboration - The student had excellent communication between the other

members of the group and put in their fair share of work within the group. The student

did an excellent job transition information between the other members of the groupthroughout the presentation process.

c. Financial Goals - Clearly mentioned; contains at least one financial goal and hasexceptional grammar.

d. Presentation - The student gave a highly effective performance by incorporating

knowledge from previous lessons, research and used new vocabulary words and used

visual arts effectively while clearly stating how they plan to achieve their financialgoal.

4. Present to the class the GRASPS.

5. After they presented their performance task in the class, ask the following questions:

a. How do the integers help you to come up with a good financial plan for yourbusiness proposal?

b. What are the things you consider as you apply the concepts of integers in your

business financial plan?

Resources:

DepED K-12 Grade 7- Mathematics: Curriculum Guides and Teaching Guides. (2012,

October 30). Retrieved October 26, 2015, from depedk12.blogspot.com/2012/10/deped-k-12-grade-7-mathematics.html

Oronce, O., & Mendoza, M. (2007). Real Number System. In E-math Elementary Algebra (1st ed.). Rex Printing Company.

Materials Needed:

A. Printed Handouts and Worksheets C. Projector and Laptop

B. Board Chalk D. Books and Internet

Goal: The goal is to recruit businessmen to invest in the business proposed. Role: The role will be a Businessman

Audience: The audience expected are businessmen and entrepreneurs

Situation: They will present a Business proposal because the companyneeds more investors.

Performance: The performance will be a Business plan presentation.

Standard: (See attachment)

Documents

Learning Plan - Integers