A Detailed Lesson PLAN IN General Mathematics PDF

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A DETAILED LESSON PLAN IN GENERAL MATHEMATICSWeek No. 8 Date: January 3-7, 2022I. Objectives: At the end of the lesson, the students will be able to:1. distinguish between exponential function and exponential equation;2. solve exponential equations;3. solve problems involving exponential functions a...

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Republic of the Philippines

UNIVERSITY OF NORTHERN PHILIPPINES Tamag, Vigan City 2700 Ilocos Sur College of Teacher Education

Office of the Laboratory Schools A DETAILED LESSON PLAN IN GENERAL MATHEMATICS Week No. 8 Date: January 3-7, 2022

I.

Objectives: At the end of the lesson, the students will be able to:

1. 2. 3. 4. II.

distinguish between exponential function and exponential equation; solve exponential equations; solve problems involving exponential functions and equations; and Reflect on the importance of exponential function in society.

Subject Matter Topic: Exponential Functions Sub-topics: Exponential Equations Reference: General Mathematics by Orlando A. Oronce (First Edition) p. 108 Next Century Mathematics General Mathematics 11 by Fernando B. Orines p. 117 Materials: PowerPoint Presentation, White Board App

III.

Procedure Teacher’s Activity A. Review Good Afternoon, class! Before we start, kindly check your internet and audio to test whether we can hear and see one another. Now that everybody is settled, may I know who are absent for today? Very good! It is nice to know that you really love my subject. Mathematics. So, let’s give everybody a round of applause. Let me remind you class that we have a Class rule.

Student’s Activity

A- Actively participate in class. N- No noise, please turn off your mic to avoid unnecessary noise from your background to give respect to person talking and to be able to do that find place that have a good signal but be sure that you are safe and comfortable in learning. N- Name before you recite. If you want to recite and ask question please turn your on mic and say your name. Lastly, open you camera for me to monitor you if you are really listening and learning.

Yes ma’am.

Is it clear class? Before we formally start our lesson class. Let us have first our review on the last topic we discussed last meeting. What was our lesson last meeting class?

Last meeting ma’am, we talk about function and its inverse. An inverse function is a function that undoes the action of another function ma’am.

Can you define what is Inverse Function ?

Okay, very good. So, what about the steps when we are solving inverse function?

Excellent! So, class as I can see you understood our last topic and you are now ready for our next topic.

B. Motivation Before we finally start our new lesson, Let’s have a game called Name IT! Are you familiar with the game name it class? If that’s the case class let me first read the

First ma’am we will replace f(x) with y, then we will be going to interchange x and y ma’am, after that we will solve for y then lastly, we will replace y with �−1.

instruction. Name it is a picture analysis class where you should figure out what mathematical words can you formed by adding or subtracting the names of the given picture. For example:

Four

Mula

So the answer is formula Understand class? Are you ready class?

Yes ma’am. Yes ma’am.

Now, your turn.

What is the mathematical word being depict in the screen?

EQUATION ma’am.

Very Good! You are correct.

What is the mathematical word being depict in the screen?

BASE ma’am.

Very Good! You are correct.

EXPONENTIAL ma’am. What is the mathematical word being depict in the screen? Very Good! You are correct.

What is the mathematical word being depict in the screen?

FUNCTION ma’am.

Very Good! You are correct.

What is the mathematical word being depict in the screen?

EXPONENT ma’am

Very Good! You are correct.

It seems like you all good at picture analysis class, that is good. Those mathematical word presented have a connection to our topic today and I hope it energized you all.

Excellent class! It was fun, isn’t it?

The mathematical words that we have find out ma’am are all connected to exponential

Thank You for actively participating on our activity. Based on our game class, do you have any idea on what will be our lesson for today?

functions ma’am.

Yes, very good!

C. Discussion Now, I think we everyone are now ready for our topic for today. So, let us start. For today class, we are going to discuss all about Exponential Function. So, what is an Exponential Function? Can you read it for the class? Anyone?

Remember class that when we are talking exponential functions, their exponents must not be fixed. Okay, so for you to understand really well what an exponential function class is, let’s have some examples.

An exponential function is defined by the rule (�) = �� where � > 0, and � ≠ 1, and x is any real number. In this notation, a is the base and x is the exponent.

Yes ma’am

Are you ready? We are task to determine the given whether it is an exponential function or not. If the given is an example of an exponential function then state RAWR but if not state UWU.

1. � = 8� So, for this one class base on our definition is this an exponential function? Why do you say so ?

RAWR ma’am

The function � = 8� is an exponential function because it follows the rules ma’am, as we can see a=8 with exponent x ma’am.

Very Good!

2. � = 2.56� Is this an exponential function class?

RAWR ma’am The function � = 2.56� is an exponential

Why do you say so?

3. � = �8 How about this class, is this a exponential function? Why no?

function because it follows the rules ma’am, as we can see a=2.5 with exponent 6x ma’am.

UWU ma’am Because the base is not a real number, and the exponent is a fixed value ma’am.

Yes! Very Good!

4. � = −4� Is this an exponential function class?

Good job! Always remember class that when we are talking about exponential functions, our “a” or base should be greater than 0 except 1, and our exponent should not be a fixed number. Before we proceed to our next topic class, do you have any question?

UWU ma’am. Because a=-4 ma’am which is not greater than 0.

None ma’am.

Okay, if none then we will proceed. Our next topic class is about exponential equations. What is exponential Equation? Can you read it for the class? Okay, so when we say exponential equation, it is an equation that involves exponential expression. For example, we have 16−� = 1 , 3�2 = 92�−1 and 22�−1 = 43�+2, 64 as we can see their exponents has a variable. Now, let’s learn solving exponential equations. In solving exponential equations, the equating-exponents property is used. Then, what is the property of equality for Exponential Equations? Can you read it for the class?

An exponential equation in one variable is an equation having a variable in the exponent.

Let a, b, and c be real numbers and � ≠ 0. Then, �� = �� if and only if b = c.

So now, let us have a short recall about the laws of exponents. What are the laws of exponents class? Do you remember them? Yes ma’am. Okay, then what are they?

i.

�� �� = ��+�

ii. iii.

(��)� = ���

iv.

� �

(��)� = ���� �� = ��−�, � ≠ 0

v. vi.

� �� 0

vi. � = 1

Okay, very good ! I just want to add the rule when we have a negative exponent, so , we will get the reciprocal so that our exponent will become positive , and also the rule when we have a fractional exponent, . I add this two so that when you will encounter something like this you will not be confuse. What does one-to-one property of exponential functions class? Can you read it?

In the words, if the bases are equal, the exponents must also be equal, or if the exponents are equal, the bases must also be equal. Okay, for example we have 2� = 4. So, what is the first thing we need to? Always remember that our goal here for us to solve the values of x is their base should be equal. So, for our base to be equal from the given equation 2� = 4, the smallest number that we can used so that both sides will be equal is 2. Therefore, our we can represent our 4 as 22. Since our base are now the same, we can now get their exponent. Always remember class that we can proceed in getting our exponents if and only if the bases are equal, we can’t equate our exponents if their base is not equal. So, going back to our equation, since their base are now equal, then we will

If �1 ≠ �2, ℎ ℎ ��1 ≠ ��2 . Conversely, if ��1 = ��2 then �1 = �2.

now get their exponents which is x=2, we copy it only therefore the value of our x here is positive 2. So when, we do the checking: 2� = 4 22 = 4 4=4 Our answer is correct! Next example: 1 � 2 = 2 How about this next example class, can you try to solve it? 125= Can you tell what is your answer?

Good Job! The x there is equal to 9. For you to be sure to your answer class, always do the checking. D. Generalization If you really understand the lesson class, how can we say that a function is an exponential function class?

125= = 3(� − 1) = 2(� + 3) 3� − 3 = 2� + 6 3� − 2� = 6 + 3 �=9

How can we say that an equation is an exponential equation?

We can say that a function is an exponential if it follows the form (�) = �� where a or the base should be greater than 0 except 1 and the x or the exponent is any real number but it should not be fixed.

What will we do if we encounter a number raised by a negative exponent?

We can say an equation is an exponential if it consists of variable in the exponent.

How can you determine if it is one-to-one property of exponential functions?

We will get the reciprocal so that our exponent will become positive.

If the bases are equal, the exponents must

Can we proceed in getting our exponents if the base isn’t equal?

No, we can’t equate our exponents if their base is not equal.

E.Fixing skills Since you now have full of knowledge lets have an activity. I need 6 students. For me to pick the 6 lucky students, I’ll going to use the lucky roulette. (Teacher use the Spin wheel) (6 spins) This game is called maTEAnik, where I have 5 Marites to spill the tea. For the 5 lucky Marites, I have here 5 flavors of tea. C

M

T

W

S

Pick the flavor you want. Behind the colors are problems you need to answer. Once, I say, “Ano ang say mo Marites” Spill your answer. Are we clear class? I’ll give you 1 minute to answer.

C

Solve the equation

M

T

also be equal, or if the exponents are equal, the bases must also be equal.

Determine whether the given is an exponent function or not.

Determine whether the given is an exponential function.

W

Determine the given whether it is an exponential function or exponential equation. ) = 500

S

Solve the equation. 4�−1 = 16

Times up! Let’s check! For the flavor chocolate, ano ang say mo?

How did you get?

Let’s check! Very good! you’ve got the correct answer. For the flavor matcha, ano ang say mo? Why? Let’s check! Very good! you’ve got the correct answer. Ano ang say mo, for Taro flavor? Why did you say so?

Not ma’am Base on the definition ma’am the criteria is not met.

Let’s check! Very good! you’ve got the correct answer. How about for the flavor Winter melon, ano ang say mo? How did you get?

It is an exponential function ma’am. Because when you evaluate the given it have same results.

Let’s check! Very good! you’ve got the correct answer. How about for the last flavor, ano ang say mo?

Exponential equation ma’am.

How did you get?

Since the given has its equal sign ma’am, I therefore conclude that it is an exponential equation.

Let’s check! Very good! you’ve got the correct answer. You are all good! Keep it up.

x=3 ma’am.

That’s all for today, before we end please turn on your camera class for our routinary checking of attendance.

= 16 = �−1=2 �=2+1 �=3

In the count of 1, 2, 3 say cheese That would be all for now. See you again next online meeting! Good bye class, thank you and keep safe!

E. Evaluation Determine whether the given is an exponential function, exponential equation or none of these. (1pt each) A. 1. 2. 3. 4. 5. B. Solve the equation. Show your complete solution. (5 pts each) 1. 2. 2. VI. Assignment Solve the following exponential equation. 1. 2.

Prepared by:

ANN CLAUDETH M. MABOLO UNP, EL 2 STUDENT

Checked by:

JEFFREY E. GALANGCO, MAME Cooperating Teacher

1. Exponential function 2. None of these 3.None of these 4.Exponential function 5.Exponential equation

1.x=4 2.x=7 3. x=3/2 or x=-1

Noted:

CHRISTIAN S. DOMONDON, MAME Asst. Principal, Senior High School Approved: AURELIA T. VITAMOG, EdD, RGC Principal, Laboratory School...