School: ABC Secondary School 
Teacher: Ng Wai Man 

Date: 12/11/2019 
Time: 1:00 – 1:45 pm 
Class: Secondary Four 
Subject: Mathematics 
Topic: Graphs of Exponential Functions and Logarithmic Functions 

Learning Prerequisites:
(a) Laws of Indices:
(i) Integral Indices
(ii) Rational Indices
(b) Exponential Functions:
(i) Exponential Equations
(c) Logarithmic Functions:
(i) Definition of Logarithms
(ii) Properties of Logarithms
(iii) Logarithmic Equations
(d) Graphs of Exponential Functions and Logarithmic Functions
Behavioral Objective:
Students will be able to
(a) Compare the graphs of exponential functions (y = ax) and logarithmic functions ( y = logax ) in different value a, and
(b) find out the relationship between the graphs of exponential functions and logarithmic functions.
Task Analysis:
Teaching Strategies:
The students in the class are not most outstanding ones, but they are able to solve the mathematics question with medium difficulty. Student are required to compare the graph of exponential functions (y = ax) and logarithmic functions ( y = logax ) by using Geogebra. It is easy to let student to find out how does the graph of those function change when the value of a changes. Also, student are easy to understand and remember those properties of the graph by observing and finding out it by themselves than teacher’s direct explanation. So, student will try to use 0.1, 0.2, 2 and 10 as the values of a to finish the task.
Moreover, there are still learning difference between students in the class. Each group will include students with difference abilities. Therefore, week students can be help from students with high ability in the lesson, especially the class activity.
Time 
Content 
Details 
Remarks 
2 mins 
Recalling the
graph of exponential functions and
logarithmic
functions 
The teacher will ask students to pair up the functions and their graph in page 1 of the worksheet. 
(Revision)
(1) The teacher will use
projector to show the
graph on the whiteboard.
(2) Students will be asked to
write down the
corresponding functions
next to the graph. 
2 mins 
Telling the goal of
the lesson 
The teacher will draw three types of graph on the board:
1.Four exponential functions,
2.Four logarithmic functions,
and
3. An exponential function and a
logarithmic function:
(a) a > 1,
(b) 0 < a < 1.
Then teacher will tell student the goad of the lesson is to compare those graphs. 
(Motivation)
(1) The teacher will ask
student how to compare those
graphs before going to the
next step.

8 min 
Comparing the graphs of exponential functions (y = ax) in different value a

4 Students will be formed as a group and asked to follow the steps and answer the questions in page 2. The goal of students in this part is:
A group of the student will share their conclusion to classmate and then teacher will point out the short summary in this page. 
Materials:
1. iPad (with Geogebra) X 6
(1 iPad per a group)
(1) The group who need to present will use airplay to show their work (Geogebra) on the board and share their idea to classmate.

8 min 
Doing exercise 
Students will be asked to finish the exercise in page 3 of the worksheet. 
(1)Teacher will ask two students to finish Ex.2 and Ex.3 on the board respectively.
(2)Teacher will show the question on the board. 
8 min 
Compare the
graphs of
logarithmic
functions (y = logax)


(1)The group who need to present will use airplay to show their work (Geogebra) on the board and share their idea to classmate. 
7 min 
Doing exercise 
Students will be asked to finish the exercise in page 5 of the worksheet. 
(1) Teacher will ask two students to finish Ex.4 and Ex.5 on the board respectively.
(2)Teacher will show the question on the board. 
8 min 
Finding out the
relationship
between the
graphs of
exponential
functions and
logarithmic
functions 
4 Students will be formed as a group and asked to follow the steps and answer the questions in page 4. The goal of students in this part is to find out the relationship between the graph of y = ax and y = logax. A group of the student will share their conclusion to classmate and then teacher will point out the short summary in this page. 
(1)The group who need to present will use airplay to show their work (Geogebra) on the board and share their idea to classmate. 
2 min 
Conclusion 
The teacher will conclude the following points:
At the end of lesson, students will
be asked to finish Ex.6 as
homework. 

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