Algebra and Trigonometry Concepts: Senior Secondary Mathematics

This assignment delves into two crucial concepts of senior secondary mathematics: trigonometry and algebra. The document begins with an introduction to mathematics curriculum and its divisions, emphasizing the importance of developing skills in problem-solving and analysis. It then provides a detailed description of trigonometry, including its functions, concept map, and rationale for its importance in calculating angles and sides of triangles. Following this, the assignment explores algebra, defining its role in simplifying equations and its relevance in solving real-world problems. The core of the assignment is the development of lesson plans for algebra, targeting Year 11 students. These lesson plans outline objectives, key concepts, curriculum links, and activities designed to enhance students' understanding of algebraic symbols, equations, and inequalities. The lesson plans include activities like translating verbal expressions into algebraic expressions, solving linear equations, and evaluating student performance through classroom activities, homework, and tests. Overall, the assignment aims to provide a structured approach to teaching and learning algebra, emphasizing its practical applications and fostering critical thinking skills.

LESSON PLANNING AND
RELATED ACTIVITIES

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
CONCEPT 1- TRIGONOMETRY..................................................................................................1
Description of concept.................................................................................................................1
Concept map................................................................................................................................2
Rationale of why this concept is important.................................................................................2
CONCEPT 2 ALGEBRA................................................................................................................3
Description of content..................................................................................................................3
Concept map of algebra...............................................................................................................4
Target group.................................................................................................................................4
Rationale of why this concept is important.................................................................................5
CONCLUSION..............................................................................................................................15
REFERENCES..............................................................................................................................16

INTRODUCTION
Mathematics is a subject that helps in development of skills, knowledge, concepts and
understanding of different kinds of methods and concepts (Anderton, Hine & Joyce, 2017).
Curriculum of mathematics is divided in five main parts: Number; Ratio, Proportion and Rates of
Change; Algebra; Statistics & Probability; Geometry & Measures. As grade of students increases
concepts within these parts also changes. Mathematics is concept that help for students in
developing decision making and analysis ability with the help of its applications and
applicability of these applications in familiar or unfamiliar situations. Mathematics at senior
secondary also helps students in development of problem- solving skills, analytics skills, and
many other kinds of skills. Senior secondary curriculum of mathematics is divided into four main
categories: Essential Mathematics, General mathematics, mathematical methods, and specialist
mathematics. In this assignment two important concepts of senior secondary mathematics will be
described that are trigonometry and algebra. But lesson plans of only algebra will be developed.
CONCEPT 1- TRIGONOMETRY
Description of concept
Trigonometry is a branch of mathematics in which study of relationship between sides
and angles of triangles is done (Widada & et. al, 2019). It is a concept in which functions of
angles, measurement of angles and sides of triangle and its calculation is done. Trigonometry is
based upon three main and important functions of angle that are used for defining and measuring
angles and sies of triangles. These three main and important functions are: Sine, Cosine and
Tangent. All the three functions are used upon right angled triangle. There are various laws,
ratio, and values of trigonometry but all of them are based upon these three important functions.
All the three functions can be explained in terms of right- angled triangle that has ratio of sides.
Sine is mostly denoted as Sin (x), cosine is denoted as Cos (x) and tangent is denoted as Tan (x)
Sine (x)= Ratio of side opposite to x angle to hypotenuse of the triangle
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Cos (x)= Ratio of side adjacent to angle x to hypotenuse of the triangle
Tan (x)= Ratio of side opposite the angle to the side adjacent to the angle
Concept map
Above concept map helps in explaining concept map of trigonometry concept. It clearly explains
lessons that this concept will cover like: defining and measurement of angles, laws of
trigonometry (law of Sine and law of Cosine), ration of trigonometry in which triangles, angles
in quadrants, related angles will be studied. Other than this, in this subject identification of
trigonometry will also be explained by solving different kinds of problems using various kinds of
formulas. This concept map can be further expanded and can be explained in terms of right
angled triangle
Rationale of why this concept is important
Trigonometry is an important concept to be learnt as it helps a student in learning to
calculate angles, sides of triangles (Wijaya, Ying & Purnama, 2020). It is especially important
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for students who want to develop their career in development field where angles, sides, edges
calculation is important like in construction.
This concept is an essential for students in understand daily routine situations where calculations
of side or angel is important
CONCEPT 2 ALGEBRA
Description of content
Algebra is a division of mathematics which is designed so that one can solve a particular
type of problem much easily and quickly. Algebra is basically the branch of mathematics that
studies about symbols and rules for manipulating the different symbols. It is all about the
quantities without including the fixed values which is known as variables (Apsari, Putri &
Prayitno, 2020). This concept is completely based upon unknown values that are called variables.
It can be used for simplifying equations to solve and find answers. Algebra in senior secondary
classes provides a foundation for solving other higher mathematics concepts (Ojaleye &
Awofala, 2018). Algebra, geometry, and probability are three different concepts of mathematics
but all of them are inter-connected with each other. It can be used for solving practical real- life
problems in a better and simplified manner (Alfiana, Pasadeta & Irawati, 2020). At higher
secondary Algebra is used for calculating volume of various packages, finding weekly wedges
based on base wage per hour, number of hours worked ad overtime done. This further helps
students to substitute numerical values in algebraic expressions to evaluate and resolve
particular type of expression in a proper manner.
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Concept map of algebra
Above diagram helps in explaining concept map of algebra concept. It clearly explains lessons
that this concept will cover. This concept map has further been expanded below for more clarity.
Target group
It is mainly targeting the student of 11th year senior secondary level student where they can learn
concept of algebra completely. These students are expected to learn, understand, and use concept
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of Algebra for solving real life practical situations. This will help for providing the brief idea
about the mathematical conceptual term such as Algebra. This lesson plan is for class of 20
students maximum because in these lesson plan on board activities, quizzes are also included and
it is extremely difficult to conduct on board activities in class of more than 20 students. Class of
20 students can be of diverse culture, ethnicity and can be from different economic background
including indigenous students. But all the students should be comfortable with English language.
There can be any number of male and female students within the class. When targeting the
student because they can improve their critical thinking skills to adapt innovative idea in their
life. Sometimes, it is important for identifying the opinion of targeted student. Therefore, it will
be sharing the more depth study about the algebra.
Rationale of why this concept is important
Algebra is one of the classical disciplines in term of mathematics. The rationale of
geometry concept which help for decision what material to use, symbol pattern to make. It plays
important role in the construction process so that student can build their own knowledge.
Afterwards, they can easily relates to real time application (Abdurrahman, Abdullah & Osman,
2020). Algebra is helping to identify the suitable location of different planets such as solar, star
through local calculation.
Algebra is considered the foundation for other classes, it means that applied what student
learn through classroom session. Learning algebra is helping to develop own critical thinking
skills among different students (Alfiana, Pasadeta & Irawati, 2020). It including the logics,
pattern, and problem solving and reasoning aspects. By using algebra equation, it also relates to
the real world from comparing the prices on same products in grocery items. It is useful for
figuring out what time need to leave from particular place. Each and every movement depend
upon the logical calculation to identify accurate outcome.
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Lesson Plan 1
Teacher: Class: Year 11
Date: Time:
Lesson Topic: Basic concept of algebra
Lesson objectives/outcomes:
The objective of Algebra related lesson plan is to indicate the desirable knowledge, skill and attitude gained. The
instructional objective is describing the focal point of lesson plan where each and every student improve their
own understanding towards algebra symbol and rules.
The targeted student will classify and prove the different logical equation congruent provide data or information
about Numerical values (Alfiana, Pasadeta & Irawati, 2020). Different model to solve the situation with the help
of algebraic properties.
Key Concepts/ideas:
 Explain the specific need or requirement for Algebra
 Determining the different Algebra symbols, rules
 Listing the earliest theorists in Algebra
 Applying the appropriate Algebra principles in order to construct the effective logical pyramid.
Curriculum/Syllabus Link: https://www.australiancurriculum.edu.au/senior-secondary-curriculum/mathematics/
general-mathematics/?unit=Unit+2
Skills: mathematical teacher should require the strong math skills and knowledge so that they able to
communicate with student in regards of math principles effectively. It needs patience and understanding in order
to promote student’s own critical thinking and utilize math logical education in everyday lifestyle.
Values and Attitude: The belief of teacher towards actions and attitude which mainly include concept of algebra,
logical equation. Teacher willingness to share their responsibility involved in the lesson, sincere sensitive to every
student motivate or inspire towards learning experience (Alfiana, Pasadeta & Irawati, 2020).
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Time Teacher’s action Student-centred activities Resources
Introduction In this lesson, it is mainly focused on the basic
concept of algebra, it will be explained where
logical verbal expression through different
symbols. in this way, it is representing the main
function of algebra. For starting the lesson, it is
an essential for teacher to provide the basic
information about the concept of algebra and then
move next level. It help for improving the own
knowledge regarding the algebra.
1. Discussion class
work
It will be divided the group
of student on the basis of
knowledge so that
discussion of main
trigonometric function
f(x) = mx + c;
Solve the linear equations
and different inequalities in
particular variable.
Sometimes, it including the
equation with coefficients
and represented in the form
of algebra expressions
(Alfiana, Pasadeta &
Irawati, 2020).
Use of different
resources such
as online
tutorial, session
and internet.
This will help
for student to
clear all
necessary
doubts in
proper manner.
Main body Translate verbal expression into algebraic
expression with three or fewer terms. It is
considered as one of important action that
performed by teacher (Alfiana, Pasadeta &
Irawati, 2020). Basically, teacher is giving the
target for student to perform verbal expression
activities on regular basis.
In the lesson plan, it is listing the operation
symbol that mainly used in Algebra and then
translating the expressions and equations.
Sometimes, it will be performing the reverse
action and translate into algebraic expressions.
The lesson will help for understanding the basic
idea about the algebra. In this way, it is
representing three expression while resolving in
step by step manner.
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Closure Student will be able to understand about the
concept of basic expression. Afterwards, it can be
used in their own real life situation or condition.
In this closure step, it will be completing the
different activities on the basis of their linear
equations.
During closure step, teacher will do cross check,
identifying that each student give their best
efforts in classroom activities.
Afterwards, it will give feedback for each student
on the basis of their performance.
Evaluation and Reflection
I will be evaluating the different activities within classroom, so that each and every student participate for
completing their lesson. In order to gain more skill and knowledge.
 Classroom activities -30%
 Homework- 20%
 Test-30%
 Reflection-20%
In my personal experience, I will be performing different action when successfully completing the lesson plan. So
that I have monitored the activities of student through classroom activities, checking homework and conducting
test series on regular basis.
As per evidence, I will show different activities in step by step manner. In order to understand the concept of
Translate verbal expression into algebraic expression with three or fewer terms. Through this lesson plan, I will
perform the different activities so that student gain more knowledge.
In additional, I will be evaluating the activities but also understanding the logical equation which mainly contain
three variable expression. It will be changing the signs, if in case it would change from left side to right side.
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Lesson Plan 2
Teacher: Class: Year 11
Date: Time:
Lesson Topic: creation of equations and inequalities into one variable
Lesson objectives/outcomes:
The objective of Algebra creation of equations and inequalities into one variable. Through this plan, it will
support for student to improve own skill or knowledge while understanding the concept of algebra. As per giving
the instruction is describing origin point where use concept of different variables into equation. The lesson plan is
providing the brief idea about the equation creation as well as inequalities into one variable.
When teacher target the student on the basis of creation of equations and inequalities into one variable.
Afterwards, student will easily understanding the logical equation while performing the actions (Alfiana, Pasadeta
& Irawati, 2020). In additional, it can be used the model to solve the equation with the help of algebraic
properties.
Key Concepts/ideas:
 Explain the specific need or requirement for Algebra in term of equation creation and inequalities into one
variable.
 Determining the different algebra variables to resolve the equation
 Listing the earliest theorists in Algebra
 Applying the appropriate Algebra principles in order to construct the effective logical pyramid.
Curriculum/Syllabus Link: https://www.australiancurriculum.edu.au/senior-secondary-curriculum/mathematics/
general-mathematics/?unit=Unit+2
Skills: mathematical teacher should require the strong knowledge about the creation of equation and solve them.
It will help for providing the brief idea about the concept of equation creation while solving through mathematical
principles. Sometimes, it also established the communication with student in regards of equation creation
principles effectively. The important thing is to promote the concept through lesson and understanding student’s
own critical thinking where how they can utilize creation of equation and inequalities within problem solving.
Values and Attitude: The actual belief of teacher towards lesson plan where they can share their own idea about
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the algebra, creation of equation. This will help for understanding the importance of teacher when they can share
their knowledge to the student. Teacher willingness to share their responsibility involved in the lesson, sincere
sensitive to every student motivate or inspire towards learning experience (Alfiana, Pasadeta and Irawati, 2020).
Time Teacher’s action Student-centred activities Resources
Introduction In this lesson, it is mainly focused on the creation
of equations and inequalities into one variable.
Afterwards, it can used them to resolve any
problem (Trigueros & Wawro, 2020). It will be
explained the logical equation by using suitable
formulas.
2.discussion within
classroom
Student will be performed
the activities in regards of
equation creation and also
discussed about the main
functions.
a 2 − b 2 = (a − b) (a + b)
(a + b) 2 = a 2 + b 2 + 2ab.
(x + a) (x + b) = x 2 + (a +
b) x + ab.
(a − b) 2 = a 2 + b 2 − 2ab.
Use of different
resources such
as online
tutorial, session
and internet.
This will help
for student to
clear all
necessary
doubts in
proper manner.
Main body Understand the different formula’s related to the
equation creation. It will be solving the equations
and arising from linear function (Alfiana,
Pasadeta & Irawati, 2020). It is commonly used
for understanding the problem and choose
appropriate formulas on the basis of
requirements.
In this lesson, it will be using the different
formulas for resolving the problem or equation
according to requirement. Each and every
formulas consists of unique properties so that it
become easier for identifying the accurate result
or outcome.
The lesson will help for student to perform the
activities while achieving the accurate result or
outcome.
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Closure Students from this lesson will be able to
understand basic equation creation formulas of
algebra. Afterwards, it will be applied to the
formula in real life situations or condition. In this
closure, it will mention all necessary information
or data so that student can learn each and every
thing about topic. Also doing cross-check and
provide the feedback from every student on the
basis of their performance.
Evaluation and Reflection
I will be evaluating the different activities within classroom, so that each and every student participate for
completing their lesson. In order to gain more skill and knowledge.
 Classroom activities -30%
 Homework- 20%
 Test-30%
 Reflection-20%
As per personal views, I always believed on the different actions performed for student improvement so that they
can easily gain more knowledge. In order to improve their capabilities towards concept of creation of equations
and inequalities into one variable. As per conducting the lesson, I will focus on the actual result that perform
during classroom activities, always monitoring the performance of student in step by step manner.
In additional I will be conducting the different tasks and also perform the test series on regular basis.
On the basis of evidence, I will be shown the different activities and also understanding the concept of creation of
equation through algebraic formulas. Through this lesson plan, I will perform the different activities so that
student gain more knowledge.
Lesson Plan 3
Teacher: Class: Year 11
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Date: Time:
Lesson Topic: Linear algebraic expressions
Lesson objectives/outcomes:
 By the end of this less students will be able to understand algebraic equations clearly.
 Students will be able to solve different kinds of practical problems using algebraic expressions
 Students will also be able to solve linear equations in which addition, subtraction, division properties will be
used.
Key Concepts/ideas:
 substitute numerical values into linear algebraic and simple non-linear algebraic expression
 Solve practical problems by focusing upon both linear and non-linear equations.
 Use of spreadsheets to construct a table of values from a formula
Curriculum/Syllabus Link: https://www.australiancurriculum.edu.au/senior-secondary-curriculum/
mathematics/general-mathematics/?unit=Unit+2
Skills: Skills required for teaching algebra equation solving lesion are: numeric skills for calculations,
measuring, learning skills to easily make students understand ways in which algebraic equations can be solved.
Teacher also require good command over English language So that teacher can understand question and develop
equations accordingly. Command over English language will also help teachers to make students learn ways in
which numeric values can be substituted into linear and non- linear algebraic expressions.
Values and Attitude: In order to make students understand algebraic expression in a clear manner teacher will
focus upon giving both classwork and home work in order to make students understand this concept clearly.
Time Teacher’s action Student-centred activities Resources
Introduction In this lesson, basic concept of algebraic
equations will be explained, but mainly it will
focus on the create and solve equation that
mainly consists of one variables on each side by
using algebra tiles (Ratnayake, 2020). It will be
using the subtraction, division and distributive
2. discussion within
classroom
Student will be performed
the activities in regards of
create and solve equation
one of variable on each
Calculator for
calculations,
workbooks for
practise and
problem
solving.
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properties to solve linear equation in proper
manner.
In this lesson, teacher will be explaining
different kinds of calculations done for linear
equations on board so that students can
understand each type of calculation done on
different kinds of linear equations.
sides.
9x=4+3x
In order to solve this
problem, should we move x
on left hand side?
 9x-3x=4
Does moving a variable on
other side change its sign?
So what will be the sign if
3x is moved to left hand
side.
After changing sign
subtraction will be
performed that gives us
 6x=4
And after this we have to
move 6 on left hand side
but now it will move in
dividend position, so what
46 will give us.
X=2/3
Internet and
system for
online tutorials
and quizes
Main body Understand the different formula’s related to the
two variables equation. It will be solving the
equation and uses both different signs
accordingly (Alfiana, Pasadeta & Irawati, 2020).
Afterwards, it will be generating accurate result
or outcome.
Students in this chapter will be able to solve
linear equations easily. They will be able to
understand when addition or subtraction is
performed and when multiplication or division is
performed. Not only this, they will also be able
to understand when variables are required to be
shifted and sign of variables is required to be
changed.
Other than this, students will also learn to
convert word problems into linear algebraic
equations in a proper manner.
Teacher will also be providing example so that
students can understand solve different kinds of
linear algebraic equations themselves and for
this teacher will be providing homework to
students so that they can practise for the same at
home as well.
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Closure Students from this lesson will be able to
understand equation of variables on each side by
using algebra tiles. Afterwards, it will be applied
to the formula in real life situations or condition.
Teacher will be evaluating classwork and
homework of students and will make then
understand mistakes one by then so that basic
concept can be cleared. Not only this, teacher
will also be conduct regular test in class room so
that students can understand things they need to
work upon and understand in a much better
manner.
Evaluation and Reflection
I will be evaluating the different activities within classroom, so that each and every student participate for
completing their lesson. In order to gain more skill and knowledge.
 Classroom activities -30%
 Homework- 10%
 Test-40%
 Reflection-20%
Class room activity will be including on board activities where each students will be called and asked to solve
on bord problem, while exampling an example, students will be randomly asked answers or nest step or in
group explanation of topic to other class members.
As pr my person view, I think students can learn and understand a mathematics concept though practise. There
are very a smaller number of students who practise mathematics problems at home. So, I have designed these
lesson plans in such a manner that that students can practise and solve maximum number of problems in class
and at home as well.
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CONCLUSION
From the above assignment it has been analysed that both trigonometry and algebra are
two important concepts of senior secondary students to be understood. Designing of lesson plan
for both the concepts can help senior secondary students to build a base so that they can learn,
understand, and use these concepts in solving real life problems. These lesson plans should help
students in understating these concepts thoroughly as both the concepts are important in different
ways for students. Like trigonometry is important for students if they want to understand angles,
sides area od triangles and ways in which it can be used for real life practical work. Whereas
algebra is important for students to solve main real life problems life calculating salaries,
calculation of working hours and many more.
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REFERENCES
Books and Journals
Abdurrahman, M.S., Abdullah, A.H. & Osman, S., (2020). Design and Development of Linear
Algebra Peer Tutoring Strategy to Develop Students Mathematical Thinking Processes
Based on Experts' Evaluation. Universal Journal of Educational Research. 8(8). pp.3592-
3607.
Ahmad, H., Yakin, A.A. & Sarbi, S., (2018). The analysis of student error in solve the problem
of spherical trigonometry application. JPhCS. 1114(1). p.012114.
Alfiana, L., Pasadeta, C.M.M. & Irawati, Y., (2020), February. Improving Mathematical
Creativity through Problem Posing Learning Model of Algebra in Junior High School.
In PRISMA, Prosiding Seminar Nasional Matematika (Vol. 3, pp. 285-289).
Anderton, R., Hine, G., & Joyce, C. (2017). Secondary school mathematics and science matters:
Predicting academic success for secondary students transitioning into university allied
health and science courses. International Journal of Innovation in Science and
Mathematics Education (formerly CAL-laborate International), 25(1).
Apsari, R.A., Putri, R.I.I. & Prayitno, S., (2020). Geometry representation to develop algebraic
thinking: A recommendation for a pattern investigation in pre-algebra class. Journal on
Mathematics Education. 11(1). pp.45-58.
Eko, Y.S., Prabawanto, S. & Jupri, A., (2018), September. The role of writing justification in
mathematics concept: The case of trigonometry. In Journal of Physics: Conference
Series (Vol. 1097012146).
Ojaleye, O. & Awofala, A.O., (2018). Blended Learning and Problem-Based Learning
Instructional Strategies as Determinants of Senior Secondary School Students'
Achievement in Algebra. International Journal of Research in Education and
Science. 4(2). pp.486-501.
Prabowo, A., & et. al, (2018, September). Interactive Multimedia-based Teaching Material for
Trigonometry. In Journal of Physics: Conference Series (Vol. 1097, No. 1).
Ratnayake, I.G., 2020. TEACHING ALGEBRA WITH DIGITAL TECHNOLOGY: FACTORS
INFLUENCING SECONDARY MATHEMATICS TEACHERS’TASK
DEVELOPMENT AND IMPLEMENTATION. Bulletin of the Australian Mathematical
Society. 101(2). pp.350-352.
Trigueros, M. & Wawro, M., (2020). Linear Algebra Teaching and Learning. Encyclopedia of
Mathematics Education. pp.474-478.
Widada, W., & et. al, (2019, October). The improvement of trigonometry ability through
connected mathematics learning models and scientific approaches. In Journal of
Physics: Conference Series (Vol. 1318, No. 1, p. 012078). IOP Publishing.
Wijaya, T.T., Ying, Z. & Purnama, A., (2020). Using Hawgent Dynamic Mathematic Software
in Teaching Trigonometry. International Journal of Emerging Technologies in Learning
(iJET). 15(10). pp.215-222.
Online
Senior secondary curriculum of Trigonometry. 2020. [Online]. Available though: <
https://www.australiancurriculum.edu.au/senior-secondary-curriculum/mathematics/
general-mathematics/?unit=Unit+1&unit=Unit+2&unit=Unit+3&unit=Unit+4 >
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