AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Playing With Numbers
Time Allotted For
The Lesson
Prerequisite
Knowledge
This lesson is divided across five modules.
It will be completed in five class meetings
Playing With Numbers: Class VI
Short Description
Of The Lesson
In this lesson, learners will be taught to express a number in its
general form. They will also learn to use the general form of
numbers to solve number tricks and puzzles. Moreover, the
learners will also be explained the use of the general form of
numbers to find the logic behind the tests of divisibility by 2, 3, 5,
9 and 10.
Objectives
Express a number in its general form
mbers to explain the
logic behind number tricks
number puzzles
Aids
Procedure
logic behind the test of divisibility by 10, 5 and 2
rs to explain the
logic behind the test of divisibility by 3 and 9
Relevant Modules from Teach Next
Other Audio Visual Aids
Access the videos relevant to the chapter ‘Playing With
Numbers’ from the Library resources.
Aids Non-Technical
None
Teacher-Student Activities
A. Warm-up Session
Begin the lesson by conducting either of the following
mathematical tricks:
Trick 1
Ask a learner to think of any two-digit number. Let’s say, the
number selected by the learner is 36. Now, tell the learner that
you can show him/her how to get number 363636 from number
36.
This is how the trick works. Ask the learner to multiply the
selected number with 3. In this case, 36 multiplied with 3 gives
the answer 108. Now, multiply this number with 7, which will give
the answer 756. Then, ask the learner to multiply 756 with 13
and finally multiply the result with 37. The learner will get 363636
as the answer. You may try this trick on different learners.
Trick 2
Ask each learner to think of any three-digit number. The learners
should not tell you the numbers they have picked. Now, ask
them to add 7 to their number, and then multiply the resulting
number with 2. Thereafter, tell the learners to subtract 4 from the
result. Now, ask them to divide the result by 2. Finally, ask them
to subtract the number they had thought of from the resulting
number. On doing so, all the learners will get 5 as their answer.
This is how the trick works. Suppose a learner has selected
number 123. Now, adding 7 to 123 gives 130 and multiplying this
number with 2 gives the answer 260. Thereafter, subtracting 4
from 260 gives 256 and then dividing this number by 2 results in
128. Further, subtracting 128 from 123 (the number the learner
had originally thought of) gives 5 as the answer.
After mentioning the tricks, tell the learners that these
mathematical tricks are based on multiplication, division, addition
and subtraction.
B. Group Activity: Numbers and General Form
In this activity, learners will write numbers in their general forms
and vice versa.
Teacher’s Notes
Note: This activity consists of two parts.
Part 1
Divide the class into small groups. Now, speak out a random
number and ask them to express the given number in its general
form. Give points to the group that answers correctly. You may
have multiple rounds of this activity. Time the activity and reward
the winner.
Part 2
Shuffle the members to form new groups. Now, speak out a
general form of a number and ask the groups to identify the
number. Give points to the group that answers correctly. You
may have multiple rounds of this activity. Time the activity and
reward the winner.
C. Game: Find the Numbers
In this activity, learners will be asked to find numbers from their
general forms.
Teacher’s Notes
Prior to the session, divide the class into small groups. Ask each
group to come up with a game in which the numbers are used in
their general forms. The actual numbers should not be revealed.
The team member should read out the general form of a
number, while the other groups have to identify the number.
After identifying the correct number, the team member should
give the next clue. The group that finds answers for all clues will
be declared the winner. One such game is provided as an
example.
Example of Game: Save the Children
‘Famous Four’ is a group of four friends who are on a mission.
Their mission is to rescue two children who have been
kidnapped and locked in a house. As the Famous Four set on
their mission, a beggar comes forward and gives them the clue –
a blue car with number MAX 5 x 100 + 3 x 10 + 8 x 1. When the
groups find the number from the given general form, they will get
the next clue. Now, the beggar tells them that the car had
stopped at a petrol pump.
The Famous Four rush to the petrol pump, where they get to
know that the car was heading towards street number 1 x 10 + 6
x 1. The groups have to identify the number from the given
general form to get the next clue.
Now, with this piece of information, the Famous Four search for
the street. Once the Famous Four enter the street, they meet a
young security guard at the gate. They ask him if he has
D. Presentation: Number Tricks and Puzzles
In this activity, learners will be asked to explain the maths behind
number tricks and puzzles.
Teacher’s Notes
Divide the class into two groups – A and B.
Group A – Number Tricks
Group B – Number Puzzles
Ask the groups to prepare a presentation on the topics provided.
In the presentation, the groups have to explain the use of
general form of numbers to solve number tricks and puzzles.
After the presentation, you may provide some number puzzles
and ask the learners to solve them in the class.
E. Charts on Divisibility Tests
In this activity, learners will be asked to explain the test of
divisibility of numbers.
Teacher’s Notes
Divide the class into small groups. Ask each group to prepare a
chart that explains the use of the general form of numbers in
finding out the logic behind the tests of the divisibility (of
numbers by 2, 3, 5, 9 and 10). Later, the charts can be displayed
in the class.
Supplemental
Activities
F. Activity on Divisibility of Numbers
In this activity, learners will make a number such that it is
divisible by 2, 3, 5, 9 and 10.
Teacher’s Notes
Provide a list of incomplete numbers. Ensure that each number
has an empty space. Now, ask the learners to fill in the blank
with an appropriate number(s) in order to make it divisible by
2/3/5/9/10. For example, you may give the number ‘65_13’ and
ask the learners to fill in the blank so that the number becomes
divisible by 9. The answer is ‘3’.
Ask the learners to do the following activities:
taught in the class.
ou
Expected Outcome
may ask your friends to solve these puzzles.
-known mathematical
genius and calculating prodigy. You may also buy some of her
books, such as Puzzles to Puzzle You, Book of Numbers, More
Puzzles and Figuring: The Joy of Numbers.
After studying this chapter, learners will be able to express a
number in its general form. They will also be able to use the
general form of numbers to solve number tricks and puzzles.
Moreover, they will be able to explain the use of the general form
of numbers to find the logic behind the tests of divisibility by 2, 3,
5, 9 and 10.
Student Derivable
Assessment
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Cubes and Cube Roots
Time Allotted For
The Lesson
This lesson is divided across three modules. It will be completed
in three class meetings.
Prerequisite
Knowledge
Exponents and Powers: Class VII
Squares and Square Roots: Class VIII
Short Description
Of The Lesson
In this lesson, learners will be introduced to the concepts of cube
numbers (or perfect cubes) and cube roots. They will also learn
about the patterns in cube numbers. Moreover, they will learn to
calculate the cube root of a perfect cube and the perfect cube
number that is nearest to a given non-perfect cube number.
Objectives
erfect cubes
method
non-perfect cube number
e cube roots using the estimation method
Aids
Relevant Modules from TeachNext
Audio Visual Aids
Access the videos relevant to the chapter ‘Cubes and Cube
Roots’ from the Library resources.
Aids Nontechnical
None
Procedure
Teacher-Student Activities
A. Warm-up Session
Begin the class by narrating the history of cubes and cube roots.
Tell your students that the method for finding the cube root of
large numbers was known to the great Indian mathematician
Aryabhata. This method is explained in ‘Ganitapada’, the
mathematical section of the ‘Aryabhatiya’. The following verse in
‘Ganitapada’ explains the method.
Also, tell them the interesting fact that the Sanskrit word
‘Ghhana’ for ‘cube’ has two meanings, just like the word ‘cube’ in
modern mathematics. ‘Ghhana’ means the number multiplied by
itself three times as well as the 3-dimensional cubical structure.
After the warm-up session, play all modules in TeachNext.
B. Search for Cubes
In this activity, students will calculate the cubes of given
numbers.
Teacher’s Notes
Make chits with different numbers written on them. Divide the
class into two groups and ask a student from each group to
select a chit for his/her group. The students in the group need to
calculate the cube of the number on the chit.
Provide scores to the teams. Continue this activity till all chits are
exhausted.
C. Patterns in Cube Numbers
In this activity, students will use the patterns in cube numbers to
perform certain calculations.
Teacher’s Notes
Make chits with different numbers written on them (for example,
53 and 64). Divide the class into two groups and ask a student
from each group to select a chit for his/her group. Based on the
number written on the chit, the students in the group need to do
either of the following calculations:
Give them scores as per the correct answers. Continue this
activity till all chits are exhausted. Additionally, ask each group to
make a presentation on the patterns in cube numbers.
D. Quest for Cube Roots
In this activity, students will calculate the cube roots of given
numbers using the appropriate method. If the number is not a
perfect cube number, then they also need to find out the nearest
perfect cube number.
Teacher’s Notes
Make flash cards with different perfect cube numbers and a few
non-perfect cube numbers written on one side. On the other side
of these cards, write the answers.
Divide the class into two groups. Ask a student from each group
to select a card for his/her group. The students in the group need
to find the cube root of the number on the card using any of the
following methods:
If the number is not a perfect cube number, the students need to
find out the smallest natural number by which the given number
should be divided or multiplied to make it a perfect cube number.
Give the bonus marks to the group if they correctly find the
nearest cube number.
Continue this activity till all the cards are exhausted.
Supplemental
Activities
Provide the list of the following perfect cubes to your students
and ask them to plot the numbers on the graph using MS Excel:
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197,
2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167,
13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791,
32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319,
64000, 68921, 74088, 79507, 85184, 91125, 97336, 103823,
110592, 117649, 125000, 132651, 140608, 148877, 157464,
166375, 175616, 185193, 195112, 205379, 216000, 226981 and
238328.
Ask them to observe the pattern of the line graph.
Expected Outcome
After completing the lesson, learners should be able to explain
the concepts of cube numbers (or perfect cubes) and cube roots.
They should also be able to explain the patterns in cube
numbers. Moreover, they should be able to calculate the cube
root of a perfect cube and the perfect cube number that is
nearest to a given non-perfect cube number.
Student Derivables
Assesment
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Factorisation
Time Alloted For
The Lesson
Prerequisite
Knowledge
This lesson is divided across four modules. It will be completed
in four class meetings.
Short Description
Of The Lessson
In this lesson, learners will study the factorisation of algebraic
expressions. They will also learn to factorise algebraic
expressions using different methods, such as identifying
common factors, regrouping the terms and using algebraic
identities. Moreover, they will learn to divide an algebraic
expression by another algebraic expression.
Objectives
the common factors
the terms
algebraic identities
ession by another algebraic
expression
Aids
Relevant Modules from Teach Next
Other Audio Visual Aids
Access the videos relevant to the lesson ‘Factorisation’ from the
Library resources.
Aids No technical
None
Procedure
Teacher-Student Activities
A. Warm-up Session
Begin the lesson with a quiz activity. You can include questions
that will help students recall the prior learning of algebraic
expressions.
You can ask the students to give the examples of simple
algebraic expressions and then identify the terms in the
expression and the factors in the terms. Also, ask the students
to identify if a given expression is a monomial, binomial or
trinomial.
Additionally, you can hold a quiz on algebraic identities. The
LHS of an identity can be given and the students can be asked
to write the RHS. Then, talk about the aim of factorisation, which
is to reduce something to its basic building blocks and includes
factorising numbers to prime numbers or polynomials to
irreducible polynomials.
B. Chit Activity
In this activity, students need to factorise algebraic expressions.
Teacher’s Notes
Divide the class into a few groups and prepare chits with
algebraic expressions written on them (one expression on each
chit). Also, mention the method (identifying common factors or
regrouping the terms) to be used by the students to factorise the
expressions. Now, present the chits to a group and ask any
student from the group to pick up a chit and write the expression
on the board. His/her group needs to solve the expression using
the method mentioned on the chit. Carry out the activity with
other groups as well.
C. Flashcard Activity
In this activity, students need to factorise algebraic expressions
using appropriate identities.
Teacher’s Notes
Divide the class into a few groups and prepare flashcards with
algebraic expressions written on them. Write an expression on
each card. Now, show a card to a group and ask a student from
the group to identify the algebraic identity that can be used to
factorise the expression.
Thereafter, the same student should write the expression and
the identity on the board and factorise the expression using the
identity. Continue the activity with other groups.
D. Dividing Algebraic Expressions
In this activity, students need to divide an algebraic expression
Supplemental
Activities
Expected Outcome
Student
Deliverables
Assessment
by another algebraic expression.
Teacher’s Notes
Write down two monomials on the board and ask the students to
divide one by the other. Then, write down a polynomial and a
monomial on the board and ask the students to divide the
polynomial by the monomial using the methods of taking out the
common factor and cancellation. Also, include problems where
a polynomial needs to be divided by another polynomial. The
students can solve the problems in their exercise books.
Ask the students to fill in the blanks in the grid after factoring the
given expressions.
After studying this lesson, learners should be able to factorise
algebraic expressions using different methods, such as
identifying common factors, regrouping the terms and using
algebraic identities. They should also be able to divide an
algebraic expression with another algebraic expression.
w questions given by the teacher
– Division of algebraic
expressions
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Rational Numbers
Time Allotted For
The Lesson
Prerequisite
Knowledge
This lesson is divided across seven modules. It will be
completed in seven class meetings.
Whole Numbers: Class VI
Integers : Class VI
Integers: Class VII
Rational Numbers: Class VII
Short Description
Of The Lesson
This lesson will introduce the learners to the basic properties of
operations on rational numbers. They will also recall their
knowledge of these properties with respect to whole numbers
and integers. They will learn to represent rational numbers on a
number line. Moreover, they will also learn to find rational
numbers between two rational numbers.
mbers,
integers and rational numbers under various
mathematical operations
Objectives
integers and rational numbers under various
mathematical operations
under various mathematical operations
integers and rational numbers under various
mathematical operations
he associative property for rational numbers
under various mathematical operations
numbers, integers and rational numbers
numbers under various mathematical operations
addition for rational numbers
subtraction for rational numbers
nal numbers on a number line
Aids
Procedure
Relevant Modules from Teach Next
Access the videos relevant to the chapter ‘Rational Numbers’
from the Library resources.
Aids No technical
None
Teacher-Student Activities
A. Warm-up Session
Begin the session by drawing a number line on the board. Call a
few students one by one and ask them to represent whole
numbers, natural numbers, integers, fractions and rational
numbers on the number line. Thereafter, recall the basic
properties of rational numbers.
B. Quiz: Properties of Integers and Whole Numbers
In this activity, students will revise the properties for whole
numbers and integers.
Teacher’s Notes
Recall the properties of integers and whole numbers. Then,
divide the class into two groups and organise a quiz. Ask the
students from both the groups about the following properties of
whole numbers and integers:
plicative Identities
C. Presentations on Properties
In this activity, groups of students will deliver presentations on
different properties of rational numbers.
Teacher’s Notes
Divide the class into five groups and assign the following
properties to the groups:
inverse properties
Ask the students to explain the properties using examples.
Since the presentation is very comprehensive, more than one
student can be asked to present it. The students can use either
Supplemental
Activities
Expected Outcome
Student
Deliverables
Assessment
chart papers or MS PowerPoint for their presentations. The
charts used in the presentation can be put up in the class later.
After the presentation, give a few questions to the students to
solve using these properties.
D. Chit Game
In this activity, students will represent rational numbers on a
number line. Further, they will also find rational numbers
between two given rational numbers.
Teacher’s Notes
Make a few chits and write a rational number on each chit. Put
these chits in a bowl. Now, call any student from the class to
pick up a chit from the bowl and read the number on the chit.
Then, he/she needs to draw the number line on the board and
represent the number on it. Similarly, you can carry out this
activity with other students.
Prepare some more chits, but this time write two rational
numbers per chit. Call a student to pick up a chit and find the
rational numbers between two rational numbers on the chit.
Ask the students to perform the following activities:
mbers
and without using these properties. Which method is easier?
Share your thoughts with the class.
After studying this lesson, students will be able to recall basic
properties of operations pertaining to whole numbers and
integers. They will be able to explain various properties of
operations on rational numbers and solve expressions using
these properties. They will also be able to represent rational
numbers on a number line and find rational numbers between
two rational numbers
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Practical Geometry
Time Alloted For
The Lesson
This lesson is divided across four modules. It will be completed
in four class meetings.
Prerequisite
Knowledge
Practical Geometry: Class VII
Understanding Quadrilaterals: Class VIII
Short Description
Of The Lesson
In this lesson, students will learn to construct unique
quadrilaterals when measurements of their sides, diagonals and
angles are given.
Objectives
sides are given
and a diagonal are given
sides and a diagonal are given
sides and two diagonals are given
Aids
adjacent sides and the measures of three angles are
given
hen the lengths of its three
sides and the measures of two included angles are
given
Relevant Modules from Teach Next
Other Audio Visual Aids
Access the videos relevant to the chapter ‘Practical Geometry’
from the Library resources.
Aids Non-Technical
None
Procedure
Teacher-Student Activities
A. Warm-up Session
Begin the lesson by holding a quiz pertaining to the following
topics:
B. Scrapbook: Construction of Quadrilaterals
In this activity, learners will construct quadrilaterals.
Teacher’s Notes
In the class, demonstrate the construction of a quadrilateral in
the following cases:
three angles are known.
nd the measures of two
included angles are known.
After the demonstration, provide a set of measurements for each
criterion and ask the learners to construct the quadrilaterals in
their books.
Thereafter, ask the groups to exchange the collages and the
measurements. The groups have to draw a replica of the collage
by constructing the quadrilaterals based on the measurements
given.
D. Competition: Designing Your Kite
In this activity, learners will be asked to construct a kite.
Teacher’s Notes
Materials Required:
Supplemental
Activities
Hold a kite designing competition in the class. To begin with, ask
the learners to construct a kite on a chart paper (the learners can
decide the measurements of their kites) with the help of a
compass and a ruler. After constructing the kite, the learners
need to cut out the kite and decorate it. Reward the three most
innovative designs. Later, the kites can be displayed in the class.
Ask learners to check objects in their houses that have shapes
of quadrilaterals. Then, ask them to record the measurements
(the lengths of sides and the measures of the angles) of these
Expected Outcome
objects. Thereafter, the learners need to draw these objects in
their books. If the quadrilaterals are too big to be drawn in their
books, they can scale them down by converting the
measurements from inches to centimetres. For example, if one
side of a rhombus shaped floor tile measures 6 inches and one
of the diagonal measures 8 inches, then the learner has to
construct a rhombus in his/her book with the sides measuring 6
centimetres and one diagonal measuring 8 centimetres.
After studying this chapter, learners will be able to construct
unique quadrilaterals when measurements of their sides,
diagonals and angles are given.
Student
Deliverables
Assessment
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Data Handling
Time Alloted For
The Lesson
This lesson is divided across four modules. It will be completed
in four class meetings.
Prerequisite
Knowledge
Short Description
Of The Lesson
Data Handling: Class VII
This lesson will introduce students to grouped frequency
distribution tables, histograms, pie charts and probability. They
will learn to organise data in a grouped frequency distribution
table and use this data to draw a histogram. They will also be
taught to create a pie chart and calculate probability of an event.
Moreover, they will learn to interpret data from frequency
distribution tables and graphs.
Objectives
graph
t and the
width of a class interval
distribution table
om a given pie chart
event
Aids
Relevant Modules from Teach Next
Other Audio Visual Aids
Procedure
Access the videos relevant to the chapter ‘Data Handling’ from
the Library resources.
Aids Non technical
None
Teacher-Student Activities
A. Warm-up Session
Begin the lesson by showing the students a collage of data,
pictograms, bar graphs and double bar graphs that they have
learnt in the previous class. You may show the data of weather
in a few cities over a period, the sales figures of a company and
the runs scored by a few batsmen. Ask the students to interpret
the data in the tables and graphs. Talk about different types of
graphs which can be used to represent data.
B. Bar Graphs and Double Bar Graphs
In this activity, students will draw bar graphs and double bar
graphs.
Teacher’s Notes
Divide the class into two groups and ask them to collect data
about the favourite cartoon characters of the students in their
respective groups. Each student can choose any one cartoon
character from the list of six or seven popular characters. For
example, Tom and Jerry, Shin Chan, Doraemon, Ben-10, HeMan and G.I. Joe. In this way, ask both the groups to collect
data, make a frequency distribution table and then represent
data on bar graphs. Later, ask both the groups to exchange data
and make double bar graphs.
C. Grouped Frequency Distribution Table and Histogram
In this activity, students will organise data in a grouped
frequency distribution table. They will also draw and interpret
histograms.
Teacher’s Notes
Divide the class into two groups and ask them to collect data
regarding the distance travelled by students from their house to
the school. Ask both the groups to collect and organise the data
using a grouped frequency distribution table. Then, you can ask
volunteers from both the groups to come and present their table.
At this point, ask the volunteers and the other members of the
group questions on the upper and lower class limit, class width
and so on.
Next, ask the groups to represent the data (organised in the
frequency distribution table) by drawing histograms. You can
also call volunteers from the two groups and ask them to
interpret the data from the histogram prepared by the other
group.
D. Circle Graph or Pie Charts
In this activity, students will draw and interpret circle graphs or
pie charts.
Teacher’s Notes
Tell the students about circle graphs or pie charts. In a pie chart,
a circle is divided into several segments or sectors and each
sector represents one piece of data. The angle of each of these
segments is proportional to the value of the piece of data. Tell
the students that the earliest pie chart was prepared by the
Scottish engineer and political economist William Playfair in his
book the Statistical Breviary. Interestingly, over the years, the
principles of making a pie chart have essentially remained the
same.
Show a few pie charts to the students and ask them to interpret
the data depicted by these charts.
Teach the students the method to prepare pie charts. Then,
divide the class into two groups and ask them to collect
information about how different students commute to school. For
example, on foot, bicycle, car, school bus, rickshaw or shared
cab. Alternatively, you may provide the data and ask the groups
to represent it on a pie chart. Once the charts are prepared,
discuss them in the class.
E. Probability
In this activity, students will learn about various concepts
pertaining to chance and probability.
Teacher’s Notes
Prepare a spinning wheel with a pointer and four sectors of
different colours (for example, yellow, green, red and blue).
Then, spin the wheel and explain the concepts of random
experiment, outcome, event and probability.
Now, ask the students to prepare a spinning wheel with eight
sectors as follows: two sectors in red, three sectors in yellow,
one sector in green and two sectors in blue. Divide the class into
groups and ask all these groups to spin the wheel 25 times and
record their findings.
Discuss other examples of probability and ask the students to
think of different activities in which they are likely to get different
outcomes. For example, drawing a particular card from a pack of
cards.
You can also tell the students about the history of the probability
theory. The concepts of probability have been in practice over
thousands of years. However, probability emerged as a
specialised branch of Mathematics only around the mid-
seventeenth century.
Supplemental
Activities
Ask the students to perform the following activities:
components (carbohydrates, proteins, vitamins, roughage and
minerals) in our daily diet.
Expected Outcome
Student
Deliverables
Assessment
share the information with the class.
After studying this lesson, students will be able to organise data
in a grouped frequency distribution table and use this data to
draw a histogram. They will also be able to create a pie chart
and calculate the probability of an event. Moreover, they will
learn to interpret data from frequency distribution tables and
graphs.
After studying this lesson, students will be able to organise data
in a grouped frequency distribution table and use this data to
draw a histogram. They will also be able to create a pie chart
and calculate the probability of an event. Moreover, they will
learn to interpret data from frequency distribution tables and
graphs.
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Introduction to Graphs
Time Alloted For
The Lesson
Prerequisite
Knowledge
This lesson is divided across four modules. It will be completed
in four class meetings.
Handling Data: Class V
Data Handling: Class VI
Data Handling: VII
Data Handling: VIII
Short Description
Of The Lesson
In this lesson, learners will be introduced to the different types of
graphs and their uses. They will also learn to plot and interpret
line graphs. Moreover, they will be taught the concept of
coordinates and the use of coordinates and the Cartesian
system in plotting linear graphs.
Objectives
he
Cartesian system
variables
Cartesian system
Aids
Relevant Modules from TeachNext
Other Audio Visual Aids
Access the videos relevant to the chapter ‘Introduction to
Graphs’ from the Library resources.
Aids Nontechnical
None
Procedure
Teacher-Student Activities
A. Warm-up Session
Bring a few graphs to the classroom. These graphs could be
from newspapers, magazines or other such sources. Ask the
students what they understand from these graphs and then
explain the purpose of graphs.
Thereafter, briefly narrate the history of graphs. Tell the students
that the study of graphs is known as the graph theory. Dénes
Kőnig, a Jewish Hungarian mathematician, wrote the first book
on the graph theory. However, this book was so complex that
very few people understood it. The first simplified book on the
graph theory was written by the American mathematician Frank
Harary and it became very popular.
B. Plot the Graphs
In this activity, students will plot the appropriate type of graph to
represent the given data.
Teacher’s Notes
Divide the class into four groups. Each group needs to collect
data to plot the graph type assigned to them. Assign the graph
types as follows:
The groups need to collect the data that can be represented
using the graph type assigned to them. After bringing the data to
the classroom, groups should justify how the data is best
represented by the graph type assigned to them. (You may also
ask them to elaborate on their data collection method.)
Thereafter, each group needs to share the data with the other
groups. The other groups need to plot the graphs based on the
data. Verify the graphs.
c. Interpreting Line Graphs: Puzzle
In this activity, students will interpret line graphs.
Teacher’s Notes
Divide the class into a few groups and ask each group to come
up with a graph puzzle. They should write one-liner stories and
plot the matching graphs for these stories. They should share all
graphs and stories with the other groups and ask them to find
out the matching pairs of graphs and stories. An example is
provided.
Graphs and One-Liner Stories:
I. We left our home for a picnic, but came back to collect the
snacks, and finally headed back to the picnic destination.
II. We left our home for a picnic, but we had a flat tire that
resulted in a long halt.
III. We left our home for a picnic. Dad was driving very slowly,
but my mom realised that we were getting late so she asked him
to speed up.
IV. We left our home for a picnic and dad was driving very fast,
so my mom asked him to slow down till he started driving at a
safe speed.
(Answer: A – III, B – II, C – IV, D – I)
Reward the group that comes up with innovative puzzles that
make the appropriate use of line graphs.
E. Fun with Coordinates and Linear Graphs
In this activity, students will plot the points on a graph paper
based on the coordinates. They will also plot a linear graph to
represent the given data.
Teacher’s Notes
Make chits with different pairs of coordinates written on them.
Divide the class into groups and ask a student from each group
to select a chit for his/her group. The students in the group need
to plot the points on a graph paper based on the coordinates.
Continue this activity till all the chits are exhausted. Give scores
to the groups as per the correct answers. Then, randomly make
a few points on the graph paper and ask the students to identify
their coordinates. Continue this activity with all the groups.
Once the activity is over, provide data in a tabular form to the
students and ask them to plot linear graphs to represent this
data. The students need to plot these graphs on graph papers.
Alternatively, you may show them a few linear graphs and ask
them to interpret these graphs.
Supplemental
Activities
Ask the students to do the following activities:
your native places for the period of a few months. You can get
this data from a local newspaper. Bring these graphs to the
classroom. Submit your graphs to the teacher who can show
these graphs to the entire class. (You may analyse the climatic
type of the native places based on the graphs. Take the help of
your Geography teacher, if required.)
during different time in a day. Share the graph with other
students in the class and ask them to interpret the graph.
Expected Outcome
After completing the lesson, learners should be able to explain
the different types of graphs and their uses. They should also be
able to plot and interpret line graphs. Moreover, they should be
able to explain the concept of coordinates. They will also be
able to use the coordinates and the Cartesian system to plot a
linear graph.
Student
Deliverables
Assessment
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Squares and Square Roots
Time Alloted For
The Lesson
Prerequisite
Knowledge
Short Description
Of The Lesson
This lesson is divided across eight modules. It will be completed
in eight class meetings.
Exponents and Powers: Class VII
In this lesson, learners will be introduced to the concepts of
square numbers (or perfect squares) and square roots.
Additionally, they will learn about the patterns and properties of
square numbers. They will also learn to calculate the square of a
number as well as the square root of a perfect square.
Objectives
on why certain numbers are at the unit place of
a perfect square
numbers and the digit at the unit place of their squares
of numbers and at the end of their squares
numbers have odd squares
numbers is a square number
that there are ‘2n’ non-square numbers between n2
and (n + 1)2, if n and (n + 1) are two consecutive numbers
starting from 1 is equal to n2
tten as
the sum of two consecutive positive integers
itself
for finding such triplets
provided
subtraction method and the prime factorisation method
method
a given non-perfect square number to make it a perfect square
number
Aids
division method
Relevant Modules from TeachNext
Other Audio Visual Aids
Access the videos relevant to the chapter ‘Squares and Square
Roots’ from the Library resources.
Aids Non technical
None
Procedure
Teacher-Student Activities
A. Warm-up Session
Begin the class by narrating the history of squares and square
roots. Tell your students that the archaeological evidences
indicate that squares and square roots were used by ancient
people across different cultures. The tablets belonging to the
Babylonian period, dating back to1800 BC and 1600 BC, depict
square roots. Even the papyrus from 1650 BC indicates that the
Egyptians were aware of extracting square roots.
Babylonian Tablet Egyptian Papyrus
The Indian and the Chinese also knew about squares and square
roots. In fact, the Indians had the knowledge of the theoretical as
well as the practical aspects of these concepts as evident from
‘Sulbha Sutras’ (written in 800-500 BC or earlier). Moreover,
Aryabhata knew the method of calculating the square roots of
larger numbers. This method is described in his famous work
‘Aryabhatiya’. The following verse in ‘Ganitapada’, the
mathematical section of the ‘Aryabhatiya’, explains the square
root extraction method.
Later, this method was introduced to the Europeans by the Italian
architect Cataneo in 1546.
B. Fun with a Chessboard
In this activity, students will learn about the concepts of square
numbers (or perfect squares) and square roots.
Teacher’s Notes
Bring a chessboard to the class. A chessboard is made up of 32
black and 32 white squares arranged in eight rows and columns.
Ask the class to assume that each small square has sides
measuring 1 inch. Ask your students what will be the area of
squares lining any one side of the chessboard (answer: 8 square
inches). Then, ask them to calculate the area of the entire
chessboard (answer: 64 square inches). Using these two
numbers and the chessboard, explain the concepts of square
numbers and square roots.
After the explanation, give some numbers to the students and
ask them to work out if these numbers are perfect squares.
C. Properties of Square Numbers
In this activity, students will make presentations on the properties
of square numbers.
Teacher’s Notes
Divide the class into four group and ask them to make the
following presentations:
on why certain numbers are at the unit place
of a perfect square
numbers and the digit at the unit place of their squares
end of numbers and at the end of their squares
and odd numbers have odd squares
Once they have made their presentations, give them a few
examples to solve. Refer to the Exercises section in the
TeachNext box for practice questions.
D. Patterns in Square Numbers
In this activity, students will design activities on various patterns
in square numbers.
Teacher’s Notes
Divide the class into four groups. Each group needs to come up
with activities/questions on various patterns seen in square
numbers:
is a square number.
-square numbers between n2 and
(n + 1)2, if n and (n + 1) are two consecutive numbers.
tarting
from 1 is equal to n2.
sum of two consecutive positive integers.
The students need to share the activities and problems with the
entire class. The activities can be conducted in the class, while
the questions can be solved either in the class or given as
homework.
E. Search for Square
Give them scores as per the correct answers. Pythagorean
Triplets will fetch them bonus points. The system of bonus points
will work as follows. If the number on the card is part of a
Pythagorean Triplet and the group correctly identifies such
number and finds the corresponding triplet, then it will get bonus
marks. Continue this activity till all the chits are exhausted.
F. Quest for Square Root: Activity
In this activity, students will calculate the square roots of given
numbers using the appropriate method. In case the number is not
a perfect square, they will need to find out the nearest perfect
square number.
Teacher’s Notes
Make flash cards with various perfect square numbers and a few
non-perfect square numbers written on one side. Make a few
cards with perfect square decimal numbers as well. On the other
side of all the flash cards, write the answers.
Divide the class into three groups. Ask one student from each
group to select a card for his/her group. The students in the
group need to find the square root of the number on the card
using any of the following methods:
g division method
Although they have freedom to use any method, it is mandatory
to use each method at least once during the entire activity.
If the number is a non-perfect square number, they need to find
out the smallest number that needs to be added to or subtracted
from the number to make it a perfect square number. Continue
this activity till all the cards are exhausted.
Supplemental
Activities
Ask your students to do the following activities:
They can draw such patterns on a chart paper as well.
patterns are given in the table.
1x1
7x7
9x9
11 x 11
67 x 67
99 x 99
111 x 111
667 x 667
999 x 999
1111 x 1111 6667 x 6667 9999 x 9999
11111
x66667
x99999
x
11111
66667
99999
In this activity, students will calculate the squares of given
numbers. They will also work out a Pythagorean Triplet when one
of its numbers is provided.
Expected Outcome
After completing the lesson, learners should be able to explain
the concepts of square numbers (or perfect squares) and square
roots. They should also be able to explain the patterns and
properties of square numbers. They should also be able to
calculate the square of a number as well as the square root of a
perfect square.
Student
Deliverables
Assessment
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Algebraic Expressions and
Identities
Time Alloted For
The Lesson
This lesson is divided across six modules. It will be completed
in six class meetings.
Prerequisite
Knowledge
Algebraic Expressions: Class VII
Short Description
Of The Lesson
In this lesson, learners will be taught to represent an algebraic
expression on a number line. They will study about terms,
factors and coefficients of expressions. They will also learn
about the different types of algebraic expressions and will learn
to identify like and unlike terms in an expression. Further, they
will be introduced to the standard identities and will learn to
solve algebraic expressions using these identities.
Objectives
and coefficients of an algebraic expression
or trinomial
given algebraic expression is a polynomial
expression
Aids
Audio Visual Aids
Relevant Modules from TeachNext
traction of Algebraic Expressions
Access the videos relevant to the lesson ‘Algebraic Expressions
and Identities’ from the Library
resources.
Aids Non technical
None
Procedure
Teacher-Student Activities
A. Warm-up Session
Begin the session with a simple activity to help students recall
their prior knowledge about algebraic expressions. Divide the
class into a few groups. Write an algebraic expression on the
board and ask the students from a group to come one by one to
the board and write the constants, variables, operators, terms,
factors and coefficients in the expression on the board. You can
give a score of one point for each question correctly answered.
That is, if the students in the group identify the constants,
variables, operators, terms, factors and coefficients correctly,
the team will get six points.
Conduct the similar activity with other groups. The team that
gets the maximum correct answers will be the winner.
B. Quiz
In this activity, students will answer questions pertaining to
algebraic expressions.
Teacher’s Notes
Divide the class into a few groups. The quiz can include the
following types of questions. You can write an expression on
the board and ask a student to identify if the expression is a
polynomial. The student also needs to justify the answer. Next,
you can write an expression and ask a student to identify if it is
a monomial, binomial or trinomial. Also, ask them to identify the
like and unlike terms in the expression. You can also write a
simple expression on the board and ask a student to represent
it on a number line. Additionally, ask students to write down
expressions with one and two variables on the board.
The team that gets maximum correct answers will be the
winner.
C. Activity for Addition and Subtraction of Expressions
In this activity, students need to add algebraic expressions or
subtract an algebraic expression from another algebraic
expression.
Teacher’s Notes
Ask a student to write an algebraic expression on the board.
Now, ask another student to write another expression on the
board with some like terms (from the first expression). Then,
ask the second student to add the two expressions. The same
activity can be conducted for the subtraction of expressions.
D. Activity for Multiplication of Expressions
In this activity, students need to multiply algebraic expressions.
Teacher’s Notes
Discuss situations where the multiplication of algebraic
expressions is required. Then, draw a rectangle on the board
and write down its length and breadth in terms of algebraic
expressions. Thereafter, ask the students to find the area of the
rectangle.
Similarly, you can draw a cuboid and write its length, breadth
and height in terms of algebraic expressions and ask the
students to calculate the volume of the cuboid. Additionally, you
can ask students to write algebraic expressions on the board
and multiply them. For example, you can begin by asking the
students to write down monomials and then multiply them. You
can also ask them to write binomials and trinomials on the
board and multiply these expressions. Multiplication can be
carried out between the different types of polynomials, namely
monomials, binomials and trinomials.
Supplemental
Activities
Expected Outcome
Student
Deliverables
Assessment
E. Identity Activity
In this activity students need to solve problems using the
standard identities.
Teacher’s Notes
You can first derive the standard identities. Then, write down a
problem on the board and ask the students to name the
standard identity to be used to solve the problem. Thereafter,
ask all the students to solve the problem in their notebook using
the identity.
Additionally, you can ask each student to derive the four
identities on a chart paper and place the chart paper on their
study table or any other suitable place for easy reference.
Ask the students to solve a few expressions using identities.
Then, they can share their problems and answers with their
neighbour and ask him/her to recognise the identities that have
been used to solve the problems.
After studying this lesson, learners will be able to represent an
expression on a number line. They will be able to identify the
terms, factors, coefficients of terms, like and unlike terms of
expressions. They will also be able to identify different types of
algebraic expressions and use standard identities to solve
algebraic expressions.
sing the standard identities
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Direct and Inverse Proportions
Time Alloted For
The Lesson
This lesson is divided across two modules. It will be completed
in two class meetings.
Prerequisite
Knowledge
Ratios and Proportions: Class VI
Fractions and Decimals: Class VII
Comparing Quantities: Class VII
Comparing Quantities: Class VIII
Short Description
Of The Lessons
In this lesson, learners will be introduced to the concepts of
direct and inverse proportions. Additionally, they will learn to use
proportions to find the values that are either directly or inversely
proportional to each other.
Objectives
each other
oncept of inverse proportion
Aids
Procedure
each other
Audio Visual Aids
Relevant Modules from Teach Next
Other Audio Visual Aids
Access the videos relevant to the chapter ‘Direct and Inverse
Proportions’ from the Library resources.
Aids No technical
None
Teacher-Student Activities
A. Warm-up Session
Begin the class by asking the students the following puzzle:
If 5 cats can catch 5 mice in 5 days, how many days will 3 cats
take to catch 3 mice?
Tell the students that they cannot use a paper and a pen to
solve the puzzle. They must find the answer by doing the
calculation in their minds. Most likely, many of them would
provide the answer ‘3 days’. Although this answer is the obvious
choice of many other people presented with this puzzle, it is the
incorrect answer.
At this point, explain the concepts of direct proportion and
inverse proportion. Then, go back to the puzzle. Explain that the
cat-mice puzzle is the example of inverse proportion. If you have
fewer cats, they will take more time to catch the mice. Tell them
that the answer of the puzzle is ‘5 days’. That is, 3 cats would
catch 3 mice in 5 days. Explain the answer by the step-by-step
calculation.
B. Direct or Inverse?
In this activity, students will find out if the given proportion is
direct or inverse. They will also solve a few examples involving
the direct and inverse proportions.
Teacher’s Notes
Make chits with questions involving either the direct proportion
or the inverse proportion. Divide the class into two groups and
ask a student from each group to select a chit for his/her group.
The students in the group need to identify if the given question
is based on the direct proportion or the inverse proportion. They
also need to provide the explanation for their answer.
Thereafter, they need to calculate the answer to the question.
Provide scores to the teams and continue the activity till all the
chits are exhausted.
C. Game of Shadows
In this activity, students will calculate the height of the shadow
by studying the proportion.
Teacher’s Notes
Place a projector or a light source on the ground in the
classroom or lab. The light source should be facing the wall and
should be placed at the distance of 20 feet from the wall.
Between the light source and the wall, make markings at the
length of every 1 foot. Then, place a chalk at the distance of 10
feet from the light source, so that it casts its shadow on the wall
as shown in the figure.
Then, ask a student to measure the height of the shadow. Now,
ask all students to guess what would happen if the chalk is
moved towards the light source and away from it. Verify their
answers by moving the chalk towards and away from the light
source by 1 foot.
Now, place the chalk at the distance of one foot from the light
source and measure the height of the shadow. Then, move the
chalk away from the light source by another foot and measure
the height of the shadow. Keep moving the chalk by a foot and
each time measure the height of its shadow.
Continue to take such measurements till you reach midway from
the wall. Ask the students to calculate the proportion between
the distance of the chalk from the light source and the height of
its shadow. Now, ask them to estimate the height of the shadow,
based on the calculated proportion, if we keep moving the chalk
away from the light source. Verify the estimated height by
actually moving the chalk and measuring the height of the
shadow.
Supplemental
Activities
proportional quantities using graphs. They need to make two
graphs, one each for the directly proportional quantity and the
inversely proportional quantity. Then, they should bring the
graphs to the class and compare the shapes. These graphs
would typically look as follows:
Explain that if a graph shows a straight line passing through the
origin, then it depicts the direct proportion, while the hyperbolashaped graphs indicate the inverse proportion.
any other object using cardboard or clay. The model should be
proportional to the reference object. The students should explain
if the model construction involves the direct or inverse
proportion and state the exact proportion that they have used
while making the model.
Expected Outcome
Student
Deliverables
Assessment
proportions, there are other two types of proportions: compound
proportion and continued proportion. Explain them that the
proportion that involves two or more quantities is known as
compound proportion. While, two or more quantities are said to
be in a continued proportion if the 1st quantity is related to the
2nd quantity, which, in turn, is related to the 3rd quantity and so
on. Ask them to find out a few examples of these types of
proportions.
After completing the lesson, learners should be able to explain
the concepts of direct and inverse proportions. Additionally, they
should be able to use proportions to find the values that are
either directly or inversely proportional to each other.
None
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Linear Equations in One Variable
Time Alloted For
The Lesson
Prerequisite
Knowledge
This lesson is divided across four modules. It will be completed
in four class meetings.
Simple Equations: Class VII
Short Description
Of The Lesson
In this lesson, students will learn to solve linear equations in
one variable. In addition, students will use linear equations to
solve word problems. Moreover, they will learn to solve nonlinear equations by reducing such equations to a linear form.
Objectives
the transposition method or by
performing mathematical operations on both sides of the
equation
Aids
-linear equations by reducing them to linear
equations
Audio Visual Aids Relevant Modules from Teach Next
Procedure
-Linear Equations
Other Audio Visual Aids
Access the videos relevant to the lesson ‘Linear Equations in
One Variable’ from the Library resources.
Aids No technical
None
Teacher-Student Activities
A. Warm-up Session
Begin the lesson by writing down a few expressions and
equations on the board. Then, ask the students to identify the
equations and give reasons to support their answers.
Thereafter, lead into the lesson.
B. Presentation: Linear Equations in One Variable
In this activity, students will explain the concept of ‘linear
equations in one variable’.
Teacher’s Notes
Make a few chits and write down different types of equations
[equations in one variable, equations in two variable,
polynomials and so on] on each chit. Divide the class into small
groups and present a chit to each group. The groups have to
identify the equations in one variable and give reasons to
support their answers.
C. Group Activity: Find the Value of the Variable
In this activity, students will solve linear equations and find the
value of their variables.
Teacher’s Notes
Write down a few linear equations on the board. Form pairs of
students and ask them to find the value of the variable present
in the equation. The pair that gets maximum correct answers
will be declared the winner.
D. Solving Practical Problems on Equations
In this activity, students apply linear equations to solve word
problems.
Teacher’s Notes
Make a few chits and write a word problem on each one of
them. Add all chits into a bowl. Divide the class into small
groups. Ask a member from each group to pick up a chit from
the bowl and solve the word problem written on it. The group
that solves the problem in the shortest time will be declared the
winner.
Supplemental
Activities
Expected Outcome
Student
Deliverables
E. Solving Non-Linear Equations
In this activity, students will solve non-linear equations by
reducing them to linear equations.
Teacher’s Notes
Draw two columns on the board. On one side of the column,
write down four to five non-linear equations
Ask the students to research on how linear equations are
represented using graphs.
After studying this lesson, students will be able to solve linear
equations in one variable as well as use linear equations to
solve word problems. Moreover, they will also learn to solve
non-linear equations by reducing such equations to a linear
form.
None
Assessment
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Understanding Quadrilaterals
Time Alloted For
The Lesson
Prerequisite
Knowledge
Short Description
Of The Lesson
This lesson is divided across seven modules. It will be
completed in seven class meetings.
Basic Geometrical Ideas: Class VI Understanding Elementary
Shapes: Class VI Lines and Angles: Class VII Congruence of
Triangles: Class VII
In this lesson, students will be introduced to the various
geometrical shapes, such as polygons, quadrilaterals and
parallelograms. Moreover, students will also get acquainted with
the properties of different types of quadrilaterals and
parallelograms.
Objectives
number of sides
gon
a polygon
t to
its sides, diagonals and angles
parallelogram
parallelogram
Aids
rectangle and a parallelogram
Relevant Modules from Teach Next
Procedure
Other Audio Visual Aids
Access the videos relevant to the lesson ‘Understanding
Quadrilaterals’ from the Library resources.
Aids Non-Technical
None
Teacher-Student Activities
A. Warm-up Session
Ask students to observe their surroundings and cite the different
geometrical shapes visible to them. The students can also
observe their school building and note the various geometrical
shapes seen in the architecture. Thereafter, lead into the lesson.
B. Flash Card Activity
In this activity, students will identify the different polygons based
on the number of sides.
Teacher’s Notes
Draw/paste images of polygons with different number of sides on
flash cards. Display the flash cards one by one in the classroom.
Ask the students to name the polygons.
C. Group Activity: Making Polygons
In this activity, students will be asked to make different types of
polygons.
Teacher’s Notes
Divide the class into small groups. Ask each group to use ice
cream sticks to make the following types of polygons:
Thereafter, ask each group to explain as to why the shape is a
convex, concave, regular or an irregular polygon.
D. Group Activity: Quadrilaterals on a Graph Paper
In this activity, students will be asked to draw different types of
quadrilaterals.
Teacher’s Notes
On a graph paper, plot different types of quadrilaterals and note
down the x and y coordinates of their vertices.
Tip: You may refer to the image given here.
For instance, the coordinates of the vertices of the square at the
bottom-left side are as follows: (5,1), (7,1), (7,3) and (5,3)
In the next part of the activity, write the x and y coordinates of
the quadrilaterals on the board. Provide a graph paper to each
student and ask him/her to draw the quadrilaterals referring to
the coordinates given on the board. The students also need to
mention the name of the quadrilateral plotted on the graph
paper.
E. Properties of Quadrilaterals
In this activity, students will create a table detailing the properties
of different types of quadrilaterals.
Teacher’s Notes
Ask each student to create a table in their books detailing the
properties of the different types of quadrilaterals. A sample
format of the table is provided here
F. Problem Solving
In this activity, students will be asked to solve problems related
to different concepts taught in the lesson.
Lesson Closure
Close the lesson by drawing the following diagram on the board
Supplemental
Activities
Ask the students to explain the relationship between the different
geometrical figures by looking at the diagram.
Tell the students that geometrical shapes are the core of
tangram—a puzzle invented by the Chinese thousands of years
ago. This puzzle involves the use of seven geometrical shapes
to form a specific shape. However, the overlapping of these
seven shapes is not allowed. Ask the students to create their
tangrams.
Materials Required:
-shaped chart paper
Procedure:
Using a scissor, cut the chart paper into:
o 2 large right triangles
o 1 medium right triangle
o 2 small right triangles
o 1 square
o 1 parallelogram
Ensure that the cutouts do not overlap each other. Refer to the
image given here
Expected Outcome
After studying this lesson, students will be able to describe
various geometrical shapes, such as polygons, quadrilaterals
and parallelograms. Moreover, students will also be able to
explain the properties of different types of quadrilaterals and
parallelograms
Student
Deliverables
Assessment
Table on Properties of Quadrilaterals
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Exponents and Powers
Time Alloted For
The Lesson
This lesson is divided across three modules. It will be
completed in three class meetings.
Prerequisite
Knowledge
Short Description
Of The Lesson
Exponents and Powers: Class VII
In this lesson, learners will be introduced to the concept of
multiplicative inverse. They will learn to calculate the value of a
number with negative exponents. They will also verify if the
laws of exponents are applicable to the numbers with negative
exponents. Moreover, they will learn to compare the standard
forms of very small or very large numbers.
Objectives
umber with negative exponents
s are applicable to the numbers
with negative exponents
standard forms and vice versa
r very large
numbers
Aids
Relevant Modules from Teach Next
Procedure
Other Audio Visual Aids
Access the videos relevant to the chapter ‘Exponents and
Powers’ from the Library resources.
Aids No technical
None
Teacher-Student Activities
A. Warm-up Session
Begin the class by recalling the knowledge of students about
exponents and powers. The main points covered in Class VII
are as follows:
comparing numbers in their exponential forms
form
.
B. Find the Larger Number
In this activity, students will compare two numbers in their
exponential forms to find the larger number. They will also
discuss the concept of multiplicative inverse.
Teacher’s Notes
Divide the class into two groups and provide them worksheets
as follows. They need to put the greater than or the lesser than
sign between the numbers.
Once the activity is over, initiate a discussion on the concept of
multiplicative inverse. Give them a few numbers and ask them
to find their multiplicative inverse.
C. Writing Numbers in the Standard Form
In this activity, students will write a few very small numbers in
their standard form.
Teacher’s Notes
Give a few small numbers to students and ask them to write
these numbers in their standard forms. For example, you may
provide them with the following facts about the animal cells and
ask them to convert these small numbers into their standard
forms. Before converting numbers into their standard forms, they
need to convert the units from micrometre and nanometre to
metre (conversion scale: 1 micrometre = 10−6 metre and 1
nanometre = 10−9 metre). Cell Organelles
Approximate
Size
Cell Nucleus
5 to 10 micrometres
Nucleolus
1 micrometres
Nuclear Envelope
40 nanometres
Nuclear Pores
120 nanometres
Cell Membrane 6 to 7 nanometres
Ribosome
25 nanometres
Lysosome
200 to 400 nanometres
Golgi Complex 2500 nanometres
Supplemental
Activities
Ask the students rewrite the following numbers in their decimal
form:
-5
-9
-6
-9
-8
-7
-9
Expected Outcome
After completing the lesson, learners should be able to explain
the concept of multiplicative inverse. They should also be able
to calculate the value of a number with negative exponents.
They should also be able to verify if the laws of exponents are
applicable to the numbers with negative exponents.
Additionally, they should also be able to compare the standard
forms of very small or very large numbers.
Student
Deliverables
Assessment
Class Test, extra questions from refreshers and Teach Next
Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Mensuration
Time Alloted For
The Lesson
Prerequisite
Knowledge
Short Description
Of The Lesson
This lesson is divided across five modules. It will be completed in
five class meetings.
Area and Perimeter: Class V
Volume and Nets: Class V
Understanding Elementary Shapes: Class VI
Perimeter and Area: Class VII
Visualising Solid Shapes: Class VII
Visualising Solid Shapes: Class VIII
Understanding Quadrilaterals: Class VIII
In this lesson, students will learn to calculate the area of
quadrilaterals and polygons. They will also learn to calculate the
surface area and volume of solids, such as cubes, cuboids and
cylinders. Moreover, they will derive the formulae for calculating
the area of quadrilaterals and polygons and the surface area of
solids.
Objectives
area of quadrilaterals
parallelogram, rhombus and trapezium
trapezium
plain the method for calculating the area of polygons
the lateral surface area of cubes and cuboids
a
of cubes and cuboids
oblique cylinders
area and the total surface area of a cylinder
the total surface
area of a cylinder
Aids
volume
Relevant Modules from TeachNext
ce Area of Cubes and Cuboids
Procedure
Other Audio Visual Aids
Access the videos relevant to the chapter ‘Mensuration’ from the
Library resources.
Aids Non technical
None
Teacher-Student Activities
A. Warm-up Session
Begin the lesson by briefly recalling the prior knowledge of
learners about quadrilaterals, polygons and solids. Ask them
questions about the methods to calculate the area of squares,
rectangles and circles. Also, ask them about the classification of
polygons and the types of quadrilaterals. Finally, recall their
knowledge about the volume of solids and their nets.
B. Area of Quadrilaterals: Presentations and Activity
In this activity, students will make presentations on deriving the
formulae for calculating the area of quadrilaterals. They will also
calculate the area of quadrilaterals using these formulae.
Teacher’s Notes
Divide the class into three groups and ask them to make
presentations as follows:
a for calculating the area of
parallelograms.
rhombus.
trapezium.
Once the presentations are done, provide each group with a few
quadrilaterals, which are cut out from paper or cardboard. Ask
them to trace the outlines of the quadrilaterals on graph papers to
find their areas as shown here.
Then, they should use the formulae (derived in presentations) to
calculate the areas of the
Then, they should use the formulae (derived in presentations) to
calculate the areas of the same quadrilaterals. Ask them to
compare the areas that they have obtained by these two
methods.
C. Area of Polygons: Activity
In this activity, students will calculate the areas of various
polygons.
Teacher’s Notes
Cut out different polygons from paper or cardboard and write the
required measurements on them. Make multiple copies of each
polygon. Divide the class into a few groups and distribute a copy
of each polygon to all the groups. Each group needs to figure out
the simplest way to calculate the area of each polygon by dividing
it into triangles and quadrilaterals and then adding up the area of
all these triangles and quadrilaterals.
D. Surface Area and Volume of Solids
In this activity, students will calculate the surface area of solids.
They will also make presentations on deriving the formulae for
calculating the surface area of solids. Moreover, they will
calculate the volume of solids.
Teacher’s Notes
Bring a few cartons that are shaped like a cube, cuboid and
cylinder in the class. Ask the students to cut open the cartons on
all sides to make a flat two-dimensional shape (the net of the
three-dimensional solid). Then, they should measure the
dimensions of rectangles, squares and/or circles in these nets
and calculate their areas. Alternatively, they may also trace the
outlines of the nets on graph paper to calculate their area. Then,
they should add up the areas of rectangles, squares and/or
circles in the nets to find the surface area of the solid.
Now, divide the class into two groups and ask each group to
make presentations as follows:
and the lateral surface area of cubes and cuboids.
Supplemental
Activities
area and the total surface area of cylinders.
Now, they should calculate the total surface area and the lateral
surface area of cartons by using these formulae. Ask the
students to compare the answers obtained by the two methods.
Ask the students to do the following activities:
uch as cubes, cuboids and cylinders.
Bring these solids to the classroom and exchange them with
classmates. Calculate the surface area and the volume of the
solids that you have received.
your classmates to calculate the areas of these polygons by
using the triangulation method. Here is an example of the image
of a polygon as well as the same image after it has been divided
into smaller triangles (using the triangulation method). Adding up
the area of smaller triangles will give the total area of the
polygon.
Expected
Outcome
After completing the lesson, learners should be able to calculate
the area of quadrilaterals and polygons. They should also be able
to calculate the surface area and the
volume of solids, such
After completing the lesson, learners should be able to calculate
the area of quadrilaterals and polygons. They should also be able
to calculate the surface area and the volume of solids, such as
cubes, cuboids and cylinders. Moreover, they should be able to
derive the formulae for calculating the area of quadrilaterals and
polygons and the surface area of solids.
Student
Deliverables
quadrilaterals
of solids
Class Test, extra questions from refreshers and Teach Next
Module.
Assessment
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Visualising Solid Shapes
Time Alloted
For The
Lesson
Prerequisite
Knowledge
Short
Description Of
The Lesson
Objectives
This lesson is divided across three modules. It will be completed in
three class meetings.
Visualising Solid Shapes: Class VII
In this lesson, learners will study to recognise two-dimensional and
three-dimensional objects. They will learn about the different views of
three-dimensional objects. They will also learn about maps and the
differences between a map and a picture. Further, they will study
about polyhedrons and the Euler’s formula.
dimensional object
te between a picture and a map
different objects
rify Euler’s formula for the given solids
Aids
Procedure
Relevant Modules from Teach Next
-Dimensional Shapes
Audio Visual Aids
Access the videos relevant to the lesson ‘Visualising Solid Shapes’
from the Library resources.
Aids Nontechnical
None
Teacher-Student Activities
A. Warm-up Session
Begin the lesson with a simple activity to help students recall two and
three-dimensional objects.
Teacher’s Notes
Get a few two-dimensional and three-dimensional objects to the
classroom and ask the students to recognise these objects.
You can also call a few students and ask them to draw threedimensional shapes (cube, cuboid, cylinder and so on) on the board,
name the shapes and recognise the two-dimensional shapes in them.
Additionally, present the students with a few nested shapes and ask
them to recognise the shapes in them.
B. Viewing Three-Dimensional Shapes
In this activity, students will be given various three-dimensional
objects and they need to draw the front, side and top views of these
objects.
Teacher’s Notes
Talk to the students about perspective and how objects look different
when viewed from different positions and angles.
Then, divide the students into groups of around four students in each
group. Get a few three-dimensional objects to the classroom and
present each group with an object. Now, ask each student of a group
to draw the three views of the object. Once a group is done with
drawing the views, exchange the object with another group. Some of
the objects that can be brought to the classroom are toys of different
shapes, flower vase, bowl, old mobile, computer mouse, photo frame,
alarm clock and so on.
C. Map Activity
In this activity, students need to interpret a map and draw a map using
proper scale and symbols.
Teacher’s Notes
Begin the activity by drawing a simple picture of the classroom on one
side of the board and a simple map of the classroom using symbols
on the other side. Discuss the differences between the two and the
advantages of a map over a picture.
You can also get an atlas to the classroom and show the students
different types of maps drawn to different scales. Also, present maps
like the agricultural or the mineral map of a state and ask the students
to interpret these maps.
Thereafter, assign a project on a map creation. Ask each student to
draw a map of their locality on a chart paper. The map should be
drawn to scale using symbols and appropriate labels.
D. Flashcard Activity - Polyhedron
In this activity, students need to identify if a given three-dimensional
shape is a polyhedron. If it is a polyhedron, ask them to categorise the
polyhedron as convex or non-convex, regular or non-regular and as a
prism or a pyramid.
Teacher’s Notes
Explain the concept of polyhedrons and non-polyhedrons to the
students with the help of images. Also, talk about prisms, pyramids,
convex, non-convex, regular and non-regular polyhedrons. Show
images for all types of polyhedrons.
Create flashcards with the images of non-polyhedrons and the
different types of polyhedrons on them. Divide the class into a few
groups. Pick out a flashcard and show it to a group. Ask the students
to identify if the image on the card is that of a polyhedron. If it is a
polyhedron, ask the students to categorise the polyhedron as convex
or non-convex, regular or non-regular and as a prism or a pyramid.
E. Activity for Euler’s Formula
In this activity, students will have to verify the Euler’s formula for a
given polyhedron. They also need to verify if a given threedimensional shape is a polyhedron using the Euler’s formula.
Teacher’s Notes
For this activity, you can make use of the flashcards used in the
previous activity. Show the images of the polyhedrons one by one to
the students and ask them to verify the Euler’s formula for each
polyhedron.
You can also draw a few three-dimensional solids on the board and
ask the students to verify if these solids are polyhedrons by using the
Euler’s formula.
Supplemental
Activities
Ask the students to create 3-D paper models of different polyhedrons.
The students need to first create the net of a polyhedron and then join
it to create the polyhedron. Once done, ask them to verify the Euler’s
formula.
The nets for some of the polyhedrons are as shown
Expected
Outcome
After studying this lesson, the learners will be able to recognise twodimensional and three-dimensional objects. They must be able to
draw the different views of three-dimensional objects. They will also
be able to draw and interpret maps and cite the differences between a
map and a picture. Further, they will be able to identify the different
types of polyhedrons and verify the Euler’s formula.
Student
Deliverables
Assessment
Class Test, extra questions from refreshers and Teach Next Module.
AIR FORCE SCHOOL HASIMARA
Lesson Plan
Board: CBSE | Class: VIII| Subject: Maths
Chapter Name: Comparing Quantities
Time Alloted For
The Lesson
This lesson is divided across six modules. It will be completed in
six class meetings.
Prerequisite
Knowledge
Short Description
Of The Lesson
Comparing Quantities: Class VII
In this lesson, learners will learn to compare quantities using
ratios and percentages. They will also learn to calculate the
change in percentage of a quantity. They will be taught about
the concepts of discount, overhead charges, profit, loss, sales
tax, value added tax, compound interest and conversion period.
Moreover, they will be explained the method to derive the
compound interest formula and calculate the compound interest
for different conversion periods using this formula.
Objectives
percentages
profit and loss
late profit or loss and its percentage
or VAT
tax) or the final price of the item when the other two
figures are known
plain the difference between simple interest and
compound interest
calculation
compound interest formula
conversion periods
calculations
Aids
Relevant Modules from TeachNext
Procedure
Other Audio Visual Aids
Access the videos relevant to the chapter ‘Comparing
Quantities’ from the Library resources.
Aids Nontechnical
None
Teacher-Student Activities
A. Warm-up Session
Begin the class by recalling students’ knowledge about
comparison of quantities. Ask them a few questions on
comparing quantities using ratios and proportions. Then, lead
into the lesson.
After the warm-up session, play all modules in Teach Next.
B. Discounts and Profit: Game
In this activity, students will apply their knowledge of
percentages, profit, loss and discounts. This activity is similar to
the activity that they had participated in the previous class.
Teacher’s Notes
The instructions for the game are as follows.
Set up shops: Set up different ‘shops’ in your classroom. These
shops should sell different items that consumers typically buy in
a market, such as clothes, shoes, bags, groceries, electronic
goods and home appliances. Students should cut out the
pictures of such items from newspaper advertisements and use
them as ‘goods’. Use ‘play money’ as currency. In case, ‘play
money’ is not available, you may create currency notes of
different denominations from paper or cardboard and use them
as ‘play money’. A few students should run shops and others
should be consumers.
Decide the prices: The shopkeepers need to attach price tags
to each item they are selling. For example, the price of a bag
can be Rs 300. One item should be kept in multiple shops and
each shop owner has the freedom to fix its price. You need to
help all shopkeepers to come up with very close prices so that
selecting the cheapest deal becomes a bit challenging for
consumers. You also need to decide the cost price for each
item. The shopkeepers need to take care that the selling price is
more than the cost price so that they can make profit.
Declare discounts: Shopkeepers can declare discounts on a
few items in their shops. For example, they can declare that
their customers would get 25% concession on a bag worth Rs
300. The shopkeepers need to ensure that the selling price after
concessions is more than the cost price (or they would incur
loss).
Start the business: Now, the game setup is ready and it is the
time to start the business. Consumers must visit different shops
and buy items from the shops that are selling them at the
cheapest prices. They have freedom to decide what they are
going to buy and in what quantity. However, they need to
exhaust all ‘play money’ given to them (or as much as possible).
Game over: Once the activity is over, check who has bought
items at the cheapest price. Also, ask the shopkeepers to
calculate their profit or loss. Based on these figures, explain to
consumers and shopkeepers how they could have done better.
Tip: Limit the number of items in shops to minimum as too many
items would make the activity very complex for the students.
C. Activity: VAT
In this activity, students will calculate the original price of the
item, VAT (or sales tax) or the final price after adding VAT (or
sales tax) when the other two figures are known.
Teacher’s Notes
Ask students to get various bills from the home. The bills should
have the following numbers mentioned on them:
Supplemental
Activities
Expected Outcome
Student
Deliverables
Assessment
Ask the students to do the following activities:
services. Make a chart with the images for the items and the
rate of VAT against each image. Arrange the images on the
chart paper in the ascending order of VAT rate.
ts to make a table with two columns:
Conversion Period and Amount after One Year. The principal is
Rs 10,000 and the rate of interest is 6%. The answer is provided
here.
Conversion Period
Amount after One
Year (Rs)
1 (yearly)
10600.00
2 (half-yearly)
10609.00
4 (quarterly)
10613.64
12 (monthly)
10616.78
52 (weekly)
10618.00
365 (daily)
10618.31
After studying the lesson the student will be able to know the
difference between simple interest and compound interest and
to calculate simple and compound interest easily.
None
Class Test, extra questions from refreshers and Teach Next
Module.