Pushpalata British International School
Mathematics Lesson Plan for Grade 07 by Brindha Yogananth
2024 – 25 – Term 3 - Week 13 [24-03-2025 and 25-03-2025]
Geometry: Surface area of 3D shapes
Session Duration: 80min
Framework Codes and Descriptions:
9Gg.05 Use knowledge of area, and properties of cubes, cuboids, triangular prisms, pyramids and
cylinders to calculate their surface area.
Learning Objectives: Children will be able to
Action: calculate the surface area
Criteria: for various 3D shapes
Condition: using the knowledge of area and geometric properties
Class Organisation: Group
Required Resources:
Teaching Learning Activities:
Motivation:
Imagine you are designing a new toy box for your younger sibling. How would you ensure it fits
perfectly in the corner of your room? Understanding the surface area of different shapes can help
you design it efficiently! Answers will be discussed.
Teacher Explanation On The Topic:

For cubes, we will use a dice as an example, discussing how each face contributes to the total
surface area.
 For cuboids, we can use a shoebox to illustrate how to calculate the surface area by measuring
its length, width, and height.
 Triangular prisms can be represented by a tent, where we will calculate the surface area
needed for fabric.
 For pyramids, we can use the example of a pyramid-shaped cake, discussing how to find the
surface area for icing.
 Cylinders can be illustrated using a water bottle, where we will calculate the surface area to
understand how much label space is available.
I shall explain that surface area is the total area of the outside surfaces, while volume measures how
much space is inside.
Students might think all shapes have the same formula for surface area. I shall provide a chart
comparing the formulas for each shape to clarify the differences.
Some students may struggle with applying the formulas correctly.
We will work through examples together step-by-step to ensure understanding.
Students may forget to include all faces of a shape when calculating surface area. I shall emphasize
the importance of counting all faces and provide a checklist.
Students might not see the relevance of surface area in real life. I shall share stories of local artisans
who use these calculations in their work.
Key Points:


Surface area is always measured in square units (e.g., cm², m², in²).
Understanding the "net" of each shape (how it would look unfolded) can be very helpful in
visualizing and calculating surface area.
Possible misconceptions that will discussed:
Learners can be supported to identify plane symmetry by asking them to imagine a mirror being sliced
through the shape. For the cross shape, learners can initially focus on the front face, for which they
should identify four lines of symmetry, which will translate into four planes of symmetry. I shall remind
learners that there is also one plane of symmetry halfway along the prism’s length, perpendicular to
the other planes of symmetry, as this often gets overlooked.
Activity:
Think like mathematician topic from Book will be discussed.
Evaluation:
Homework:
Homework will be assigned from WB.
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Pushpalata British International School
Mathematics Lesson Plan for Grade 07 by Brindha Yogananth
2024 – 25 – Term 3 - Week 13 [26-03-2025 and 27-03-2025]
Numbers: Rational and Irrational
Session Duration: 80min
Framework Codes and Descriptions:
9Ni.01 Understand the difference between rational and irrational numbers.
Learning Objectives: Children will be able to
Action: classify given numbers as either rational or irrational.
Criteria: with the knowledge of terminating/repeating decimals vs. non-terminating/non-repeating
decimals
Condition: given some rational or irrational numbers
Class Organisation: Group
Required Resources:
Teaching Learning Activities:
Motivation:
I shall start by asking,


What is three squared?
What is the cube root of 64?
Answers will be discussed.
Then,
 What is the square root of 19?
 How could you estimate the answer?
Learners should realise that the answer will not be a whole number, since 19 is not a square
number. I shall proceed by introducing surd.
Recollection of Prior knowledge: pi
Teacher Explanation on The Topic:
Establish that √19 is irrational. They should recognise that √19 lies between 4 and 5, since 19 lies
between 42 and 52. Introduce the term surd, explaining that when we cannot simplify a number to
remove a square or cube (or other) root, then it is called a surd.
Rational numbers are numbers that can be expressed as a fraction of two integers, while irrational
numbers cannot be expressed in this way.
For example, 1/2 is rational, but √2 is irrational. We will explore these definitions, their properties,
and how to identify them in real-life situations.
Examples
1/3 is a rational number because it can be expressed as a fraction.
The number π (pi) is irrational because it cannot be expressed as a simple fraction.
0.75 is rational because it can be written as 3/4.
The square root of 3 is irrational because it cannot be expressed as a fraction.
Numbers like 2, -5, and 0 are all rational because they can be expressed as fractions (2/1, -5/1, 0/1).
Potential Misunderstandings
Students may think that all decimals are irrational.
 I shall explain that decimals can be rational if they terminate or repeat, like 0.333... (1/3) or
0.5 (1/2).
Some students may confuse irrational numbers with large numbers.
 I shall clarify that irrational numbers are not defined by their size but by their inability to be
expressed as fractions.
Students might think that all fractions are rational.
 I shall Discuss that fractions with non-integer values in the numerator or denominator can
still be rational.
Students may believe that all whole numbers are rational.
 I shall explain that whole numbers can be expressed as fractions (e.g., 5 = 5/1).
Students might think that irrational numbers are not useful in real life.
 I shall provide examples of how irrational numbers appear in nature, such as in
measurements of circles.
I shall remind learners that a rational number is a number that can be made by dividing an integer by
an integer. They should understand that if a number is not rational then it is irrational.
I shall ensure learners understand that some roots (e.g. √2, √3, √5) are irrational but some roots are
rational (e.g. √4 is rational as it is equal to 2). Also shall ensure learners understand that π is an
example of an irrational number.
Possible solutions to be given as notes:
 rational ÷ rational
always rational

irrational + rational
always irrational

irrational + irrational
always irrational

irrational ÷ rational
always irrational

irrational ÷ irrational
π ÷ π is rational
π ÷ √2 is irrational

irrational  irrational
√2  √2 is rational
π  π is irrational
Activity:
LB HOTS questions will be discussed.
Here is a decimal: 5.020 020 002 000 020 000 020 000 002…
Arun says:
Are the following statements true or false?
1. Is Arun correct? Give a reason for your answer.
2. Compare your answer with a partner’s. Do you agree? If not, who is correct?
3.



Are these true or false?
The sum of two integers is always an integer.
The sum of two rational numbers is always a rational number.
The sum of two irrational numbers is always an irrational number.
4. Here is a calculator answer: 3.646 153 846
The answer is rounded to 9 decimal places.
Can you decide whether the number is rational or irrational?
Without using a calculator, find an irrational number between
4 and 5
Evaluation:
Without using a calculator, estimate
a.
√190 to the nearest integer
b.
∛190 to the nearest integer.
2. find
where N is a positive integer.
3.
Homework:
Homework will be assigned from WB.
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Pushpalata British International School
Mathematics Lesson Plan for Grade 07 by Brindha Yogananth
2024 – 25 – Term 3 - Week 13 [28-03-2025]
Numbers: Rational and Irrational
Session Duration: 40min
Framework Codes and Descriptions:
9Ni.01 Understand the difference between rational and irrational numbers.
Learning Objectives: Children will be able to
Action: classify given numbers as either rational or irrational.
Criteria: with the knowledge of terminating/repeating decimals vs. non-terminating/non-repeating
decimals
Condition: given some rational or irrational numbers
Class Organisation: Group
Required Resources:
Teaching Learning Activities:
Activity:
Three WB HOTS question will be discussed.
Homework:
Home work will be assigned from WB
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