Mathematics - Junior Secondary 3

TERM: 2^ND TERM

WEEK 5
Class: Junior Secondary School 3
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Geometry II
Focus: Calculating Lengths, Areas, and Volume of Similar Figures
SPECIFIC OBJECTIVES:
By the end of the lesson, pupils should be able to:

Identify similar figures.
Understand the relationship between the corresponding sides and angles of similar figures.
Calculate lengths, areas, and volumes of similar figures using proportionality.
Solve problems on similar figures and apply in real-life situations.
INSTRUCTIONAL TECHNIQUES:
Question and answer
• Guided demonstration
• Discussion
• Real-life application
• Problem-solving exercises
INSTRUCTIONAL MATERIALS:
• Geometric shapes (physical or drawn)
• Graph paper
• Whiteboard and marker
• Ruler
• Calculators (optional)

PERIOD 1 & 2: Identifying Similar Figures and Proportionality
PRESENTATION:

Step	Teacher’s Activity	Pupil’s Activity
Step 1 - Introduction	Explains the concept of similar figures, focusing on the proportionality of sides.	Pupils listen and ask questions.
Step 2 - Explanation	Defines the relationship between similar figures and their corresponding angles and sides. Demonstrates with examples.	Pupils observe and ask questions for clarification.
Step 3 - Demonstration	Uses two similar triangles (drawn or models) to compare their corresponding sides and angles.	Pupils identify the similarities and calculate the missing sides using proportions.
Step 4 - Practice	Guides pupils in solving problems on proportionality in similar figures.	Pupils solve practice problems individually.

NOTE ON BOARD:

Two figures are similar if their corresponding angles are equal and the lengths of corresponding sides are proportional.
Formula for similarity: side 1 = side 3

Side 2 = side 4

EVALUATION (5 exercises):

Given two similar triangles with sides 5 cm, 8 cm, and 10 cm, find the missing side if the other corresponding side is 6 cm.
If two similar squares have a ratio of 3:4, and one side of the smaller square is 12 cm, what is the side of the larger square?
Determine the missing side of two similar rectangles if the sides are 2:3 and one side is 5 cm.
Two similar triangles have corresponding areas of 25 cm² and 36 cm². Find the ratio of their sides.
Calculate the missing side of a similar figure with given proportional sides of 7 cm and 9 cm.

CLASSWORK (5 questions):

If two triangles are similar and their corresponding sides are in the ratio 2:3, find the missing side if one side of the smaller triangle is 6 cm.
Two similar circles have areas of 100 cm² and 144 cm². Find the ratio of their radii.
If two cubes have a volume ratio of 8:27, find the ratio of their corresponding sides.
Given two similar trapeziums with areas in the ratio 1:4, find the ratio of their corresponding sides.
Calculate the length of the second side of a rectangle if the first side is 10 cm and the sides are in a ratio of 3:5.

ASSIGNMENT (5 tasks):

Solve for the missing side of two similar rectangles with given dimensions.
Draw two similar triangles and label their sides.
If two similar cylinders have volumes in the ratio 8:27, find the ratio of their heights.
Solve a problem on proportionality involving similar figures in a real-life situation.
Calculate the area of two similar rectangles given the ratio of their sides.

PERIOD 3 & 4: Calculating Areas and Volumes of Similar Figures
PRESENTATION:

Step	Teacher’s Activity	Pupil’s Activity
Step 1 - Introduction	Reviews the formula for the area and volume of geometric shapes. Introduces the concept of scaling areas and volumes of similar figures.	Pupils listen and ask questions.
Step 2 - Explanation	Explains how the area and volume of similar figures scale. Uses examples to show that areas scale by the square of the ratio and volumes by the cube.	Pupils observe and take notes.
Step 3 - Demonstration	Demonstrates with two similar spheres and cubes how to calculate their areas and volumes using proportionality.	Pupils follow along and ask questions.
Step 4 - Practice	Leads pupils through practice problems calculating areas and volumes of similar shapes.	Pupils solve examples and ask for clarification if needed.

NOTE ON BOARD:

Area ratio: (side1side2)2\left(\frac{side_1}{side_2}\right)^2
Volume ratio: (side1side2)3\left(\frac{side_1}{side_2}\right)^3

EVALUATION (5 exercises):

Two similar rectangles have lengths of 4 cm and 6 cm. Find the ratio of their areas.
The ratio of the sides of two similar cubes is 2:3. What is the ratio of their volumes?
Calculate the area of two similar triangles with a side ratio of 3:5 and an area of 27 cm² for the smaller triangle.
Two similar cylinders have radii of 4 cm and 6 cm. Find the ratio of their areas.
The ratio of volumes of two similar spheres is 8:27. Find the ratio of their radii.

CLASSWORK (5 questions):

If the ratio of the sides of two similar cones is 1:4, find the ratio of their volumes.
Given two similar rectangles with areas of 40 cm² and 100 cm², find the ratio of their corresponding sides.
Calculate the area of two similar squares if the ratio of their sides is 2:3.
A cylinder and a cone are similar. If the radius of the cylinder is 3 cm and the volume is 90 cm³, calculate the volume of the cone with a radius of 5 cm.
Given two similar circles with radii of 2 cm and 5 cm, find the ratio of their areas.

ASSIGNMENT (5 tasks):

Calculate the areas and volumes of two similar pyramids with given side lengths.
Solve a problem involving the scaling of areas in real-life situations (e.g., maps, blueprints).
Find the volume of a similar object if the original volume and scaling ratio are known.
Draw two similar three-dimensional objects and calculate their areas and volumes.
Solve a real-world problem involving similar shapes and their areas/volumes.

PERIOD 5: Application of Similar Figures to Life Situations
PRESENTATION:

Step	Teacher’s Activity	Pupil’s Activity
Step 1 - Introduction	Introduces real-life applications of similar figures in fields such as architecture, engineering, and art.	Pupils listen and ask questions.
Step 2 - Examples	Provides examples of real-life problems where similar figures are applied.	Pupils discuss and identify similar figures in the examples.
Step 3 - Problem-Solving	Guides pupils through solving problems where they use similar figures to find solutions to life situations.	Pupils work on problems individually or in groups.
Step 4 - Review	Summarizes the importance of understanding similar figures in practical applications.	Pupils participate in the review discussion.

EVALUATION (5 exercises):

A model of a building is made using similar figures. If the height of the model is 2 m, and the height of the real building is 50 m, find the scale ratio.
A triangular park has sides 20 m, 30 m, and 40 m. If it is similar to another park with sides 10 m, 15 m, and 20 m, find the scale factor of the areas.
Solve a problem on finding the volume of a similar-shaped container when the dimensions of the original container are given.
Use a real-life example to show how similar figures help architects in scaling down designs for models.
Create a word problem using similar figures and solve it.

CLASSWORK (5 tasks):

A statue of a bird is made in the ratio of 1:5. If the model’s wingspan is 50 cm, what is the wingspan of the real bird?
Two similar bridges have lengths of 100 m and 200 m. Find the area ratio if the height ratio is 1:2.
Find the volume of a container made from a similar model with a scale of 1:3.
Use a real-world example to apply the concept of similar figures in architecture.
Solve a problem involving similar figures in a map to find actual distances.

ASSIGNMENT (5 tasks):

Create and solve a problem involving the use of similar figures in a construction project.
Calculate the area of a room using similar figures based on a floor plan.
Solve a problem on the scaling of distances between two cities using a map’s scale.
Apply the concept of similar figures to find

the dimensions of a similar model.
5. Draw and solve a problem using similar figures in designing a park or garden.

Mathematics - Junior Secondary 3 - Geometry II