Mathematics - Junior Secondary 1 - Three-Dimensional Shapes

Three-Dimensional Shapes

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TERM: 3RD TERM

WEEK 5
Class: Junior Secondary School 1
Age: 12 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Three-Dimensional Shapes
Focus: Basic properties of cylinders and spheres, Volume of cubes and cuboids

SPECIFIC OBJECTIVES:
By the end of the lesson, pupils should be able to:

  1. Identify and describe the basic properties of cylinders and spheres.
  2. Calculate the volume of cubes and cuboids.
  3. Understand the difference between three-dimensional shapes and their two-dimensional counterparts.
  4. Apply the formulae for volume of cubes and cuboids in real-life situations.
  5. Recognize the properties of 3D shapes in everyday objects.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Hands-on activities
  • Problem-solving exercises

INSTRUCTIONAL MATERIALS:

  • Models of cylinders and spheres
  • Measuring tapes
  • Calculators
  • Whiteboard and markers
  • Cubes and cuboid shapes for hands-on activities

PERIOD 1 & 2: Basic Properties of Cylinders and Spheres

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces cylinders and spheres. Shows models of each.

Pupils observe and ask questions about the shapes.

Step 2 - Explanation

Discusses the properties of cylinders (e.g., two circular faces, curved surface) and spheres (e.g., no edges, all points on the surface are equidistant from the center).

Pupils listen and take notes on the properties.

Step 3 - Demonstration

Uses models to explain the 3D nature of cylinders and spheres.

Pupils touch and observe models to understand the properties.

Step 4 - Note Taking

Writes key properties on the board for students to copy.

Pupils take notes on the properties of each shape.

NOTE ON BOARD:

  • Cylinder: 2 circular faces, curved surface, height
  • Sphere: No edges, all points equidistant from the center

EVALUATION (5 exercises):

  1. Identify the shape that has no edges.
  2. Which shape has two circular faces?
  3. Draw a cylinder and label its parts (faces, height, radius).
  4. Draw a sphere and label its properties.
  5. Explain how a cylinder is different from a sphere.

CLASSWORK (5 questions):

  1. Name a real-life object that is a cylinder.
  2. Name a real-life object that is a sphere.
  3. Describe the surface area of a sphere.
  4. What are the properties of a cylinder?
  5. Identify the shape of a basketball.

ASSIGNMENT (5 tasks):

  1. Find a cylindrical object around the house. Describe its properties.
  2. Find a spherical object. How is it similar to a sphere in geometry?
  3. Compare the properties of cylinders and spheres.
  4. Identify the height and radius of a cylindrical object.
  5. Draw a diagram of a sphere and label its features.

 

PERIOD 3 & 4: Volume of Cubes and Cuboids

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces the formulae for volume of cubes and cuboids.

Pupils listen and take notes on the formulae.

Step 2 - Explanation

Explains that volume = length × width × height for cuboids and the formula for a cube is volume = side³.

Pupils observe and ask questions for clarification.

Step 3 - Demonstration

Solves examples on the board using different values for cubes and cuboids.

Pupils solve similar problems with guidance.

Step 4 - Note Taking

Teacher writes examples and formulae on the board.

Pupils copy and solve additional problems.

NOTE ON BOARD:

  • Volume of a Cube = side³
  • Volume of a Cuboid = length × width × height
    Example:
    For a cube with side = 5 cm, Volume = 5³ = 125 cm³
    For a cuboid with length = 6 cm, width = 4 cm, height = 3 cm, Volume = 6 × 4 × 3 = 72 cm³

EVALUATION (5 exercises):

  1. Find the volume of a cube with side length 7 cm.
  2. Find the volume of a cuboid with dimensions 3 cm × 2 cm × 5 cm.
  3. Calculate the volume of a cube with side length 10 cm.
  4. What is the volume of a cuboid with dimensions 4 cm × 4 cm × 4 cm?
  5. A cube has a volume of 512 cm³. What is the length of one side?

CLASSWORK (5 questions):

  1. What is the volume of a cuboid with length = 8 cm, width = 2 cm, and height = 4 cm?
  2. A cube has a side length of 6 cm. Find its volume.
  3. A cuboid has dimensions 5 cm × 3 cm × 10 cm. What is its volume?
  4. Calculate the volume of a cube with side length 2.5 cm.
  5. A cuboid has a volume of 120 cm³. If its height is 5 cm, what are the length and width?

ASSIGNMENT (5 tasks):

  1. Calculate the volume of a box (cuboid) in your house using the formula.
  2. Find the volume of a cube with side length 12 cm.
  3. Create your own cuboid with specific dimensions and find its volume.
  4. Calculate the volume of a cube if the side length is doubled.
  5. Draw a diagram of a cuboid and a cube and label the dimensions.

PERIOD 5: Application to Real Life

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Discusses the real-life applications of volume and shapes.

Pupils listen and reflect on real-world examples.

Step 2 - Examples

Provides examples such as packaging, shipping, and construction.

Pupils identify objects around them that relate to cubes and cuboids.

Step 3 - Drill

Pupils solve real-life problems based on volume and shapes.

Pupils solve the problems and discuss their solutions.

EVALUATION (5 questions):

  1. How can the volume of a box affect its capacity to hold items?
  2. Where might the volume of a cylinder be important?
  3. How does the volume of a cube relate to its size?
  4. Why is the volume of a cuboid important in construction?
  5. How do you use volume to calculate the amount of liquid a container can hold?

CLASSWORK (5 tasks):

  1. Calculate the volume of a gift box (cuboid).
  2. How much space is needed to pack 10 cubes of 5 cm each?
  3. Find the volume of a cylindrical can.
  4. How would you calculate the volume of a swimming pool (cuboid)?
  5. A small rectangular container holds 30 liters of water. Find its volume in cubic meters.

ASSIGNMENT (5 tasks):

  1. Calculate the volume of a refrigerator (cuboid) at home.
  2. Find the volume of a spherical ball.
  3. Write a paragraph explaining the real-life importance of volume.
  4. Calculate how many spheres of a given volume fit into a cuboid.

Use a formula for the volume of a cuboid to find out how many books can fit in a shelf.