Volume and Capacity Mathematics Primary 5 Second Term Lesson Notes Week 10

Subject: Mathematics

Class: Primary 5

Term: Second Term

Week: 10

Topic: Volume and Capacity

Sub-topic: Meaning, How to Calculate, Worked Out Examples

Duration: 45 minutes

Entry Behaviour: Students should be able to identify basic shapes and understand basic measurement concepts.

Key Words: Volume, capacity, cubic units, liters, milliliters, calculate, rectangular prism, cylinder, jug, bottle.

Behavioural Objectives: By the end of the lesson, students should be able to:

1. Define volume and capacity.
2. Calculate the volume of basic shapes such as rectangular prisms and cylinders.
3. Understand the concept of capacity and apply it to real-life situations.

Embedded Core Skills: Problem-solving, critical thinking, measurement.

Learning Materials:

• Lagos State Scheme of Work for Mathematics
• Mathematics Textbook Book 5
• Chalkboard/Whiteboard and markers
• Objects representing shapes (e.g., cubes, rectangular prisms)
• Measuring jug
• Empty bottles and containers
• Worksheets with examples

Content:

Volume and Capacity 📏

1. Meaning:
   • Volume: Volume is the amount of space occupied by a three-dimensional object. It is measured in cubic units such as cubic centimeters (cm³) or cubic meters (m³).
   • Capacity: Capacity is the maximum amount that something can hold. It is measured in units like liters (L) or milliliters (mL).
2. How to Calculate:
   • Volume: To calculate the volume of a shape, multiply the length, width, and height together.
     • Example: The volume of a cube with sides of 3 cm is 3 cm × 3 cm × 3 cm = 27 cm³.
   • Capacity: To find the capacity of a container, pour in water and measure how much it holds.
     • Example: A jug can hold 1 liter of water.
3. Worked Out Examples:
   • Volume Example: Find the volume of a rectangular prism with length 5 cm, width 2 cm, and height 4 cm.
     • Volume = length × width × height
     • Volume = 5 cm × 2 cm × 4 cm = 40 cm³
   • Capacity Example: If a bottle can hold 500 mL of juice, how many bottles are needed to hold 2 liters?
     • 1 liter = 1000 mL
     • Number of bottles = 2000 mL ÷ 500 mL = 4 bottles

Remember, volume is about how much space an object takes up, while capacity is about how much a container can hold! 📦💧

Measuring the volume of a cube or cuboid using a formula is another way to find the amount of space inside a 3D shape.

1. The formula for finding the volume of a cube is V = s^3, where s is the length of one side of the cube. For example, a cube that measures 5cm on each side has a volume of 5^3 = 125 cubic cm.
2. The formula for finding the volume of a cuboid is V = l x w x h, where l is the length, w is the width, and h is the height. For example, a rectangular shaped box that measures 10cm x 8cm x 6cm has a volume of 10 x 8 x 6 = 480 cubic cm.
3. The formula for finding the volume of a cylinder is V = πr²h, where r is the radius of the base, h is the height and π is a mathematical constant. For example, a cylinder that measures a radius of 3cm and a height of 6cm has a volume of 3.14 x 3² x 6 = 113.09 cubic cm.
4. The formula for finding the volume of a sphere is V = 4/3 x π x r³, where r is the radius of the sphere and π is a mathematical constant. For example, a sphere that measures a radius of 4cm has a volume of 4/3 x 3.14 x 4³ = 268.08 cubic cm.
5. The formula for finding the volume of a triangular prism is V = b x h x l, where b is the base, h is the height, and l is the length. For example, a triangular prism that measures 8cm x 6cm x 4cm has a volume of 8 x 6 x 4 = 192 cubic cm.

Evaluation

1. What is the formula for finding the volume of a cube? a) V = s^3 b) V = l x w x h c) V = πr²h d) V = 4/3 x π x r³
2. What is the formula for finding the volume of a cuboid? a) V = s^3 b) V = l x w x h c) V = πr²h d) V = 4/3 x π x r³
3. How do you find the volume of a cylinder? a) V = s^3 b) V = l x w x h c) V = πr²h d) V = 4/3 x π x r³
4. How do you find the volume of a sphere? a) V = s^3 b) V = l x w x h c) V = πr²h d) V = 4/3 x π x r³
5. How do you find the volume of a triangular prism? a) V = b x h x l b) V = l x w x h c) V = πr²h d) V = 4/3 x π x r³
6. What is the volume of a cube with side length of 4cm? a) 12 cubic cm b) 16 cubic cm c) 64 cubic cm d) 128 cubic cm
7. A rectangular shaped box measures 8cm x 6cm x 4cm, what is its volume? a) 24 cubic cm b) 32 cubic cm c) 48 cubic cm d) 192 cubic cm
8. A cylinder has a radius of 2cm and a height of 3cm, what is its volume? a) 4π cubic cm b) 6π cubic cm c) 12π cubic cm d) 18π cubic cm
9. A sphere has a radius of 5cm, what is its volume? a) 25π cubic cm b) 50π cubic cm c) 100π cubic cm d) 125π cubic cm
10. A triangular prism has a base of 4cm, a height of 6cm and a length of 8cm, what is its volume? a) 32 cubic cm b) 48 cubic cm c) 64 cubic cm d) 96 cubic cm

Volume and Capacity:

1. What is volume?
   • Volume is how much space an object takes up.
2. How do we measure volume?
   • We measure volume using cubic units like cubic centimeters or cubic meters.
3. What is capacity?
   • Capacity is how much a container can hold.
4. How do we measure capacity?
   • We measure capacity using units like liters or milliliters.
5. Can volume and capacity be the same?
   • No, they are different. Volume is about space, and capacity is about how much a container can hold.
6. How do we find the volume of a shape?
   • We multiply the length, width, and height together.
7. How do we find the capacity of a container?
   • We pour water into the container and measure how much it can hold.
8. What units do we use for volume?
   • We use cubic units like cm³ or m³.
9. What units do we use for capacity?
   • We use liters (L) or milliliters (mL).
10. Why is it important to understand volume and capacity?
    • It helps us measure and compare how much space objects take up and how much liquid containers can hold.

Evaluation :

1. A sphere with a radius of 2cm has a volume of approximately 33.51 cubic cm. A cuboid with the dimensions of 2cm x 2cm x 2cm has a volume of 8 cubic cm. The cuboid has a larger volume than the sphere, even though they have the same radius.
2. A sphere with a radius of 5m has a volume of approximately 523.60 cubic m. A cuboid with the dimensions of 5m x 5m x 5m has a volume of 125 cubic m. The cuboid has a larger volume than the sphere.
3. A sphere with a radius of 1km has a volume of approximately 4188.79 cubic km. A cuboid with the dimensions of 1km x 1km x 1km has a volume of 1 cubic km. The cuboid has a smaller volume than the sphere.
4. A sphere with a radius of 3cm has a volume of approximately 113.10 cubic cm. A cuboid with the dimensions of 2cm x 2cm x 3cm has a volume of 12 cubic cm. The sphere has a larger volume than the cuboid.
5. A sphere with a radius of 0.5m has a volume of approximately 0.52 cubic m. A cuboid with the dimensions of 0.5m x 0.5m x 0.5m has a volume of 0.125 cubic m. The sphere has a larger volume than the cuboid.
6. How many cubic centimeters are in 1 liter? a) 100 b) 500 c) 1000 d) 5000
7. How many liters are in 5000 cubic centimeters? a) 0.05 b) 5 c) 50 d) 500
8. A container holds 2 liters of liquid, how many cubic centimeters is this equivalent to? a) 2000 b) 200 c) 20 d) 2
9. A container holds 500 cubic centimeters of liquid, how many liters is this equivalent to? a) 0.5 b) 5 c) 50 d) 500
10. How do you convert liters to cubic centimeters? a) Multiply by 1,000 b) Divide by 1,000 c) Add 1,000 d) Subtract 1,000
11. How do you convert cubic centimeters to liters? a) Multiply by 1,000 b) Divide by 1,000 c) Add 1,000 d) Subtract 1,000
12. A tank holds 250 liters of water, how many cubic centimeters is this equivalent to? a) 250000 b) 25000 c) 2500 d) 250
13. A container holds 1 liter of oil, how many cubic centimeters is this equivalent to? a) 1000 b) 100 c) 10 d) 1
14. A cylinder has a radius of 5cm and a height of 20cm, what is its volume in liters? a) 0.314 b) 3.14 c) 31.4 d) 314
15. A container holds 0.5 liters of liquid, how many cubic centimeters is this equivalent to? a) 500 b) 50 c) 5 d) 0.5
16. What is the difference between volume and capacity? a) Volume is the amount of space an object takes up, while capacity is the amount of liquid an object can hold. b) Volume is the amount of liquid an object can hold, while capacity is the amount of space an object takes up. c) Volume and capacity are the same thing. d) Volume is the weight of an object, while capacity is the amount of space an object takes up.
17. What is the formula for finding the volume of a cube? a) V = s^3 b) V = l x w x h c) V = πr²h d) V = 4/3 x π x r³
18. How can you measure the volume of a cylinder? a) By using unit cubes b) By using the formula V = πr²h c) By using a graduated cylinder d) By using a ruler
19. What is the relationship between liters and cubic centimeters? a) 1 liter is equal to 1 cubic centimeter b) 1 liter is equal to 10 cubic centimeters c) 1 liter is equal to 1000 cubic centimeters d) 1 liter is equal to 100 cubic centimeters
20. How do you convert from liters to cubic centimeters? a) Divide the number of liters by 1000 b) Multiply the number of liters by 1000 c) Add 1000 to the number of liters d) Subtract 1000 from the number of liters
21. How do you convert from cubic centimeters to liters? a) Divide the number of cubic centimeters by 1000 b) Multiply the number of cubic centimeters by 1000 c) Add 1000 to the number of cubic centimeters d) Subtract 1000 from the number of cubic centimeters
22. What is the volume of a cube with a side length of 6cm? a) 36 cubic cm b) 216 cubic cm c) 6 cubic cm d) 1296 cubic cm
23. A container holds 2 liters of liquid, how many cubic centimeters is this equivalent to? a) 2000 b) 200 c) 20 d) 2
24. A cylinder has a radius of 3cm and a height of 10cm, what is its volume in liters? a) 0.028 b) 0.283 c) 2.83 d) 28.3
25. A container holds 0.5 liters of liquid, how many cubic centimeters is this equivalent to? a) 500 b) 50 c) 5 d) 0.5
26. The amount of space an object takes up is called __________.
27. The formula for finding the volume of a cube is __________.
28. The formula for finding the volume of a cylinder is __________.
29. The formula for finding the volume of a sphere is __________.
30. The formula for finding the volume of a triangular prism is __________.
31. To convert from liters to cubic centimeters, you would __________ the number of liters by 1000.
32. To convert from cubic centimeters to liters, you would __________ the number of cubic centimeters by 1000.
33. A container holds 2 __________ of liquid.
34. The relationship between liters and cubic centimeters is that __________ is equal to 1000 cubic centimeters.
35. The volume of a cube with a side length of 6cm is __________ cubic cm.

Objective Questions:

Previous lesson

• Revise the previous lesson which was Plane Shapes : Area of Regular and Irregular Shapes

1. Example 1: Volume of a Rectangular Prism
   • Given: Length = 5 cm, Width = 3 cm, Height = 2 cm
   • Calculation: Volume = Length × Width × Height
   • Solution: Volume = 5 cm × 3 cm × 2 cm = 30 cm³
2. Example 2: Capacity of a Jug
   • Given: Jug can hold 1 liter of water
   • Solution: Capacity of jug = 1 liter
3. Example 3: Volume of a Cube
   • Given: Side of cube = 4 cm
   • Calculation: Volume = Side × Side × Side
   • Solution: Volume = 4 cm × 4 cm × 4 cm = 64 cm³
4. Example 4: Capacity of a Bottle
   • Given: Bottle can hold 500 mL of juice
   • Solution: Capacity of bottle = 500 mL
5. Example 5: Volume of a Cylinder
   • Given: Radius = 2 cm, Height = 6 cm
   • Calculation: Volume = π × Radius² × Height
   • Solution: Volume = π × (2 cm)² × 6 cm = 24π cm³

1. The _______ is the amount of space occupied by a three-dimensional object.
   • a) Area
   • b) Volume
   • c) Perimeter
   • d) Diameter
2. To calculate volume, we multiply the length, width, and _______ together.
   • a) Perimeter
   • b) Diameter
   • c) Height
   • d) Circumference
3. Capacity is measured in units like liters or _______.
   • a) Centimeters
   • b) Meters
   • c) Milliliters
   • d) Kilograms
4. To find the capacity of a container, we pour in water and measure how much it can _______.
   • a) Run
   • b) Jump
   • c) Hold
   • d) Talk
5. The formula for volume of a rectangular prism is length × width × _______.
   • a) Perimeter
   • b) Diameter
   • c) Height
   • d) Circumference
6. The unit used to measure volume is _______.
   • a) Centimeters
   • b) Kilograms
   • c) Cubic units
   • d) Meters
7. Capacity is the measure of how much a _______ can hold.
   • a) Person
   • b) Shape
   • c) Container
   • d) Animal
8. To calculate volume, we multiply the length, width, and _______ together.
   • a) Perimeter
   • b) Diameter
   • c) Height
   • d) Circumference
9. The capacity of a jug is 2 liters. How many milliliters is this?
   • a) 100 mL
   • b) 1000 mL
   • c) 200 mL
   • d) 2000 mL
10. If a rectangular prism has a length of 4 cm, a width of 3 cm, and a height of 2 cm, what is its volume?
    • a) 8 cm³
    • b) 12 cm³
    • c) 24 cm³
    • d) 72 cm³

Presentation :

1. Introduction: The teacher revises the previous topic of measurement and basic shapes, asking students to recall what they have learned.
2. Presentation: The teacher introduces the new topic of volume and capacity, explaining the meanings of each and providing examples to illustrate.
3. Interactive Session: The teacher engages students by asking them to calculate the volume of simple shapes like rectangular prisms and cylinders. Students are encouraged to participate actively and ask questions.

Teacher’s Activities:

• Revises the previous topic of measurement and basic shapes.
• Introduces the concepts of volume and capacity.
• Demonstrates how to calculate volume using examples.
• Facilitates student participation and corrects misconceptions.

Learners Activities:

• Listen attentively to the teacher’s explanation.
• Participate actively in calculations and discussions.
• Ask questions for clarification when needed.
• Solve problems and work out examples on worksheets.

Assessment: The teacher assesses students’ understanding through:

• Observation of students’ participation and engagement during activities.
• Reviewing students’ completed worksheets and calculations for accuracy.

Evaluation Questions:

1. What is volume?
2. How do we measure volume?
3. Can you give an example of an object with a volume of 10 cubic centimeters?
4. Define capacity.
5. What units do we use to measure capacity?
6. Calculate the volume of a rectangular prism with length 5 cm, width 3 cm, and height 2 cm.
7. How do we calculate the volume of a cylinder?
8. If a jug can hold 1 liter of water, how many milliliters is this?
9. Why is it important to understand volume and capacity?
10. Describe a real-life situation where you would need to calculate capacity.

Conclusion: The teacher goes round to mark students’ work and assesses their understanding of the topic. Any misconceptions are addressed, and the teacher reinforces key points discussed during the lesson.