Cubes and Cube Numbers
Interactive 45-Minute Mathematics Lesson for Class 8
Prior Concepts / Skills
Before starting this lesson, students should be familiar with:
- Reading and writing numbers with multiple digits along with expanded forms
- Basic arithmetic operations: addition, subtraction, multiplication, and division
- Understanding of squares and square roots
- Knowledge of exponents and powers
- Prime factorization of numbers
- Ascending and descending order of numbers along with values
Hook Activity 4 minutes
Begin by showing students a physical cube or the 3D visualization below. Ask:
"How many small cubes of side 1 cm would you need to build a larger cube of side 2 cm?"
Allow students to guess and discuss. Then demonstrate with the visualization.
Explain that just like we built a 2×2×2 cube from 8 smaller cubes, we can explore the concept of cube numbers.
Experience and Reflection
Ask students to think about real-life examples of cubes:
- Dice used in board games
- Sugar cubes
- Building blocks
Discuss how understanding cubes helps in calculating volume and understanding 3D space.
Vocabulary
- Cube: A symmetrical three-dimensional shape with all sides equal
- Patterns: A repeated design, numbers etc.
- Multiple of Numbers: A number that is the product of a given number and some other natural number
- Perfect Cube: A number that can be expressed as the cube of an integer
Explicit Teaching / Teacher Modelling (I Do) 8 minutes
Revise the concept of cubes from the previous lesson:
2 × 2 × 2 = 2³ = 8
3 × 3 × 3 = 3³ = 27
Demonstrate how to calculate cube numbers using the table below:
| Number | Cube | Calculation |
|---|---|---|
| 1 | 1 | 1 × 1 × 1 = 1 |
| 2 | 8 | 2 × 2 × 2 = 8 |
| 3 | 27 | 3 × 3 × 3 = 27 |
| 4 | 64 | 4 × 4 × 4 = 64 |
| 5 | 125 | 5 × 5 × 5 = 125 |
Explain that numbers like 1, 8, 27, 64, 125 are called perfect cubes.
Question: Is 9 a cube number?
Answer: No, 9 is not a cube number. We can see that 2×2×2=8 and 3×3×3=27. There is no whole number that when multiplied by itself three times gives 9.
Group Work (We Do) 16 minutes
Divide students into groups of 5. Each group will complete the following tasks:
Task 1: Complete the Cube Table (1 to 10)
| Number | Cube | Check Answer |
|---|
Task 2: Answer These Questions
1. How many perfect cubes are there between 1 and 100?
Answer: There are 4 perfect cubes between 1 and 100: 1, 8, 27, and 64.
2. Explore the one's digit of cubes of numbers ending in 2, 3, 4, etc.
Answer:
- Numbers ending in 1, 4, 5, 6, 9, 0 have cubes ending in the same digit
- Numbers ending in 2 have cubes ending in 8
- Numbers ending in 3 have cubes ending in 7
- Numbers ending in 7 have cubes ending in 3
- Numbers ending in 8 have cubes ending in 2
3. What is the nature of cubes of even numbers? (Are they even or odd?)
Answer: The cube of an even number is always even.
4. What is the nature of cubes of odd numbers? (Are they even or odd?)
Answer: The cube of an odd number is always odd.
Independent Work (You Do) 8 minutes
Students will solve the following problems individually:
Find the one's digit of the cube of each number:
(i) 3331
Answer: Since 3331 ends with 1, its cube will also end with 1.
(ii) 8888
Answer: Since 8888 ends with 8, its cube will end with 2.
(iii) 149
Answer: Since 149 ends with 9, its cube will also end with 9.
(iv) 1005
Answer: Since 1005 ends with 5, its cube will also end with 5.
(v) 1024
Answer: Since 1024 ends with 4, its cube will also end with 4.
(vi) 77
Answer: Since 77 ends with 7, its cube will end with 3.
(vii) 5022
Answer: Since 5022 ends with 2, its cube will end with 8.
(viii) 53
Answer: Since 53 ends with 3, its cube will end with 7.
Homework Assigned at end of class
1. How many perfect cubes are there between 1 and 1000?
Answer: There are 10 perfect cubes between 1 and 1000: 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000.
2. Evaluate the cube of the following numbers:
- 9³ =
729
- 15³ =
3375
- 19³ =
6859
- 17³ =
4913
3. Which of the following are cubes of even numbers?
- 216 -
Yes (6³)
- 729 -
No (9³, and 9 is odd)
- 512 -
Yes (8³)
- 3375 -
No (15³, and 15 is odd)
- 1000 -
Yes (10³)
Closure 4 minutes
Review key concepts:
- A cube number is obtained when a number is multiplied by itself three times
- Perfect cubes are numbers like 1, 8, 27, 64, etc.
- The cube of an even number is even, and the cube of an odd number is odd
- There are patterns in the ones digit of cube numbers
Ask students to reflect on what they learned and how they can apply this knowledge in real life.
