Period 6.1: LO - Students will be Introduced to Cubes
Sub-topic 6.1: Introduction to Cubes
By M.RajaRao, MSc, MEd
Welcome, Future Mathematicians!
Hook Activity (4 Mins)Have you ever played with building blocks or dice? Imagine understanding the math that perfectly describes them. That's what we're exploring today! It's like unlocking a secret code to describe 3D shapes.
So, are you ready to explore the amazing world of 'Cubes and Cube Roots'?
Let's Warm Up Our Brains!
Let's check some concepts you already know.
Cubes in Real Life
Cubes aren't just in math class; they're everywhere! Think about ice cubes, boxes, or even some buildings. Why do you think so many things are cube-shaped?
Discussion Questions:
1. What cube-shaped objects can you find in your home or school? Describe them.
2. Can you think of practical reasons why objects are designed in cube shapes? (Hint: Think about stacking and packing!)
Let's Learn About Cubes!
The Story of a Special Number
A famous story in mathematics involves two great mathematicians, Hardy and Ramanujan. Ramanujan, who was sick in the hospital, told Hardy that the number of his taxi, 1729, was very interesting. Why? Because it's the smallest number that can be expressed as the sum of two cubes in two different ways!
1729 = 1728 + 1 = 123 + 13
1729 = 1000 + 729 = 103 + 93
What is a Cube Number?
Just like a square is a number multiplied by itself (2 × 2 = 22), a cube is a number multiplied by itself three times.
1 × 1 × 1 = 13 = 1
2 × 2 × 2 = 23 = 8
3 × 3 × 3 = 33 = 27
Let's Build with Cubes!
Imagine you have small, 1x1x1 unit blocks. How many would you need to build a larger, solid cube?
Can you see the pattern? Instead of counting every single block, can we use math to find the total number of blocks in a 10x10x10 cube? Of course! That's the power of cubes!
Your Turn to Practice!
1. Represent this in exponential form: 5 × 5 × 5
2. What is the value of 43?
3. Fill in the blanks: __ × __ × __ = 73
Great Job Today!
Closure (4 Mins)WHAT WE FOUND: A cube number is a number multiplied by itself three times (like n × n × n = n3).
HOW WE FOUND IT: We explored real-world objects, learned from the story of Ramanujan's number, and built virtual cubes to see how the side length relates to the total volume.
The key takeaway is that understanding cubes helps us quickly calculate the volume of cube-shaped objects without counting every single part!
Continue Your Journey
Ready for more practice? Complete the questions below to master your new skills.
1. Find the cube of 6.
2. What is the value of 113?
3. Which of the following is a perfect cube: 100, 216, 500?
4. If a cube has a side length of 8cm, what is its volume?
Answer Key
- 1. 63 = 6 × 6 × 6 = 216
- 2. 113 = 11 × 11 × 11 = 1331
- 3. 216 is the perfect cube (63).
- 4. Volume = 83 = 8 × 8 × 8 = 512 cm3
Introduction to Cubes
Cubes and Cube roots | Lesson 6.1
- 1³ = 1 × 1 × 1 1
- 2³ = 2 × 2 × 2 8
- 3³ = 3 × 3 × 3 27
- 4³ = 4 × 4 × 4 64
- 5³ = 5 × 5 × 5 125
- 6³ = 6 × 6 × 6 216
- 7³ = 7 × 7 × 7 343
- 8³ = 8 × 8 × 8 512