Cube Roots - Interactive Lesson Plan
Teaching Learning Process
Hook Activity (4 Minutes)
Helps to grab students' attention and activates prior knowledge to set the context.
Problem Scenario
If the volume of a cube is 64 cm³, what would be the length of its side?
To get the length of the side of the cube, we need to know a number whose cube is 64.
Explicit Modelling (8 Minutes)
Teacher demonstrates the skill or concept clearly, setting a strong example.
What is a Cube Root?
Finding the square root is the inverse operation of squaring. Similarly, finding the cube root is the inverse operation of finding a cube.
We know that 2³ = 8; so we say that the cube root of 8 is 2. We write ∛8 = 2.
Cube Root of a Perfect Cube
If x³ = y, then ∛y = x
The cube root of 64 equals 4,
∛64 = 4
because
4 × 4 × 4 = 64
Examples of Cube Roots
| Statement | Inference |
|---|---|
| 1³ = 1 | ∛1 = 1 |
| 2³ = 8 | ∛8 = 2 |
| 3³ = 27 | ∛27 = 3 |
| 4³ = 64 | ∛64 = 4 |
| 5³ = 125 | ∛125 = 5 |
CFU (Check for Understanding): What is meant by a cube? How can we calculate the cube of any number?
A cube is a number multiplied by itself three times. To calculate the cube of any number, multiply the number by itself twice (n × n × n).
Group Work (16 Minutes)
Encourages collaboration, discussion, and peer learning.
Activity: Create a Cube Roots Chart
Divide into small groups and create a chart showing cube roots of numbers from 1 to 10.
Perfect Cubes Reference
| ∛1 = 1 | ∛216 = 6 | ∛1331 = 11 |
| ∛8 = 2 | ∛343 = 7 | ∛1728 = 12 |
| ∛27 = 3 | ∛512 = 8 | ∛2197 = 13 |
| ∛64 = 4 | ∛729 = 9 | ∛2744 = 14 |
| ∛125 = 5 | ∛1000 = 10 | ∛3375 = 15 |
Discussion Question: What patterns do you notice in the cube roots of perfect cubes?
Perfect cubes increase rapidly, and their cube roots are whole numbers. The cube root of a negative number is negative. Every number has exactly one real cube root.
Independent Work (8 Minutes)
Allows students to apply learning individually, reinforcing understanding.
Practice Problems
1. What is the cube root of 216?
∛216 = 6, because 6 × 6 × 6 = 216
2. If a cube has a volume of 343 cm³, what is the length of its side?
Side length = ∛343 = 7 cm
3. Calculate ∛1000
∛1000 = 10, because 10 × 10 × 10 = 1000
4. What number cubed gives 512?
8, because 8³ = 512 and ∛512 = 8
Homework
Create a chart of cube roots for numbers from 1 to 20. Include both perfect cubes and non-perfect cubes with their approximate cube roots.
Closure (4 Minutes)
Wraps up the lesson with a quick review, reflection, or takeaway to solidify learning.
Key Takeaways
- The cube root of a number is a value that when cubed gives the original number
- Cube root is the inverse operation of cubing a number
- The symbol for cube root is ∛
- Perfect cubes have whole number cube roots
Vocabulary Review
Cube Root: A value which when multiplied by itself thrice produces the original value.
Perfect Cubes: Numbers that are the cube of integers (1, 8, 27, 64, ...).
