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Subject: Mathematics
Semester: 2
Period: 4
Week: 21
School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 21
Lesson Duration: 45 minutes
Week & Period: Week 21, Period 4
Topic: Cubes and Cube Roots
Sub-topic: Factorization Method
Learning Objectives
By the end of the lesson, students should be able to:
- Define cube of a number.
- Find cubes of whole numbers up to 10³.
- Define cube root and find it using factorization method.
- Recognize perfect cubes.
- Solve word problems involving cubes and cube roots.
Previous Knowledge
Students already know multiplication and squares.
Instructional Materials
Mathematics textbook, cube-shaped objects, number charts.
Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher shows a dice (cube) and asks: “If one side measures 3 cm, what is its volume?”
B – Building Knowledge (Main Lesson Body)
Time: 25–30 minutes
Definitions and Explanations
- Cube of a Number
- The cube of a number is the result of multiplying the number by itself three times.
- Symbol: n³ (read as “n cubed”).
- Examples:
- 2³ = 2 × 2 × 2 = 8
- 3³ = 3 × 3 × 3 = 27
- 4³ = 4 × 4 × 4 = 64
- 5³ = 5 × 5 × 5 = 125
- Perfect Cubes
- Perfect cubes are numbers that can be expressed as the cube of whole numbers.
- Examples:
- 1³ = 1
- 2³ = 8
- 3³ = 27
- 4³ = 64
- 5³ = 125
- … up to 10³ = 1000
- Cube Root (³√)
- The cube root of a number is the value that, when cubed, gives the original number.
- Example:
- ³√64 = 4 (since 4 × 4 × 4 = 64).
- ³√125 = 5.
- Cubes and cube roots are inverse operations.
Method of Finding Cube Roots
- Prime Factorization Method
- Step 1: Express the number as a product of prime factors.
- Step 2: Group the prime factors into triplets.
- Step 3: Multiply one from each triplet to get the cube root.
Example: Find ³√216
- 216 = 2 × 2 × 2 × 3 × 3 × 3
- Group into triplets: (2 × 2 × 2) × (3 × 3 × 3)
- ³√216 = 2 × 3 = 6
Example: Find ³√1000
- 1000 = 2 × 2 × 2 × 5 × 5 × 5
- Triplets: (2 × 2 × 2) × (5 × 5 × 5)
- ³√1000 = 2 × 5 = 10
Worked Examples
- Find 7³.
- 7 × 7 × 7 = 343
- Find ³√729 using factorization.
- 729 = 3 × 3 × 3 × 3 × 3 × 3 = (3³) × (3³)
- ³√729 = 3 × 3 = 9
- A cube-shaped water tank has volume 512 m³. Find the side length.
- Side = ³√512 = 8 m
- Which of the following are perfect cubes: 27, 81, 125, 200?
- √³27 = 3 → Perfect cube
- √³81 ≈ 4.3 → Not a cube
- √³125 = 5 → Perfect cube
- √³200 ≈ 5.8 → Not a cube
Word Problems
- A cube box has a volume of 729 cm³. What is the side length?
- Side = ³√729 = 9 cm
- A dice is a cube of side 6 cm. Find its volume.
- 6³ = 216 cm³
- A cube-shaped block has side 15 m. Find its volume.
- 15³ = 3375 m³
- A cube has volume 1000 cm³. Find its side length.
- ³√1000 = 10 cm
Learners’ Activities (Expanded)
- Students calculate cubes of numbers from 1–10 and write the list in their notebooks.
- In groups, use prime factorization to find cube roots of 216, 512, 729, and 1000.
- Draw a cube on graph paper, label its side, and calculate its volume.
- Solve word problems about cube-shaped boxes, dice, and containers.
- Use counters or blocks to build small cubes (e.g., 2³, 3³) to visualize cube growth.
Assessment Checks
- Quick oral questions:
- What is ³√27? (Answer: 3)
- What is 6³? (Answer: 216)
- Is 50 a perfect cube? (Answer: No)
- Written short exercises:
- Find ³√512.
- Write the first 12 perfect cubes.
- A cube has side 12 cm. Find its volume.
- Which are perfect cubes: 64, 200, 343?
Notes (Expanded & Detailed)
- Cubes grow numbers faster than squares (example: 10³ = 1000).
- Cube roots undo cubing and are used in reverse calculations.
- Perfect cubes help in 3D geometry, volume calculations, and real-life measurements like storage, packaging, and construction.
- Prime factorization is the most reliable method for larger cubes.
- Understanding cubes and cube roots prepares learners for algebra, mensuration, and advanced geometry.
C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher highlights cube, cube root, and real-life cube objects.
Evaluation Method (Expanded):
Exit slip/quiz:
- Write cube of 7.
- Find ³√343.
Assignment (Expanded):
Find cube roots of 729 and 1000.
Follow-up Activity:
Students identify cube-shaped items at home and calculate volumes.
Differentiation / Inclusive Strategies
Provide step-by-step factorization for learners needing support. Challenge others with non-perfect cubes.
Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low