Squares and Square Roots

Grade 6 · Mathematics

Semester 2 | Period 4 | Week 20

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Subject: Mathematics

Semester: 2

Period: 4

Week: 20

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 20
Lesson Duration: 45 minutes
Week & Period: Week 20, Period 4
Topic: Squares and Square Roots
Sub-topic: Definition, Recognition, and Applications

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

  1. Define squares and perfect squares.
  2. Recognize and list perfect squares up to 15 × 15.
  3. Find square roots using factorization method.
  4. Find square roots by repeated subtraction.
  5. Apply squares and square roots in solving area-related word problems.

Previous Knowledge
Students already know multiplication facts and basic area calculation of squares.

Instructional Materials
Mathematics textbook for Grade 6, multiplication table, flashcards, square grid paper.

Lesson Development – ABC Model

A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher asks: “What is 5 × 5? What is 12 × 12?” Students respond and teacher introduces the word “square numbers.”

 

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

Definitions and Explanations

  1. Square of a Number
  • The square of a number is the result of multiplying the number by itself.
  • Symbol: n² (read as “n squared”).
  • Examples:
    • 7² = 7 × 7 = 49
    • 12² = 12 × 12 = 144
    • 20² = 20 × 20 = 400
  1. Perfect Squares
  • Perfect squares are numbers that can be expressed as the square of whole numbers.
  • Examples:
    • 1² = 1
    • 2² = 4
    • 3² = 9
    • 4² = 16
    • 5² = 25
    • … up to 20² = 400.
  • Non-perfect square example: 18 is not a perfect square because no whole number multiplied by itself equals 18.
  1. Square Root (√)
  • The square root of a number is the value that, when multiplied by itself, gives the original number.
  • Example:
    • √49 = 7 (since 7 × 7 = 49).
    • √121 = 11.
    • √169 = 13.
  • Square and square root are inverse operations.

 

Methods of Finding Square Roots

  1. Prime Factorization Method
  • Break the number into its prime factors.
  • Pair the prime factors and take one from each pair.
  • Multiply them to get the square root.
  • Example:
    • 144 = 2 × 2 × 2 × 2 × 3 × 3 = (2 × 2 × 3)² = 12².
    • √144 = 12.
  • Another Example:
    • 225 = 3 × 3 × 5 × 5 = (3 × 5)².
    • √225 = 15.
  1. Repeated Subtraction Method
  • Subtract successive odd numbers (1, 3, 5, 7, …) from the number until you reach 0.
  • The number of steps taken is the square root.
  • Example: √25
    • 25 – 1 = 24
    • 24 – 3 = 21
    • 21 – 5 = 16
    • 16 – 7 = 9
    • 9 – 9 = 0
    • Steps = 5 → √25 = 5.
  1. Using Area of Squares
  • If a square has an area, the square root gives its side length.
  • Example: Area = 100 m² → Side = √100 = 10 m.

 

Worked Examples

  1. Find 11².
    • 11 × 11 = 121.
  2. Find √196 using factorization.
    • 196 = 2 × 2 × 7 × 7 = (2 × 7)².
    • √196 = 14.
  3. A square playground has area 225 m². Find the length of one side.
    • √225 = 15 m.
  4. Which of the following are perfect squares: 36, 48, 64, 90?
    • √36 = 6 → Perfect square.
    • √48 ≈ 6.9 → Not perfect.
    • √64 = 8 → Perfect square.
    • √90 ≈ 9.48 → Not perfect.

 

Word Problems

  1. A farmer has a square plot of land with area 400 m². What is the length of each side?
    • √400 = 20 m.
  2. A wall is shaped like a square of side 12 m. Find the area.
    • 12² = 144 m².
  3. A square mat has an area of 49 cm². What is the side length?
    • √49 = 7 cm.
  4. A box cover is square-shaped with area 169 cm². Find its side.
    • √169 = 13 cm.

 

Learners’ Activities (Expanded)

  1. Draw squares of sides 2 cm, 3 cm, 4 cm, and 5 cm on graph paper. Calculate their areas and match them to their squares.
  2. Use bottle tops or counters to form perfect square patterns (1, 4, 9, 16, 25, …).
  3. In groups, perform factorization of 144, 225, and 256 to find their square roots.
  4. Practice repeated subtraction with small perfect squares like 9, 16, and 25.
  5. Solve real-life word problems about fields, mats, and plots of land shaped like squares.

 

Assessment Checks

  1. Quick oral questions:
    • What is √121? (Answer: 11)
    • What is 15²? (Answer: 225)
    • Is 50 a perfect square? (Answer: No)
  2. Short exercises:
    • Find √64 using factorization.
    • Write the first 12 perfect squares.
    • A square garden has side 18 m. Find its area.
    • Which are perfect squares: 81, 120, 144?
    • Use repeated subtraction to show √16.

 

Notes (Expanded & Detailed)

  • Squaring makes numbers grow very quickly (e.g., 20² = 400).
  • Square roots are the reverse process of squaring.
  • Perfect squares are easy to recognize and useful in geometry, algebra, and measurements.
  • Factorization method is reliable for large numbers.
  • Repeated subtraction is a simple way to understand square roots for smaller numbers.
  • Square roots are widely used in real life: building construction, designing square tiles, calculating land plots, and in physics formulas.

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher revises definition of square, perfect square, and square roots with examples.

Evaluation Method (Expanded):
Exit slip/quiz:

  1. Write three perfect squares greater than 100.
  2. Find √81 using factorization.

Teacher will collect slips and provide oral feedback.

Assignment (Expanded):
Find the square roots of 169 and 196 by factorization.

Follow-up Activity:
Students find areas of square objects at home.

Differentiation / Inclusive Strategies
Visual aids for weaker learners; extra challenge (square roots above 20²) for advanced learners.

Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low