Understanding Square Numbers
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P6 Mathematics - Term I

Understanding Square Numbers

P6 Mathematics - Term I, Topic 4

Lesson 2 of 4

Learning Objectives:

  • Define and identify square numbers
  • Calculate squares from 1 to 12
  • Represent squares visually using grids
Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Mental Warm-Up! 🧠

Calculate quickly:

  • 3 × 3 = ?
  • 5 × 5 = ?
  • 7 × 7 = ?

Notice anything special?
Each number is multiplied by ITSELF!

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Mental Warm-Up: Answers

  • 3 × 3 = 9
  • 5 × 5 = 25
  • 7 × 7 = 49

These are called SQUARE NUMBERS!

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

What is a Square Number?

Definition

A square number is the result of multiplying a number by itself.

Examples:

  • 3 × 3 = 9 → 9 is a square number
  • 5 × 5 = 25 → 25 is a square number
  • 10 × 10 = 100 → 100 is a square number
Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

The Squared Notation

Instead of writing 3 × 3, we write:

3² = 9

This is read as "three squared equals nine"

The small 2 means "multiply by itself"

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

More Examples

Written Form Notation Answer
4 × 4 16
6 × 6 36
8 × 8 64
10 × 10 10² 100
Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Why "Square" Numbers? 🤔

Because we can arrange them into a perfect SQUARE shape!

Think of tiles or counters arranged in rows and columns...

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Visual: 1² = 1

1 row × 1 column = 1 unit

One single square!

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Visual: 2² = 4

2 rows × 2 columns = 4 units

■ ■
■ ■

A 2 × 2 square!

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Visual: 3² = 9

3 rows × 3 columns = 9 units

■ ■ ■
■ ■ ■
■ ■ ■

A 3 × 3 square!

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Visual: 4² = 16

4 rows × 4 columns = 16 units

■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■

A 4 × 4 square!

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Visual: 5² = 25

5 rows × 5 columns = 25 units

■ ■ ■ ■ ■
■ ■ ■ ■ ■
■ ■ ■ ■ ■
■ ■ ■ ■ ■
■ ■ ■ ■ ■

A 5 × 5 square!

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

The Key Pattern

Rows = Columns = The Number

n² means:

  • n rows
  • n columns
  • n × n total units

That's why it makes a perfect SQUARE!

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Building the Squares Table

Let's calculate squares from 1 to 12...

n n
1 1 7 49
2 4 8 64
3 9 9 81
4 16 10 100
5 25 11 121
6 36 12 144
Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Memorize These! 📝

First 12 Squares:

1, 4, 9, 16, 25, 36,
49, 64, 81, 100, 121, 144

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Pattern Discovery 1

Differences Between Squares

  • 4 - 1 = 3
  • 9 - 4 = 5
  • 16 - 9 = 7
  • 25 - 16 = 9
  • 36 - 25 = 11

The differences are ODD NUMBERS: 3, 5, 7, 9, 11...

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Pattern Discovery 2

Last Digits of Square Numbers

Look at: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100...

Last digits: 1, 4, 9, 6, 5, 6, 9, 4, 1, 0

Square numbers only end in: 0, 1, 4, 5, 6, or 9

Never: 2, 3, 7, or 8!

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Practice: Calculate Squares

Find each square:

  1. 6² = ?
  2. 8² = ?
  3. 11² = ?
  4. 12² = ?
Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Practice: Answers

  1. 6² = 6 × 6 = 36
  2. 8² = 8 × 8 = 64
  3. 11² = 11 × 11 = 121
  4. 12² = 12 × 12 = 144
Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Practice: Identify Square Numbers

Which are square numbers?

  1. 15
  2. 49
  3. 64
  4. 75
  5. 100
Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Practice: Answers

  1. 15 → NO (between 9 and 16)
  2. 49 → YES (7² = 49)
  3. 64 → YES (8² = 64)
  4. 75 → NO (between 64 and 81)
  5. 100 → YES (10² = 100)
Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Real-Life Example 1

Garden Area

A square garden has sides of 9 metres.
What is its area?

Solution:
Area = side × side = 9² = 81 m²

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Real-Life Example 2

Floor Tiles

You have 144 tiles to make a square floor.
How many tiles on each side?

Solution:
We need a number that × itself = 144
12 × 12 = 144
So: 12 tiles on each side

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Quick Assessment ✓

  1. What is 7²?

  2. Is 50 a square number?

  3. What number times itself gives 81?

  4. Complete: 5² = ___

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Quick Assessment: Answers

  1. 7² = 49

  2. 50 is NOT a square number (between 49 and 64)

  3. 9 × 9 = 81

  4. 5² = 25

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Summary: Square Numbers

  • Square number = a number × itself
  • Notation: n² means "n squared"
  • Visual: Forms a perfect square array
  • First 12: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
  • Pattern: Differences are odd numbers
Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Homework 📚

  1. Write out the squares of 1 to 15

  2. Draw square arrays for 1², 2², 3², 4², and 5²

  3. Find three square numbers between 50 and 150

  4. A square field has area 64 m². What is the length of one side?

Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Remember! 💡

Key Square Numbers to Memorize:

1² = 1 5² = 25 9² = 81
2² = 4 6² = 36 10² = 100
3² = 9 7² = 49 11² = 121
4² = 16 8² = 64 12² = 144
Topic 4: Patterns and Sequences | Lesson 2 of 4
P6 Mathematics - Term I

Well Done! 🌟

You now understand square numbers!

Next lesson: Square Roots

Keep practicing your squares!

Topic 4: Patterns and Sequences | Lesson 2 of 4