Learning Objectives:
Calculate quickly:
Notice anything special? Each number is multiplied by ITSELF!
These are called SQUARE NUMBERS!
A square number is the result of multiplying a number by itself.
Examples:
Instead of writing 3 × 3, we write:
This is read as "three squared equals nine"
The small 2 means "multiply by itself"
Because we can arrange them into a perfect SQUARE shape!
Think of tiles or counters arranged in rows and columns...
1 row × 1 column = 1 unit
■
One single square!
2 rows × 2 columns = 4 units
■ ■ ■ ■
A 2 × 2 square!
3 rows × 3 columns = 9 units
■ ■ ■ ■ ■ ■ ■ ■ ■
A 3 × 3 square!
4 rows × 4 columns = 16 units
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
A 4 × 4 square!
5 rows × 5 columns = 25 units
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
A 5 × 5 square!
n² means:
That's why it makes a perfect SQUARE!
Let's calculate squares from 1 to 12...
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
The differences are ODD NUMBERS: 3, 5, 7, 9, 11...
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!
A square garden has sides of 9 metres. What is its area?
Solution: Area = side × side = 9² = 81 m²
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
What is 7²?
Is 50 a square number?
What number times itself gives 81?
Complete: 5² = ___
7² = 49
50 is NOT a square number (between 49 and 64)
9 × 9 = 81
5² = 25
Write out the squares of 1 to 15
Draw square arrays for 1², 2², 3², 4², and 5²
Find three square numbers between 50 and 150
A square field has area 64 m². What is the length of one side?
You now understand square numbers!
Next lesson: Square Roots
Keep practicing your squares!