Square numbers as square arrays

The Maths Habit

1

Find the factors of 12.

1 row2 rows3 rows1 and 122 and 63 and 41, 2, 3, 4, 6, 122

Write the first 4 multiples of 5.

51015205, 10, 15, 203

Factor or multiple? 3 is a … of 18.

factor

Which of these are squares? How do you know?

A
B
C
D

A and C: the same number of rows as in each row.

Square number
A number made by multiplying a whole number by itself.
Squared
Multiplied by itself.
Square root
The number that was multiplied by itself to make the square number.

4rows4in each row
  1. A square number makes a square array.The same number of rows as in each row.
  2. Side × side gives the square number.4 × 4 = 16

Is it a square?

No: 4 rows of 5

It is a square. How many are in each row?

6rows 6

How many dots are in this square? Side × side gives the square number. 3 × 3 = 9

rowsin each row33

How many dots are in this square? Side × side gives the square number. 7 × 7 = 49

7rowsin each row7

How many dots are in this square? Side × side gives the square number. 3 × 3 = 9

rowsin each row33

How many dots are in this square? Side × side gives the square number. 10 × 10 = 100

rowsin each row1010

How many dots are in this square? Side × side gives the square number. 3 × 3 = 9

rowsin each row33

How many dots are in this square? Side × side gives the square number. 2 × 2 = 4

rowsin each row22

How many dots are in this square? Side × side gives the square number. 3 × 3 = 9

rowsin each row33

How many dots are in this square? Side × side gives the square number. 9 × 9 = 81

rowsin each row99

How many dots are in this square? Side × side gives the square number. 3 × 3 = 9

rowsin each row33

How many dots are in this square? Side × side gives the square number. 11 × 11 = 121

rowsin each row1111

Square numbers as square arrays worksheet, page 1

What does 42 mean?

4 × 4 = 16

Which is right: 32 = 6 or 32 = 9?

32 = 3 × 3 = 9

5rows5in each row
  1. 52 is said 5 squared.It means 5 × 5 = 25. Never 5 × 2.
  2. The side is the square root.The square root of 25 is 5: √25 = 5.

Work out 62. Side × side gives the square number. The side is the square root. 6 × 6 = 36

rowsin each row66

This square array has 49 dots. Find √49. Side × side gives the square number. The side is the square root. √49 = 7

rowsin each row77

Work out 62. Side × side gives the square number. The side is the square root. 6 × 6 = 36

rowsin each row66

This square array has 81 dots. Find √81. Side × side gives the square number. The side is the square root. √81 = 9

rowsin each row99

Square numbers as square arrays worksheet, page 2

Answer sheet

Thumbs up: true. Thumbs down: false.

  1. 42 = 16

    True

  2. 32 = 6

    False

  3. √25 = 5

    True

  4. 102 = 20

    False

  5. 12 = 1

    True

  1. Which square number is between 60 and 70?

    64

  2. Add two square numbers to make 25.

    9 + 16

  3. 1, 4, 9, 16, 25: what do you add each time? What do you notice?

    3, 5, 7, 9: odd numbers

  1. Work out 42. Side × side gives the square number.

    16

  2. What is √81?

    9

  3. Is 40 a square number? Explain.

    No: 62 = 36, 72 = 49
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