Let's investigate

15 multiplied by itself gives a three-digit number.
$1\,\,5 \times 1\,\,5 = 2\,\,2\,\,5$
What is the largest two-digit number that can be multiplied by itself to give a three-digit number?
$......\,\,......\, \times ......\,\,...... = ......\,\,......\,\,......$

1) These patterns of dots show the first four square numbers.

Draw a dot pattern for the fifth square number.

2) Look at these numbers.
Write down the numbers which are:

(a) multiples of 6.
(b) multiples of 7.
(c) square numbers.

3) Copy the sorting diagram. Write a number between 50 and 100 in each space.

number not a square	square number
		even number
		not an even number

4) Use the digits $1,2,5$ and 7 to complete these statements.
You can use each digit as many times as you like.
$......\,\,......$ is a multiple of 3.
$......\,\,......$ is a multiple of 9.
$......\,\,......$ is a square number.

5) This sequence shows multiples of 4:
$4,8,12,16,20,...$
Will 114 be in the sequence?
Explain how you know.

6) Find two square numbers to make each of these calculations correct.
(a) $? + ? = 10$
(b) $? + ? = 20$
(c) $? + ? = 40$
(d) $? + ? = 50$
(e) $? + ? = 80$
(f) $? + ? = 90$
(g) $? + ? = 100$

7) Solve these number riddles.
(a) The number is:
• a square number
• a multiple of 3
• less than 25
(b) The number is:
• a square number
• an even number
• a single-digit number
(c) The number is:
• a two-digit number less than 30
• a multiple of 4
• a multiple of 5