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Number Series 3

Number Series 3 introduces square numbers, a special type of sequence. Pupils learn how these patterns connect maths, logic, and shapes in 11 Plus Verbal Reasoning tests.

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Fascinating Fact:

The square numbers 1, 4, 9, 16 can be shown as perfect squares made from pebbles or tiles.

In 11 Plus Verbal Reasoning, pupils explore number patterns such as squares and cubes. Recognising these sequences helps build problem-solving skills and strengthens mathematical reasoning for exam success.

Key Terms

Square Number: A number made by multiplying an integer by itself, like 4 = 2 × 2.
Sequence: A list of numbers that follow a clear mathematical rule.
Pattern: A repeated or predictable arrangement of numbers, shapes, or objects.

For extra practice and advice, see our guide to 11 Plus sample questions.

Frequently Asked Questions (Click to see answers)

What is a square number in maths?

A square number is made by multiplying a number by itself, such as 1, 4, 9, 16, or 25.

How can square numbers be shown visually?

Square numbers can be arranged into perfect square shapes using objects like pebbles, counters, or tiles.

Why are square numbers important in the 11 Plus?

Square numbers are important because they appear in number sequences, puzzles, and reasoning problems that test logical thinking in the 11 Plus.

Try These Related Quizzes

Example: What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.

2 4 6 8 10 (?)

12
11
14
2

The correct answer is 12 because the numbers are going up by 2 each time. 10 + 2 = 12.

1 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
49, 36, 25, 16, (?)

The correct answer is 9 because the numbers are the squares of 7, 6, 5 and 4. We are looking for the square of 3 = 9

2 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
22, 66, 198, 594, (?)

1827

1728

1782

1872

The correct answer is 1782 because the numbers are three times the number to their left so we are looking for 594 x 3 = 1782

3 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
12, 21, 24, 42, (?)

360

The correct answer is 36 because the number pattern is: the first number is reversed (12 becomes 21) then multiplied by 2 (24) then reversed (42) so we are looking for what it would be if multiplied by 3 = 36. This way the first, third and fifth numbers are 12, 24, 36

4 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
8, 27, 64, 125, (?)

200

212

216

214

The correct answer is 216 because the numbers are all the cubes of 2, 3, 4 and 5. We are looking for the cube of 6. 6 x 6 x 6 = 216. Aryabhata was an ancient Indian mathematician who first explained how cubed numbers worked. He was alive over 1500 years ago

5 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
58, 127, 196, 265, (?)

334

336

338

330

The correct answer is 334 because the numbers are going up by 69 each time. The only way to work this out is to subtract the second number from the first, the third from the second, and so on

6 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
1, 5, 2, 6, (?)

The correct answer is 3 because the numbers alternate (skip one in the pattern). So the first number is 1, the third number is 2, making the fifth number 3

7 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
27, 37, 29, 39, (?)

The correct answer is 31 because every other number is going up by 2 each time (27, 29, 31) and the other numbers are also going up by 2 each time (37, 39). Only 31 works

8 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
240, 216, 192, 168, (?)

142

144

146

148

The correct answer is 144 because the numbers are going down by 24 each time. 168 - 24 = 144

9 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
16, 32, 48, 64, (?)

The correct answer is 80 because the numbers are the 16 times tables. 16 x 5 = 80. Sixteen is a darts player's favourite number when trying to hit a 'double'. If they miss and hit the single, they can still try for double 8, then double 4, double 2 and finally double 1. 32 is the highest score on a dartboard that can be halved all the way down to 1

10 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
27, 81, 243, 729, (?)

2187

2134

2156

2178

The correct answer is 2187 because the numbers are multiplied by 3 each time. 729 x 3 = 2187. If you are working through these quizzes in order, you have just completed the third of four Number Series quizzes. Well done!

Author: Stephen O'Hara