## Each of the digits in the number ninety four is a square number. Let's call all numbers like that squigits!

1. Can you find a squigit which is divisible by 7 and larger than 50?

2. Which two squigits have a difference of 100?

3. Find a squigit whose square root is also a squigit.

4. Find a squigit that's also a prime number.

5. How many years last
century were squigits?

## A Mathematics Lesson Starter Of The Day

Topics: Starter | Number

• S.Singh, Maltby Comprehensive, Rotherham
•
• Surely 0 is a square number so your answer for the years should also include 1900, 1901, 1904, 1909, 1910, 1940, 1990 making 16 in total.
• Steve Eastop, Margate, Kent.
•
• Although you can not form a square in reality from 0 items, (or a square of 0 by 0 items) nor can you form one from negative integers neither. For example, you can not draw a picture of a square containing say -9 points by -9 points (columns x widths). It is accepted, however, in Number Theory that the product of any two negative quantities always result in a POSITIVE AMOUNT! Therefore, one can 'square' a negative quantity (that doesn't exist in reality into a positive result that does)!
The first respondent was correct in that 0 SHOULD be included within the results/ solutions to these questions! The reason being that a SQUARE NUMBER is defined as: "A number that is the square of an integer: 1, 4, 9, 16, etc." Furthermore, an INTEGER is defined as: "The positive and negative whole numbers: 0, + or - 1, + or - 2, + or- 3,...." Hence 0 IS an integer and thus it CAN be squared as in the context of first definition of a square number given!
These defintions occur in the The Penguin book entitled: 'THE PENGUIN DICTIONARY OF MATHEMATICS' by John Daintith & R.D. Nelson! (Pages 175 and 306 respectively).

[Transum: Thanks for all of your comments. The answers below have now been altered to include zero as a square number.]
• Year 5, Primet Primary School
•
• The children at Primet Primary school would like to know if 0 is a square number. We have been having discussions and they believe if you have nought and multiply it by nought then you cannot make a square.
The children really enjoyed this challenge and found many different answers for each problem.
Thanks.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

Previous Day | This starter is for 29 June | Next Day

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon link. As an Amazon Associate I earn a small amount from qualifying purchases which helps pay for the upkeep of this website.

Educational Technology on Amazon

## GCSE Revision and Practice

Whatever exam board you use for GCSE Mathematics, this book by David Rayner remains an all-round winner. With this latest edition presented in full colour and completely updated for the new GCSE(9-1) specifications, this uniquely effective text continues to increase your chance of obtaining a good grade.

This book is targeted at the Higher tier GCSE, and provides a wealth of practice with careful progression, alongside substantial revision support for the new-style grading and exam questions. With all the new topics included, and a dedicated section on using and applying mathematics, this unique resource can be used either as a course book over two or three years or as a revision text in the run-up to exams. more... #ad