Squigits

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


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Topics: Starter | Number

  • S.Singh, Maltby Comprehensive, Rotherham
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  • 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.
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  • 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
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  • 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.

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Answers

1. 91.... but there are many other correct answers.

2. 11 and 111.... but there are many other correct answers.

3. 1.... but there are many other correct answers.

4. 11.... but there are many other correct answers.

5. 16. (1900, 1901, 1904, 1909, 1910, 1911, 1914, 1919, 1940, 1941, 1944, 1949, 1990, 1991, 1994, 1999)



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Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.

Transum.org/go/?Start=June29

Here is the URL which will take them to a student activity about square numbers.

Transum.org/go/?to=SquareShoot

 

 


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