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# Secondary Magazine - Issue 50: Focus on

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 15 December 2009 by ncetm_administrator
Updated on 05 January 2010 by ncetm_administrator

# Focus on...50

The word ‘fifty’, according to the Merriam-Webster dictionary, is derived from the old English word fiftig. Fif meaning five and tig meaning group of 10.

50 = 5 × 10, and 5 and 10 are the two smallest numbers that are each the sum of two squares.

50 is the smallest number that can be written as the sum of two squares in two different ways:

50 = 12 + 72
50 = 52 + 52

The next few are 65, 85, 125 and 130. 65 is the first that can be written so that all of the squares are different.

50 is also the sum of three consecutive square numbers:

50 = 32 + 42 + 52

50 is a Harshad Number, that is, it is a number that can be exactly divided by the sum of its digits:

5 + 0 = 5 and 50 ÷ 5 is an integer

In 1994, Helen Grundman showed that there is no sequence of more than 20 consecutive Harshad Numbers. She also found the smallest sequence of 20 consecutive Harshad numbers, each member of which has 44 363 342 786 digits.

50% = ½ = 0.5 which often leads to 50% being an introduction to percentages and fractions. The Maths4Life Fractions booklet suggests a resource in which students are invited to draw diagrams of as many different halves they can think of and to write down calculations to show you can calculate half of anything.

There are 50 states in the USA. The name of the television programme Hawaii Five-O was taken from the fact that Hawaii is the 50th state.

There have been 50 editions of the NCETM Secondary Magazine so far! The first ten looked very different to this one and included department workshops which colleagues might work through together. The format changed again in Issue 21 which is also the issue in which the first Up2d8 resource was included.
What would you like to see in the next 50 editions? Leave a comment and let us know.

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