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NUMBERS

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Katie Smee

on 17 November 2014

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Transcript of NUMBERS

NUMBERS
Calendars
But why are calendars relevant to Mathematics?

Calendars came around during the Roman times, and we still work from their calendars today. However, Roman's had:
10 months in a year
304 days in a year


So how could we use a calendar in Mathematics to improve a child's knowledge?



Roman Numerals


Roman numerals originated during the roman empire:
27bc – 1453ad when the byzantine empire ended
System was used in ancient Rome
There are only hypotheses about the origin of roman numerals

Roman Numerals Today
Hindu – Arabic numerals were introduced in the 11th century

Roman numerals persistent even in the 15th century

Roman numerals still not replaced today



The National Curriculum
The History of the Number System
The Babylonians lived around 3500BC. Their number system was based on a system which used a base of 60, whereas we use a base of 10 today.
Around 3000BC the Egyptians developed their number system which used their complex hieroglyphic writing.
Roman Numerals where later introduced. The Roman's system used letters as symbols for numbers and there is a lot still seen today.
Another number system we all recognise is the Indian number system. The system used a set of 10 symbols where each had a place value. This number system has developed over time and is now what we know as the Hindu/ Arabic number system.
The Hindu/ Arabic system, which was brought in to Europe by a Mathematician named Fibonacci, is a number system which has influenced a lot of our mathematical teachings in number.

By Lois Wagstaff, Ifrah Naseer and Katharine Smee
Activity
Instructions:

1. Pick out one piece of paper from each envelope (one envelope contains months and the other contains a sum in Roman numerals)

2. Work out the answer to the sum - this, together with the month chosen, will be the date

3. Find the date on the calendar and note the day of the week this falls on

4. The board lists the 7 days of the week - put a counter on the day and leave it there

5. Put the pieces of paper back in the correct envelope after your turn

6. The next player has their turn

7. Each player is looking to have a counter on every
day of the week

8. If you can’t go (because you already have a counter on one of the days or the number you select does not fall on a day of the month - eg 30 February) – you miss a turn

9. The first person to land on every day of the week wins!

XVIII XI MMXIV
18 11 2014
One hypothesis is that they derive from notches on tally sticks

Alfred Hooper's hypothesis is about relation to hand signals

The Hypotheses of Roman Numerals
Where did they originate?
Why are Numbers Important?
We simply need numbers to count
Numbers are used in daily life for everybody – it is a universal language
Without numbers we wouldn’t be able to read the date or time, have no value of money, construct buildings or make medicines, we would have no phone numbers and wouldn’t be able to calculate distance
Numbers are used in every subject

Why is the History of Mathematics Important?
Recommended texts:
The Really Useful Maths Book: A guide to interactive teaching - Tony Brown and Henry Liebling

Fun with Roman Numerals - David A. Adler

Roman Numerals I to MM - Arthur Geisert
Recommended websites:
Year 4 - Roman numerals should be put into their historical context so that pupils can understand that there have been different ways to write whole numbers. Also, they need to know that the important concepts of zero and place value were introduced over a period of time.
Why should Roman numerals be put in to their historical context?
Lower Key Stage 2 - to be able to tell and write the time including Roman numerals from I to XII.

Year 4 - to be able to read Roman numerals to 100 and know that over time the number system changed to include the concept of zero and place value.

Upper Key Stage 2 - to be able to read Roman numerals to 1,000 and recognise years in Roman numerals.
Cross-curricular links:

MFL - Using the same activity, but this time, with the months and numbers in a foreign language. The children can note down their answers on a sheet, so assessment for learning is available.
Day trips!
The British Museum

Roman Workshop - inside classroom or outside of school

Fishbourne Roman Palace
Fibonacci
Fibonacci, as a little boy, travelled with his father around Bugia where he learnt about the Hindu/ Arabic number system.
He was inspired by this system so he travelled around the Mediterranean to study under the leading Arab Mathematicians.
When Fibonacci returned he wrote a book.
Lower ability:
Roman numerals in their envelope - simple form.
Help sheet (key), showing Roman numerals as numbers.

Middle ability:
Roman numerals in their envelope - simple form, with some sums.


LO:
To be able to read and recognise Roman numerals
To understand how the number system has developed over a period of time
To be able to work out sums using Roman numerals
References:
National Centre for Excellence in the Teaching of Mathematics (2010)
Primary Magazine - Issue 20: A little bit of history.
[Online] Available at:
https://www.ncetm.org.uk/resources/22776
(Accessed: 7 November 2014)
Knapp, J. (2014) 'Number System (including Games) through History: Session 2, Year 2', QB5032: Mathematics Subject specialism. Kingston University. Unpublished.
Ancient Roman Numbers:
http://gwydir.demon.co.uk/jo/numbers/roman/index.htm
A little bit of history - Roman numerals:
https://www.ncetm.org.uk/resources/11689
A little bit of history - Famous Mathematician - Fibonacci:
https://www.ncetm.org.uk/resources/22776

Sussex Past. (No date)
The Sussex Archaeological Society.
[Online] Available at:
http://sussexpast.co.uk/properties-to-discover/fishbourne-roman-palace/learning-at-fishbourne
(Accessed: 3 November 2014)

Sussex Past. (No date)
The Sussex Archaeological Society.
[Online] Available at:
http://sussexpast.co.uk/properties-to-discover/fishbourne-roman-palace/learning-at-fishbourne/learning-programme-what-you-can-do-at-fishbourne-21
(Accessed: 3 November 2014)

Department of Education. (2013) Mathematics programmes of study: key stages 1 and 2 National curriculum in England. [Online] Available from:
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/335158/PRIMARY_national_curriculum_-_Mathematics_220714.pdf
[Accessed: 27 October 2014].

Maths Is Fun. (2014) The Evolution of Numbers. [Online] Available at:
http://www.mathsisfun.com/numbers/evolution-of-numbers.html
[Accessed: 16 October 2014].

Paul Lewis. (2005) Roman numerals – Modern uses. [Online] Available at:
http://www.web40571.clarahost.co.uk/roman/use.htm
[Accessed: 20 October 2014].

Know the Romans. The Epic Guide to Roman numerals. [Online] Available at:
http://knowtheromans.co.uk/Categories/SubCatagories/RomanNumerals/
[Accessed: 18 October 2014].

Jo Edkins. (2006) Ancient Roman Numerals. [Online] Available at:
http://gwydir.demon.co.uk/jo/numbers/roman/index.htm
[Accessed: 20 October 2014].

Encyclopaedia Britannica Inc. (2014) Numerals and numeral systems. [Online] Available at:
http://www.britannica.com/EBchecked/topic/682032/numerals-and-numeral-systems/233814/Roman-numerals
[Accessed: 20 October 2014]



Tes Connect. (2014)
GAME: Calendar Spin.
[Online] Available at:
www.tes.co.uk/teaching-resource/GAME-Calendar-Spin-6425686/
(Accessed:20 October 2014)

Tondering, C. (2014)
The Roman Calendar.
[Online] Available at:
http://www.tondering.dk/claus/cal/roman.php
(Accessed on: 3 November 2014 )
Roman Arithmetic:
http://turner.faculty.swau.edu/mathematics/materialslibrary/roman/
Differentiation
Full transcript