We are planning for Maths Week 2016. If you have any suggestions/ comments about how we can make it better or what you would like to see or engage with, please send us a note at mathsweek@wit.ie. We need your input.
Maths Week Newsletter June 2016
Welcome to this June issue of Maths Week Ireland Newsletter. No doubt all primary school teachers and post primary teachers in Northern Ireland and their students are now winding down for this academic year and finalising assessments and reports! Unless you’ve been buried under those report books for June you will also be aware that both the Republic of Ireland and Northern Ireland are part of the UEFA Euro 2016 opening stages – we have both fingers and toes crossed that both teams make it through to the next stage! With that in mind we have developed a ‘low threshold high ceiling’ problem for your primary pupils based on the opening group stages for Euro 2016 – scroll down to find out more.
We are also busy getting ready for Maths Week Ireland 2016 and would love to hear your thoughts about what you would like to see included in this year’s programme. Please let us know by dropping us an email at: mathsweek@wit.ie .
In this issue:
Bloomsday
Maths Week Programme Manager appointed
Celebrating Jerome Bruner
New standardised maths tests on the way for primary
LearnStorm: online maths initiative
The importance of engineering, technology and maths today
What not to say to a Leaving Certificate student this month
More about George Boole
UEFA 2016 challenge
Douglas Buchanan: Maths beyond the Textbook
Coming Events
Bloomsday
Today is Bloomsday celebrating James Joyce’s Ulysses which followed the lives of Dubliners on 16th June 1904. Aficionados today breakfasted on offal and cycled around on butcher boy bicycles and paraded in Edwardian dress. Widely regarded as one of the most important works of the 20thCentury, the book is often cited as an example of this country’s talent for the arts. What is not commonly acknowledged is the amount of mathematical and scientific references in Ulysses, usually in the musings of (an often confused) Leopold Bloom. It illustrates that maths and science could be part of everyday discussion. It would appear that nowadays maths and science are confined to the workplace or classroom and have no place in our broader cultural exchange. How has this come about? This will be explored at the Robert Boyle Summer School in Lismore next week with leading speakers from the world of maths, science, history and the arts. Special rates still apply if you go here
http://www.robertboyle.ie/programme
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Maths Week Programme Manager Appointed
We are delighted to announce that Ms Claire Flynn will be joining the Maths Week team as programme manager. Claire has a background in primary school teaching leading many maths initiatives. She comes to us from Mathematical Mastery in London.She will make Maths Week even better and we look forward to this new phase of Maths Week.
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Jerome Bruner
It was with great sadness that we learned of the death of Jerome Bruner this month. Bruner, born in America in 1915, was a renowned cognitive psychologist and made major contributions to educational psychology. One of his biggest influences on maths education was his Theory of Development: he believed that children should not learn by rote memorisation but rather through three stages of representation. These are more commonly known in the educational world today as the concrete, pictorial and abstract approach. This approach is implemented by teachers and educational bodies worldwide.
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New standardised maths tests on the way for primary
Primary reading and maths assessments are reportedly being overhauled in response to the success of targets set in the 2011 – 2020 National Literacy and Numeracy Strategy for primary level.
The tests currently used in schools were last standardised in 2006 and 2007. The Educational Research Centre at St Patrick’s College Dublin will be developing the new tests. The revisions for the assessments have been sanctioned but are expected to take place over the coming two and a half years. Read the full article here.
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Learnstorm
30 000 Irish students took part in an online maths initiative in Dublin Castle this month. LearnStorm, a free nine-week “maths and mindset challenge” was aimed at building students’ confidence and competence at maths. Students had two months leading up to this main event where the top 200 gathered to complete team based activities and problem solving exercises.
“It’s designed to reward the hard work and persistence of each student, something that the traditional method of maths education isn’t able to measure,” said Adam Bargroff from Camara Ireland.
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Importance of STEM
Last month our very own, Sheila Donegan (a Director of Calmast), was one of three people who featured in an article about how science and technology shaped her career. Sheila highlights the importance of STEM in Ireland and how Calmast encourages and promotes maths in Ireland across all age groups. You can read the full article here.
http://www.irishtimes.com/news/education/innovation-is-in-our-dna-1.2650971
What not to say to an exam student
We are of course thinking of all the secondary pupils completing junior and leaving certificate exams this month. Click here to listen to some tips of what you should and shouldn’t say to them this month.
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More on George Boole
We spent a lot of last year highlighting George Boole. We're glad to pass on the news that a book about Boole's family is coming out. The Booles and the Hintons Two dynasties that helped shape the modern world by Gerry Kennedy is published by Cork University Press. It will be launched by Boole's greatest friend, Professor Des MacHale on Wednesday 29 June 2016 at UCC
For further information contact Cork University Press Tel: 00 353 (0)21 4902890
Further details of the book at www.corkuniversitypress.com
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UEFA Maths Challenge
Can you calculate how many games it would take to qualify from your group?
UEFA Facts:
- There are 4 teams in a group.
- Each team plays every other team once.
For example, France, Switzerland, Albania and Romania are all in Group A. How many matches will be played in total in this group?
Can you draw a diagram to show how you found the answer?
What would happen if there were 6 teams in a group – how many matches would be played then?
What diagram would you draw to show your answer?
Based your two (or more) calculations can you figure out a formula that will tell you how many matches are needed for any given group size, for example if there were 8 teams in a group or 12 teams?
What if….
It was a knockout group and there are 16 teams in the group (with no replays for draw results) how many matches will there have to be to get a winner?
What if there is to be a playoff to select 3rd place: how would this effect the number of matches?
Can you find a pattern that relates numbers of teams with numbers of matches? Can you write this as a mathematical expression?
How many matches would be needed if there are 64 teams?
These numbers(16 & 64) are all powers of 2 – what happens if we start with a number of teams that is not a power of 2? How would we handle an odd number?
Solutions can be found at the end of this newsletter.
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Coming Events
The 5th Robert Boyle Summer School will address the theme of “Science and Irish Identity”. Mathematics will be considered as part of Irish Scienceand among the speakers will be Dr David Attis (author of Mathematics and the Making of Modern Ireland). The school attracts many teachers and others who like to explore the place of science and maths in our heritage.
More info here
www.robertboyle.ie
http://www.robertboyle.ie/programme
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In Service Courses for Primary Teachers
The in-service summer courses for RoI primary teachers feature many maths / problem solving courses at many locations. The booklet is organised by location and can be found here
http://www.ecdrumcondra.ie/images/Rpt_Publication_180516.pdf
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European Maths Congress
The European Mathematical Society is organising the 7th European Mathematics Congress in Berlin July 18 – 22nd.
http://www.7ecm.de/
On the 20th July there will be a session organised by the EMS Raising Public Awareness committee which will feature the following case studies:
- Roberto Natalini: Raising Public Mathematical Awareness in Europe
- Eoin Gill: How you can organize a Maths Week and survive
- Andreas Matt & Betul Tanbay: Imaginary.org, theory and applications
- Sylvie Benzoni: How Mathematics is necessary to the life of planet Earth
There will also be “Mathematik für die Öffentlichkeit zum ECM 2016” (“mathematics for a general public at the occasion of the ECM2016”).
The idea is to be present at three underground stations in the center of Berlin where many people and tourists are to be expected. We will be trying out some Maths Week Ireland activities on Berliners and Tourists alike. We plan to be active from 10 am to 4 pm on July 18th and 19th(Monday and Tuesday).
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International Congress on Mathematics Education
ICME13 International Congress on Mathematics Education will take place in Hamburg 24th - 31st July. This conference will bring thousands together to cover all aspects of maths education and here again Irish maths will be on the programme. Dr Maurice O’Reilly is coordinating and Irish National Presentation on Saturday 30th July. This will be be a 90-minute presentation (16:30-18:00) on Mathematics Education in Ireland. This will comprise a an introduction to the Irish education system (with an emphasis on where mathematics is situated within it) and a summary ofpolicy relating to mathematics education; the second session will outline the Irish curriculum (relating to mathematics) and an overview ofresearch in mathematics education in Ireland.
In addition, there will be a booth where materials relating to the INP can be presented.
See here for conference website
or paste http://icme13.org/ into your browser.
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MathsJam
The MathsJam Annual Gathering 2016 will take place from November 12 – 13 at Yarnfield (between Birmingham and Manchester). This is run by Maths Week regular Colin Wright who is indefatigably enthusiastic about all things mathematical. The fun weekend is for people interested in puzzles and recreational maths.
Colin assures us “there are discounts for the unwaged, and a 10% discount if you book and pay early. Exactly how early is a moveable feast, but it's most likely going to be valid until the end of August, possibly a little longer.”
http://www.mathsjam.com/conference/index.php
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DCBEAGLE Challenges
Douglas Buchanan
www.dcbeagle.com
douglas@dcbeagle.com
DCBEAGLE MATHS BEYOND THE TEXTBOOK
June 2016 Douglas Buchanan
~ douglas@dcbeagle.com ~
~www.dcbeagle.com ~
@dcbeagle1
Puzzle of the month
Heat Wave puzzle
4 married couples went on a picnic and they took 32 bottles of lemonade – remember theses puzzles come from a 1950s book. Mary only disposed 1 bottle, Ann had two and Jane had three bottles and finally Liz consumed 4. John McGregor drank the same quantity as his better half. Lloyd Jones drank twice as much as his wife and William Smith drank 3 times as much as his wife and Patrick Dolan disposed of 4 times as much as his wife. Which man was married to which woman?
Websites of the month
1001 mathproblems (http://www.1001mathproblems.com)
This is an ideal website for the summer holidays for Key Stage 2 pupils. The puzzles are varied with many old favourites and they can be done as a family project.
Math Salamanders (http://www.math-salamanders.com)
This website covers a much wider age range and all the puzzles can be printed out if required.
Videos of the month
BBC Maths Channel - http://www.bbc.co.uk/programmes/b007cnyb - click on clips. Key Stage 2
Maths Mansion – click here – https://www.youtube.com/watch?v=v1G6PXayO3Q&list=PL47Eq6-2EcXLwkwMHK9qQEyh2L-DXRBUu
Channel 4 series … still one of my favourites.
Donald Duck in MathMagic – click here https://www.youtube.com/watch?v=2J886dbCg6c
Final words
It has been a wonderful year for me and I would like to thank you for supporting the newsletter and my events. My aim is always to put something back into education during my retirement years. With the hype of the summer holidays looming and the exciting school events leading up to it you will not be really interested in reading my newsletter so the next publication will be in September. Happy holidays!
.
Douglas
www.dcbeagle.com
douglas@dcbeagle.com
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UEFA Challenge Solution
Group stage – every team plays every other team once. Remember that each team cannot play against themselves!
This approach is a special area of maths called "graph theory". It is used for analysing connections and relationships. As you can imagine it is a really important branch of mathematics today with the internet, mobile phones and social media. In graph theory Graphs show points (vertices) and connections (edges) and the scale doesn't matter just who's connected to who!
If we call the number of teams in each group ‘n’ then we can calculate the number of matches played for any given group size. For example, if there are 6 (n) teams in a group then the first team can play against every other team meaning there will be 5 matches (n – 1). The second team has already played the first team so it cannot be recounted: they have four other matches to play (n – 2). This can then be repeated for the third team, who cannot play against the first or second team again (n – 3) and fourth team (n – 4), etc… This then results in the expression:
(n-1) + (n-2) + (n-3) + (n-4) +….+ (n-n)
If n = 6:
5 + 4 + 3 + 2 + 1 + 0 = 15
A formula for calculating the number of matches m, when there are n teams in a group is
m = (n-1) n/2
This formula can be used to calculate the number of matches for any given number of teams in a group stage.
Pupils may also have recorded the pattern using a table. By doing so they should observe that the increase in the number of matches each time is one less than the number of teams in the group. They could then apply this to calculate that if there are seven teams in a group they will have 15 matches plus 6 which is equal to 21.
| Teams |
Matches |
Increase in number of matches with each additional team. |
| 1 |
0 |
0 |
| 2 |
1 |
1 |
| 3 |
3 |
2 |
| 4 |
6 |
3 |
| 5 |
10 |
4 |
| 6 |
15 |
5 |
| 7 |
? |
? |
Solution to knockout puzzle:
If there are 16 teams in the tournament to begin with they will each play another team leaving eight teams knocked out and eight teams remaining (after eight matches). This will then repeat and there will be four teams knocked out and four remaining (after another four matches). Once the remaining four teams have played against each other there will be two teams remaining (after two matches). The winner of the tournament will then be decided by the final match. There will have been 15 matches.
8 + 4 + 2 + 1 = 15
This is 16 - 1
This can also be explored with a diagram. Here is one for 8 teams.
4 + 2 + 1 = 7 matches - That's 8-1 =7
Does this always hold - in a knockout tournament is there one less match than the number of teams? You can explore this by trying other numbers.It works out nice and evenly when we have a power of 2 : 4,8,16, 32 etc. For other numbers we will have to let teams have a "bye" into a further round. Let's take 5 as an example.
Here we can see 4 matches - n-1 again.
We can reason this by seeing that if there is a knockout tournament of n teams then one team is knocked out at each match leaving one winner in the end. Therefore n-1 teams must be knocked out. Therefore we need n-1 matches.
(If we wanted a 3rd place we would play off the losing semi-finalists giving one additional match.)
|
