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![Page 1: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/1.jpg)
© University of Reading 2007 www.reading.ac.uk
University of West Indies
April 18, 2023
Greetings from England!
Dr Geoff [email protected]
![Page 2: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/2.jpg)
2
It’s cold in England right now…
![Page 3: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/3.jpg)
3
A sign we don’t get back home…
![Page 4: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/4.jpg)
4
Hurrah for her Majesty the Queen!
![Page 5: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/5.jpg)
5
Hurrah for Jamaican Independence!
![Page 6: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/6.jpg)
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And hurrah for mathematics!
![Page 7: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/7.jpg)
A problem I’d like to share with you…
Which is guaranteed to provoke a spontaneous gasp of awe and wonder!
You’ll need pen and paper….
….and I need a volunteer with a loud clear voice
![Page 8: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/8.jpg)
Think of a three digit number, with the first and last digits different. So 123 would be fine but 121 isn’t
Reverse the digits – so 123 becomes 321
Subtract the smaller from the larger: in this case 321 – 123
If your number is less than 100 then put in 0s to make it three digits – so 75 becomes 075
Reverse the digits – so 075 becomes 570
Add the two last numbers together: in this case 075 + 570
Now can my volunteer open the envelope and read out the contents!
So here’s the problem!
![Page 9: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/9.jpg)
A competition with a (very) smallprize per year group
Why does this always happen?
Note: full solution is hard, very interested in responses like, “What I noticed is that after the subtraction the numbers always……”
Email me at [email protected]
If I have a lot of responses I’ll ask the Principal to invite me back!
![Page 10: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/10.jpg)
Mathematics: a great subject to study…
-Intrinsically interesting, with beautiful connections eg. between algebra and geometry;
-Useful in everyday life – numeracy, problem-solving techniques;
-Underpins many lines of work – engineering, business, accountancy, science, actuarial science, ICT, meterology, economics, teaching, many others.
See http://www.mathscareers.org.uk/ for more information.
![Page 11: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/11.jpg)
A special thank you…
…to all the mathematics teachers;
…and to all the teachers here.
May God bless you:
-Here at Holy Childhood School;
-As you leave and enter the adult world.
![Page 12: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/12.jpg)
Thank you for having me…
May God blessyou always
Dr Geoff TennantInstitute of Education, University of Reading, UK
Visiting lecturer at the University of West Indies until March 23rd
![Page 13: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/13.jpg)
Think of a three digit number, with the first and last digits different. So 123 would be fine but 121 isn’t
Reverse the digits – so 123 becomes 321
Subtract the smaller from the larger: in this case 321 – 123
If your number is less than 100 then put in 0s to make it three digits – so 75 becomes 075
So here’s the problem (1)!
![Page 14: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/14.jpg)
If your number is less than 100 then put in 0s to make it three digits – so 75 becomes 075
Reverse the digits – so 075 becomes 570
Add the two last numbers together: in this case 075 + 570
Now can my volunteer open the envelope and read out the contents!
So here’s the problem (2)!
![Page 15: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/15.jpg)
Let’s try this – the counterfeit coin problem.
I have 9 coins that look and feel identical. One is lighter than the other 8.
I can use a weighing scale to balance coins against each other, but I have limited access, so need to use it as few times as possible.
How many uses of the
OK, so you know that problem (1)
![Page 16: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/16.jpg)
How many uses of the weighing scales do I need to identify the one counterfeit coin?
What is the maximum number of coins from which I can identify one counterfeit lighter coin from with 3 uses of the balance? 4? 5?
Challenge (very difficult!) How do you identify one counterfeit coin, which may be either lighter or heavier, with 3 uses of the scales with 12 coins altogether?
OK, so you know that problem (2)
![Page 17: © University of Reading 2007 University of West Indies April 30, 2015 Greetings from England! Dr Geoff Tennant g.d.tennant@reading.ac.uk.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649ca35503460f94963dde/html5/thumbnails/17.jpg)
A competition with a (very) small prize per year group
Email me at
with any solutions you have to any of these problems. I promise to reply to all emails.
If I have a lot of responses I’ll ask the Principal to invite me back!