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Carrot-eating Critters

Thursday 1st August 2019

This is the Transum Newsletter for the month of August 2019. It begins, as usual with the puzzle of the month.

In a field there are 20 animals (donkeys, goats and rabbits) who between them eat 20 carrots. Each donkey eats 3 carrots, each goat eats 1.5 carrots and each rabbit eats half of a carrot.

How many of each kind of animal are in the field?

Carrot Critters

The answer is at the end of this newsletter.

While you think about that here are some of the key resources added to the Transum website during the last month.

When I was a lad I was a Sea Scout. Thinking back to the happy days spent boating on Patshull Pool I came up with the idea of Scouts in Boats. It is a more classroom-safe version of an old puzzle from 1850 and is presented in increasing levels of difficulty. The task is easily understood but not so easy to implement. Be prepared!

Scouts In Boats

Not all school mathematics should be exciting and fun. There’s place for good old fashioned drill and practice too but there is no law to say it cannot be enjoyable in its own right. The new activity called Three Prime Sum provides practice recalling prime numbers and flexing the mental arithmetic muscles at the same time. This exercise is based on the Goldbach Conjecture - every integer greater than 5 can be written as the sum of three prime numbers, such as 25 = 11 + 7 + 7. There is more to the Goldbach Conjecture and articles found in books and online would make interesting reading for the inquisitive learner.

As usual I have a mathematics book to tell you about this month. Geometry Snacks (Bite Size Problems and Multiple Ways to Solve Them) is one of those books that turns out to be better than I thought it would be. I now have a new set of strategies for solving geometrical problems just when I thought I knew it all. In fact I was so impressed with this book that I contacted the publisher, Tarquin, and asked permission to include one of the 'snacks' as an Advanced lesson Starter. I would love to know how this Geometry Snack Starter works with your higher achieving mathematicians.

Many of you are enjoying the long school holiday at the moment (though for many others it's business as normal) and your pupils are slowly forgetting a lot of the mathematics they learnt last term. It's not completely out of the question to send them an email with a link to some Holiday Maths Activities - Just a thought!

Maths Holiday Activities

I have just finished listening to the wonderful Mr Barton Podcast in which a large number of educators each talk about one thing they have learnt during this last year. One of the contributors who made me smile was Rob Eastaway (puzzle adviser to the New Scientist magazine) who talked about the link between humour and creativity and highlighted the lack of humour in examination questions. I have included a small extract of his ‘Slice of Advice’ in the podcast version of this newsletter in which he advocated a little more humour in mathematics learning.

Although I can offer a ‘bolt on’ contribution in the form of Maths Jokes the real need is for a ‘built in’ relaxed atmosphere in lessons where humour is the norm whether it be an ability to laugh at ones errors or having ‘in jokes’ to help remember mathematical concepts. I hope that the Transum activities resound with this notion.

Don't forget you can listen to this month's podcast which is the audio version of this Newsletter. You can find it on Stitcher or Apple Podcasts. You can follow Transum on Twitter and 'like' Transum on Facebook

Finally the answer to this month's puzzle is 2 donkeys, 5 goats and 13 rabbits. A similar puzzle appeared in the Bakhshali Manuscript in the year 350 and is essentially a situation that can be described with two simultaneous equations involving three variables. These variables however need to be whole numbers. I solved it using systematic listing mixed with trial and improvement. Technology helped!

That's all for now,

John

PS. I am determined to count backwards from a thousand; I will stop at nothing.


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