# Square in Rectangle Puzzle

Despite this being the middle of the exam season for some I would still like to take your mind off your daily routine to present you with a puzzle.

Imagine a 10cm by 15cm rectangle. What is the largest square that can be drawn snuggly in one corner that just touches the rectangle’s diagonal. The answer will be at the end of this newsletter.

Now let’s dive into the new activities added to the Transum website this last month.

The Value of Places is, as the title suggests, a place value quiz. It can be sometimes difficult to find more challenging place value activities for Secondary students as they have been learning about place value since early Primary and have probably done the usual types of activity. This online exercise challenges pupils to figure out how many times bigger the value represented by one digit is than the value of another digit in the same number.

Prime Pairs Game is for two players who take it in turns to add a numbered card to either end of a row of cards so that every adjacent pair of cards adds up to a prime number.

Graph Paper has been updated. I think it is the quickest way you can print a sheet of graph paper with numbered axes to suit any graph you may need to draw.

eQuation Generator has also been updated. Its only function is to present you, the teacher, with an endless supply of linear equations that you can project in front of your class. The update improves the delicate balance between providing more of the same while presenting many variations of the chosen type of equation.

Likelihood is a new title given to the probability sorting activity. A pupil’s ordering of the given situations is matched against the average ranking of all the other people who have done the activity.

Loci Land is live but not yet finished at the time of writing this newsletter. I do expect it to be completed in the next week. It currently contains  two real life situations that pupils copy on to squared paper then draw the constructions in order to answer the loci question. More questions will be added soon.

I heard an interesting fact on a podcast I subscribe to last month. Did you know that rather than (in the UK) having 1p, 2p, 5p etc. coins it would be mathematically more efficient to have 1p, 3p, 11p and 37p coins? I have included the excerpt from the podcast in the Transum podcast for this month which you can find at Transum.org/Podcast. If anyone would like to share a proof of that in a form that pupils could understand please let me know and if facts like that are your thing, don’t miss the Maths Trivia page.

On a different subject I am happy to say that you now have the option of viewing Transum webpages via https: as well as http:. This development took place last month when the more secure protocol was implemented. SSL (Secure Sockets Layer) is the standard security technology for establishing an encrypted link between a web server and a browser. This link ensures that all data passed between the web server and browsers remain private and integral. SSL is an industry standard and is used by millions of websites around the world.

Finally the answer to this month’s puzzle is that the area of the biggest square would be 36 square centimetres. You can see the diagram and my method on the ‘Square in Rectangle’ Advanced Starter page.

That’s all for this month,

John

P.S. If a got 50 pence for every time I failed a maths exam I’d have about £6.30 now

# December 2015 News

Happy Christmas. This is the December Transum newsletter coming to you with lots of festive cheer and good wishes for the future.

Here is the puzzle for this month. Noel and Merrie received some Christmas presents. The number of presents Noel received was a power of 3. The number of presents Merrie received was a power of 2. The number of Christmas presents they received were consecutive numbers and less than ten. How many presents did they receive?

You will probably arrive at a first answer fairly quickly but there are actually four different answers. Can you find all four? The answers will be given at the end of this newsletter after a rundown of the notable new features on the Transum website.

Although they are not a new idea, many teachers have never used mini whiteboards in class. The fact is that most classrooms are more likely to have pupils with computing devices than mini whiteboards so this simple facility allows you to make alternative use of the devices. Pupils write or draw their answer to plenary questions on this whiteboard simulator then hold up their devices so the teacher can see. This is a much better idea than putting hands up! This way the teacher can instantly see what everyone is thinking rather than just one person.

I would like to say that I am surprised that the Broken Chessboard Puzzle has been completed by so many people. The puzzle was first made popular by Henry Ernest Dudeney (1857 – 1930) who was an English author and mathematician. The puzzle appeared in his book ‘The Canterbury Puzzles and Other Curious Problems’ in 1907. I thought solving the puzzle would be too difficult for most people but I have been proved wrong. Congratulations to all those people who have earned a trophy for finding a correct solution.

The Starters for 6th March and 4th December have both been replaced with new ideas. The first is the Goat Grazing situation I have used for decades to introduce the topic of Loci. The latter challenges pupils to imagine a dice reflected in two mirrors. Quite a challenge for many.

The number of printable worksheets available only to subscribers is rapidly increasing. Even in these days of hi-tech it a good idea to provide variety to the learning experience with more practical activities particularly relevant to some Maths topics more than others.

Finally I would like to say how much I have enjoyed a new app I downloaded (free) to my iPad. It is called Sumaze and has been produced by MEI. Perfect for Year 12 students who need practice with inequalities, the modulus function, indices, logarithms and primes. It is also useful lower down the school but certain sections such as the logarithm puzzles would of course be inaccessible. Solving the thoughtfully constructed puzzles brings an enhanced understanding of the basic mathematical concepts in a fun setting. I’m stuck on the final level in Fermat’s Room so any suggestions gratefully received.

Are you having a problem thinking what to write in the Christmas cards you are sending to your Maths teacher colleagues? How about this:

It reads ‘Complements of the (Cs) season (2u) to you’.

Talking of Christmas and puzzles, here are the four answers to this month’s seasonal puzzle which is also the Starter for 16th December and called The Power of Christmas: