# 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

# March 2016 News

Welcome to the March 2016 Transum Mathematics newsletter.

I hope you made use of the 29th February Starter last month because it only appears every four years.

The Tower of Hanoi Puzzle

As usual we will begin with the puzzle of the month. What is the smallest square number (greater than one) that cannot be expressed as the sum of two prime numbers? The answer is at the end of this newsletter.

There’s nothing like a good puzzle involving prime numbers. Opportunities to remind pupils of what prime numbers are and how important they are as the building blocks of the number system are perhaps too infrequent for many pupils. Transum has a number of activities which can be found by typing the word prime into the search box at the bottom of any Transum page.

‘Prime Numbers’ is one of the few school mathematics topics that occasionally appears in the news. A new prime more than 22 million digits long, five million longer than the previous largest known prime was found recently. This number, the 49th known Mersenne prime, was discovered by Dr Curtis Cooper at the University of Central Missouri. Large prime numbers are important in computer encryption and help make sure that online banking, shopping and private messaging are secure.

Don’t forget to include some of the amazing facts about prime numbers when you are teaching the basics. It will capture the imagination of some pupils and ensure the learning is long-lasting. The podcast version of this newsletter contains many more interesting prime facts.

So what has changed on the Transum website since the last newsletter? Each page gets a makeover when it reaches its third birthday but also new content is being added every month.

A Similar Shapes self-marking exercise has been added. This topic is one that typically defies intuition. When the dimensions of a solid are doubled, its volume increases by a factor of eight and facts such as that are quite hard for pupils to appreciate.

Another self-marking exercise provides practice in finding the nth term of quadratic sequences. It is not a skill every pupil will need, only those on course for higher grades, but this randomly generated quiz should prove to be a handy tool for the busy teacher.

The Human Graphs visual aid is proving to be hilarious. It has not failed to bring a smile to the faces of all those who have used it so far. It makes fun the process of recognising the shapes of the graphs of simple polynomials and really brakes the ice in any Maths lesson.

The Ludicross Puzzle challenges pupils to arrange the given numbers on the cross so that the sum of the numbers in both diagonals is the same. It is quite easy to find one solution but finding all the possible different solutions is another challenge.

Once the basics of arithmetic with negative numbers has been mastered, the Negative Magic puzzles will provide some of the practice required to consolidate the understanding. This is another randomly generated, self-marking activity that can be used many times with the same pupils.

There are many versions of the Tower of Hanoi puzzle on the internet but this one encourages pupils to find a pattern in the number sequence generated. There are a total of ten different levels but it is not expected that anyone will have the time to do the higher levels as far too many moves are required. Level 10 of this puzzle featured in an episode in the 1966 Doctor Who story called The Celestial Toymaker. The villain forces the Doctor to work on a ten-piece Tower of Hanoi puzzle (which they call The Trilogic Game) and if the Doctor manages to complete the puzzle, the Toymaker’s domain would disappear.

Finally sometimes the simplest ideas are the most useful. The Place Value Chart is certainly nothing new but the functionality it provides may help you make sense of this important yet basic topic.

Your thinking time is up! The answer to the puzzle posed at the beginning of this newsletter is 121. Did you, in the process of arriving at this answer notice that every other sum of two primes adding up to a square number included the number two? Can you think of an explanation for that?

Enjoy the month of March

John

ps. All prime numbers except 2 are odd, this makes 2 the oddest prime!