Tag Archives: Prime Numbers

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.

594The 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!

 

December 2014 News

Dear All,

This months’ newsletter is a few days early due to an email received from Fox News but more about that later.

This newsletter is for December so may I begin by wishing you a very happy Christmas. Many schools have special festive events in the weeks leading up to Christmas and Mathematics lessons can also have a seasonal theme. Here at Transum Mathematics there is a ChristMaths page linking to all sorts of yuletide linked mathematics. One of the time-honoured seasonal mathematical puzzles involves working out the total number of gifts received according to the song ‘Twelve Days of Christmas’. If you don’t know the song there are many versions of it online but the gist is that the obsessed lover delivers more and more presents on each of the 12 days of the holiday. Pupils are usually able to arrive at the answer themselves but there is no better way to check the answer than with some music. Scroll down the Twelve Days of Christmas starter page to find a musical excerpt from a Natalie Cole song in which she sings the answer!

Last week I received an email from the Fox News and Business Network in New York. They were asking for permission to use a diagram on Transum Mathematics in a forthcoming news programme. Unfortunately the numbers on the diagram were made-up figures for illustrative purposes only so it seemed the time was right to gather some real data. That is the reason this newsletter is being sent early. I would like to ask you to add to the data before the broadcast next week. I haven’t told you exactly the mathematical twist here but that will become evident when you answer the eight very simple questions:

 Transum.org/go/?to=Survey

… and if you could get your pupils to answer the questions online too that would be a real bonus!

Last Month’s Updates

The most surprisingly successful new activity on Transum Mathematics is the Dump-A-Dice Race game. It is designed for pupils needing practice recognising square and prime numbers up to 100 (that’s everyone isn’t it?) and is presented in the form of an online board game. It can be played by up to four players so provides an ideal opportunity to break from individual work. As the name suggests, the moves are determined by rolling online dice but, so that it is not purely a game of chance, three dice are rolled and the player has to decide which two should provide the total for their move. This means that skill is involved as the players have to choose the best way trough the numbered stepping stones.

The True Or False activity was updated. The updating process did reveal a couple of interesting thoughts. Would your pupils be able to sketch an irregular hexagon in which all of the external angles were 60 degrees? Also would they think a semicircle has to have a diameter as one of its sides or could a circle be cut into two equal area semicircles using a wavy line?

In addition to many pages on the website being updated, Matchstick Patterns has been added and in the next few days a new series of exercise on algebraic fractions will appear. Please let me know if you have any suggestions for new activities.

Comments

Many comments were received this month prompted by the Firewords starter with lots of new words being found.

On the subject of the Ice Cream starter, Dr Duxbury from Edwinstree Middle School says “A rather ambiguous question! Does ‘different’ mean you cannot have the same flavour twice (e.g. two strawberry scoops which I like) or that you count strawberry on the bottom and chocolate on top the same as chocolate on the bottom and strawberry on top (most ice-cream sellers rarely put the ice-cream side by side!). Do you have to have two scoops or can you have just one scoop? Many assumptions made here which makes for a very good discussion with your class where they can find a variety of answers! At the end of the day as long as students can justify and explain their answers, this is all that matters.”

After trying the Five Digits starter Glen from Brentwood says “I would argue that a multiple mode solution, e.g. {2,2,3,3,5}, is a contradiction. I.e. the mode equals the mean, and the mode does not equal the mean. I would also argue for allowing {0,0,0,0,0} as a solution. Our results are: {0,0,0,0,0}, {1,2,2,2,3}, {2,4,4,4,6}, {3,6,6,6,9}, {2,5,5,6,7}, {3,4,5,5,8}. Nice problem, thanks.”

Year 5 from Middlemarch School tried the activity called Satisfaction. The task, as it stands is impossible, but it certainly generates a great deal of mathematical thinking, reasoning and hypothesising. They say “We got 12 numbers on the grid and we are only Year 5! It should be called UNSATISFACTION.”

Finally, on the subject of the Wordles starter, JW from Luton says “Realised I could use this to prompt meaning of unfamiliar words/phrases, and maybe use the same idea to get the students to produce wall displays – to help them in class, and other students too.”

Thanks everyone for their comments, keep them coming!

Puzzle Answer

There were 364 presents delivered in the song “The Twelve Days of Christmas”

That’s all for now.

ps. If it’s cold this Christmas go and stand in the corner, because it is 90 degrees there!