Monthly Archives: September 2015

October 2015 News

In the days before Wikipedia and Google we might refer to an encyclopedia to find answers to our questions. The puzzle for this newsletter is based on a set of ten volumes of an encyclopedia on a bookshelf arranged in order with volume one on the left and volume ten on the right.

A bookworm eats through from the front cover of volume one to the back cover of volume ten. What is the length of the bookworm’s meal if each encyclopedia is 5cm thick (the pages are 4cm and each cover is 0.5 cm thick)?

The answer is at the end of this newsletter but, be warned, it is not the obvious answer.

This puzzle is a version of the February 2nd Starter of the Day which presents a random number of encyclopedias and randomly generated measurements for the pages and covers. It provides an opportunity for pupils to engage in some decimal addition and multiplication before being surprised by the actual answer.

Now the pages on the Transum website should be a little easier to find as the search facility has been upgraded. Now when you search for a term you get two sets of results. The first is directly from the Transum database and is a search on page titles and descriptions. Lower down the page you will see the Google search results which include snippets of text found on the pages.

510

You may like to try out the new search feature to find this month’s new additions. Firstly the Car Park Puzzle challenges you to get your car out of the very crowded car park by moving other cars forwards or backwards. It is the Transum version of a puzzle that has been available in different formats for many years but the real challenge for students is to devise a level 6 puzzle that is possible but requires more moves than level 5. The way the students record moves and consider the advantages of working backwards (doing and undoing) give this challenge a strong mathematical connection.

Polybragging is another new activity that is also based on an idea that has been around for a long time. This is a game for two or more players. Each played needs a tablet, computer or smartphone with the page loaded.

If you have ever played a card game called Top Trumps you will know the main idea of this game already. Each player is given a shape that the computer selects at random. The players each choose a shape property and whichever player has the highest value for that property wins a point.

The properties available include the size of the largest interior angle, number of pairs of parallel lines, number of lines of symmetry and the order of rotational symmetry.

Hopefully, by playing the game, pupils will develop more familiarity and a greater knowledge of the properties of polygons.

Other new additions to the site include a Dice and Spinners page to use if you can’t find the real things and a Reaction Time activity which collects data about how quickly we recognise even compared to odd numbers.

Finally some more traditional Maths exercises have been added. These include Multi-step Problems and Decimal Times. These exercises are self-marking, printable and every pupil gets a slightly different version thanks to the in-built random number generator.

Thanks to everyone who has added comments and suggestions to the site this month. Your input keeps the site alive. One comment waiting for your opinion is that made by Leslie Jackson on the 16th December Starter page. Do you think powers of two are 2, 4, 8 .. or do you think they are 4, 9, 16 …?

Finally the answer to this month’s puzzle. The answer is not 50cm surprisingly. If you picture the ten volumes arranged on the shelf you will notice that the front cover of volume one is actually on the right, next to volume two! So if the bookworm starts by eating through that cover it has missed the pages and back cover of volume one altogether. Similarly the back cover of volume ten is on the left so the bookworm stops before eating the pages and front cover of volume ten.

The correct answer is 50cm – 2(4cm + 0.5cm) = 41cm

Enjoy October and don’t miss the Halloween Starter at the very end of the month.

John

ps What do you get if you divide the circumference of a Halloween lantern by its diameter?

A: Pumpkin Pi

 

September 2015 News

It seems such a long time since the last newsletter but here it is again to welcome the month of September 2015. I have had a wonderful summer (northern hemisphere) and managed to visit lots of places and catch up with many old friends. I always had my laptop with me so found the time to write more puzzles, quizzes and activities to add to the ever-growing Transum collection.

Before going any further let’s go straight to the puzzle for this week. This is to give you something to think about as you commute, exercise or relax today so don’t look at the answer at the bottom of this newsletter if you want to enjoy the challenge.

Three very logical mathematicians walk into a bar (change this to a sweet shop if you are telling it to your pupils). The barman asks if they all wanted a drink. The first mathematician said “I don’t know”, the second mathematician said “I don’t know” but the third mathematician said “Yes we do”. Can you explain how the third mathematician could be so certain?

While you think about that here’s a mention of some of the new activities created since the last newsletter.

The Fractal Mosaic is an interactive, animated version if the Snowflake Squares activity. A fractal-like pattern can be created by following a very simple set of instructions that are repeated a number of times. The end result makes excellent display material. Talking of which, a new section called Maths On Display has been created giving you some ideas of how your pupils can engage in mathematical activities that produce very pleasing results.

Fractal Mosaic

Follow the rule repeatedly to create this beautiful pattern

Following the success of the Bridge Crossing starter a challenge called ‘Without Lifting the Pencil’ provides pupils with six designs that they have to decide whether they can trace according to the rules. Instead of actually using a pencil and paper the Transum interactive version allows them to click dots (the nodes) to simulate the tracing and makes it easier for them to try many different routes quickly and not worry about making mistakes.

A Frequently Asked Questions section has been added for subscribers but, thus far, there are not many questions and answers posted. The plan is to add to this slowly but surely over the coming months. If you have any questions about using Transum Mathematics please let me know as your question might be suitable for this FAQ page.

The One Torch Tunnel challenge has been added as an interactive page which I hope will be as popular as River Crossings is. It is quite easy to get all four people through the tunnel but not so easy to do it in the optimal time.

A Fibonacci Quest section has been added. The plan is to, over a period of time, add fascinating Fibonacci facts to these pages but each new page will have an interactive aspect to it so that pupils learn by doing!

The Probability Washing Line is certainly not a new idea. Pupils are invited to hang out the shirts, each containing a probability word, on a line stretching from impossible to certain. The software will check their attempts according to some very loose rules.

There was nothing on the website to practise Telling the Time … but now there is! Lots of analogue clocks with some mixed questions thrown into level four. As with all other activities on the site let me know if you think this section should be expanded.

The answer to the puzzle asked at the beginning of this newsletter can be explained as follows.

If the first mathematician did not want a drink he would be certain that not all three wanted a drink as there was at least one of them (himself) that did not. He would have therefore replied “No” instead of “I don’t know”. The third mathematician was therefore sure that the first mathematician did want a drink due to his answer.

The same argument can be also applied to the second mathematician who must also have wanted a drink.

The third mathematician was quite certain he wanted a drink himself bringing the total to three.

That’s all for now. Enjoy September and if it’s the beginning of your school year enjoy all that newness and new-beginning enthusiasm that’s around at the moment.

John

ps How many times can you subtract 7 from 83, and what is left afterwards?

Answer: I can subtract it as many times as I want, and it leaves 76 every time!