# Go Figure the best problem solving strategy

In a break with tradition I am going to choose a puzzle of the month that I have already used as the monthly puzzle a couple of years ago. The reason is that two weeks ago I heard the most wonderful new solution to the puzzle that I’m sure you will appreciate so let’s start with the puzzle:

Three people enjoyed a meal at a restaurant. The waiter brings the bill for £30 so each person pays £10. Later the chef realises that the bill should have only been £25 so he sends the waiter back to the table with five pound coins. The waiter could not figure out how to divide the £5 so he gave each person a £1 and kept £2 for himself.

So….the three people have paid nine pounds each for the meal:  3 x £9 = £27
The waiter kept two pounds:   £27 + £2 = £29
What happened to the other pound?

The new answer will be at the bottom of this newsletter but before that here are some of the new resources added to the website this last month.

Go Figure is a number placing puzzle in which interconnected addition, subtraction. multiplication and division calculations have to be completed using the digits one to nine.

I got quite excited when I saw pupils using this activity for the first time and heard them talk about their insights. The puzzle can be used to introduce a new problem-solving strategy for this kind of task. Rather than concentrate on which digits could go in the available spaces, make a list of the digits that could not possibly go into the spaces. You really need to try this yourself to see how the properties of the four rules are analysed in the puzzle solving thinking. Make sure you click the ‘Show Tags’ button to assist you find the solution.

Olympic Rings was put together to coincide with the Winter Olympics but the relevance of the puzzle will live on during this inter-Olympic time. There are three levels of difficulty with the lower levels being made easier with some pre-placed digits. This makes the puzzle accessible to younger children but also provides a starting point for an advanced level proof investigation.

Map Scales came about because, after being asked for a good exercise on ratios as used in map scales, I couldn’t find one! There are two levels and the second level introduces the tricky and not necessarily intuitive notion of area scale factors.

Barmy BIDMAS Is a new advanced Lesson Starter. You will need to know about the order of operations and factorial notation to appreciate the subtly of this mathematical wonder. Students could be challenged to make a similar calculation with the surprising value of 6!

Time Sort is the latest additions to the ‘Telling the Time’ collection. There are three levels including digital times, analogue clocks and phrases to represent times. Try using it with pupils working in pairs and listen to the discussion generated.

Sum to One is a set of decimal numbers on virtual cards which can be used for a matching activity. A pairs game, a multiple choice quiz, a tug-of-war game and a snap game. Is that too much choice?

The book I am reading at the moment is Craig Barton’s new book How I Wish I’d Taught Maths: Lessons learned from research, conversations with experts, and 12 years of mistakes. I am a great fan of Craig’s podcasts (I listen to them on my Tuesday morning cycle ride) and this book collects together the insights Craig has collected from all of the educational experts he has interviewed. At the time of writing, 93% of the reviewers on Amazon had awarded the book five out of five stars. I thoroughly recommend this book to you here.

Thanks to those of you who have posted photographs on Twitter of the Transum activities being used in the classroom. It is so good to see that the work that went in to producing the resources was worthwhile. Thanks

If you follow me on Twitter (@Transum) you may have noticed that my list of ‘Hidden Gems on the Transum Website’ has been growing from the 19 included in the last newsletter. I think I will stop when I get to 50.

Now let’s continue the search for the missing pound from the puzzle of the month. One hour later two elderly ladies came into the restaurant and enjoyed a meal together. The waiter brings the bill for £30 so each lady pays £15. The chef again tells the waiter that the bill should have only been £25 so he sends the waiter back to the table with five pound coins. The waiter could not figure out how to divide the £5 so he gave each lady a £1 and kept £3 for himself.

So….the two ladies have paid fourteen pounds each for the meal:  2 x £14 = £28

The waiter kept three pounds:   £28 + £3 = £31

So there is the missing pound! Genius isn’t it? I heard this solution on the Danny Baker radio show and have included the audio excerpt towards the bottom of the June 19th Starter of the Day. It’s worth listening to. Enjoy.

All the best for the month ahead

John

P.S. Always wear glasses to Maths lessons. They help with division!

# August 2014 News

This is the August 2014 Transum Newsletter bringing you the latest news from Transum Mathematics. If you are in the UK or US you are probably enjoying your well earned summer holiday right now but if you are in Australia or New Zealand it’s business as normal I presume.

I have now returned from my holiday on the island of Koh Mook where I read Alex’s Adventures in Numberland by Alex Bellos. It inspired me to create the Magic Square Puzzle (see below) and set my mind wondering about the database of Sudoku puzzles he describes. I really enjoyed it and recommend it as fascinating Maths teacher holiday reading.

I now need to read his other book, maybe another holiday is needed!

Alex Through the Looking-Glass: How Life Reflects Numbers and Numbers Reflect Life

## Did You Know?

Did you know that you can keep track of the progress your pupils are making on Transum Mathematics? Enter the names of the pupils in your class in the Class Admin application and enter the email addresses used by the pupils when registering their trophies. Click on the ‘more’ button on the main Class Admin page then scroll down to find the Trophies button. The table records instantly the trophies earned by your pupils in a compact table so you can see who is doing well and who may need some help.

Shunting Puzzles was created. An interactive activity to go with the 9th January Starter. Though this activity is not explicitly mathematical it does require abstract thought, logical deduction and the generation of a strategy. The real skill is to have more than one tram moving at the same time to minimise the time taken to complete the task. Currently the record for level 1 is 27 seconds! Can you beat that?

Double Take and Cat Apult are two modern style computer games that are very addictive. Unfortunately they don’t work on older web browsers such as Internet Explorer 8 but most people using the Transum website are using more up-to-date software thankfully.

The T Puzzle has been around since the year 1900 but the Transum version was born at 1900hrs on the 19th July. There are links lower down the T Puzzle page linking to the other Transum Tangram activities.

I was surprised when creating the Magic Square Puzzle to find how many different groups of four numbers added up to the magic total. A recommended activity for pupils of all abilities.

Finally you can now generate isometric paper from the Graph Paper Shine+Write page and the Sieve of Eratosthenes has been updated with assorted comments each time a task is completed.

John

ps There are 10 types of people in this world. Those who understand binary and those who don’t.