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Path Puzzle, Poem, Percentages and Pranks

Monday 1st April 2019

The first day of April is April Fool's Day. Let me know if your pupils were fooled by the Maths lesson Starter for 1st April called One out of Ten which is not what it seems.

This is the Transum Newsletter for the month of April 2019 and here is the puzzle of the month:

Obadiah Sloop has seven horses in his stable and enough feed to keep them for twelve days. After three days he sells four of the horses. How long will the remaining feed last the horses left?

The answer is at the bottom of this newsletter.

Path Puzzle

At the beginning of last week I uploaded a new activity to the Transum website. It is called Path Puzzle and as soon as it went live over fifty people had a go and earned a trophy for the first two levels.

The inspiration for this activity comes from The Black Path Game (also known by various other names, such as Brick) which is a two-player board game invented by Larry Black in 1960. The game features in Martin Gardner’s Sixth book of Mathematical Diversions and a mathematical analysis of various strategies can be seen in Game and Puzzle Design volume 1 By Cameron Browne.

The Transum version is presented as a puzzle rather than a game but the level 8 game board can be used to play the game if pupils are seated in pairs at the computer.

All together there are eight levels and the difficulty increases quite dramatically between the levels. No one, including myself, has managed level eight yet but it definitely is possible.

In my retirement I have become a bit of a digital nomad. I have just bought a brand new Dell laptop and am now looking forward to benefiting from its higher specs to update the website from wherever I am in the world. I feel like a kid with a new toy on holiday right now.

Every week I upload new exam-style questions to the website. These are questions that have appeared on recent GCSE/IB/A-level papers but the wording and numbers are slightly changed so that pupils have something different to practise with. At this moment there are. 352 Higher and beyond questions all with complete worked solutions. These are ideal for projecting in the classroom as the solutions can be revealed line by line as the pupils work through the various parts of the question. It saves you, the teacher, an awful lot of preparation time. In addition, there are 175 Foundation level questions each in a Weekly Workout which can be answered online or on a very stylish A4 size colour print (enable printing of background colours and images). 

For those of you that like the daft, unusual yet mathematical activities on the Transum website here's something new in the form of a Powerpoint-style presentation:

This poem is numeric
It starts at one then rises.
Each number gets a four-line verse
Packed full of Maths surprises.
The challenge is to make a guess
To predict the final line.
What properties will be revealed
Of the numbers one to nine?

Go to the Number Rhyme page to see the rest of this crazy idea for your Maths lesson.

Changing the subject to percentages; don't forget to tell your pupils that if they are struggling to mentally work out 24% of 50 you can switch the numbers round and work out 50% of 24 instead. Finding 50% is very easy isn’t it? You will get the same answer.

Finding a percentage of a quantity is an example of a commutative calculation. Not all operations are commutative. Subtraction certainly isn’t as 10 minus one is not the same as one minus ten. 

Pupils can use this trick to improve their ability to do this type of calculation quickly if they find the switch makes it easier.  They can practise with 12% of 50, 4% of 25, 75% of 10 and lots, lots more.

This last month I welcomed new or returning subscribers from Australia, Canada, Cayman Islands, China, Hong Kong, India, Italy, Korea, New Zealand, Singapore, the United Kingdom and the United States. It is truly wonderful to receive comments from all around the world and to know that pupils of many nationalities are benefitting from the Transum mathematical activities.

Don't forget you can listen to this month's podcast which is the audio version of this newsletter. You can find it on Stitcher or Apple Podcasts. You can follow Transum on Twitter and 'like' Transum on Facebook

Finally the answer to this month's puzzle:

The total amount of horse feed at the beginning is 7 × 12 = 84 portions

The amount of horse feed eaten during the three days is 3 × 7 = 21 portions

The amount remaining at the beginning of day 4 is 84 − 21 = 63 portions

This will last the remaining three horses 63 ÷ 3 = 21 days

That's all for now,


PS. I tried to come up with a really mean joke for the end of this newsletter but it turned out average!


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