Newsletter

Jigsaw Puzzle

Sunday 1st June 2025

This is the Transum Newsletter for the month of June 2025. It begins, as usual, with the puzzle of the month.

A rectangular jigsaw puzzle has 864 pieces. The number of pieces along its length and width have a lowest common multiple that is six times their highest common factor. How many pieces of the puzzle do not have any straight edges?

If you get an answer, I'd love to hear how you solved the puzzle (or your students solved it). Drop me an email to: gro.musnarT@rettelsweN. There are, in fact, two possible correct answers.

While you think about that, here are some of the key resources added to the Transum website during the last month.

Prime Path Pace is a new activity featuring a 10-by-10 grid in which the numbers one to 100 are placed semi-randomly. The aim is to click on cells, starting at the top left and tracing a route to the bottom right, by selecting only prime numbers. A timer introduces the 'pace', encouraging pupils to attempt the challenge repeatedly and beat their personal bests. Many secondary teachers may be surprised to discover that the UK Year 5 curriculum includes the objective 'pupils should be taught to establish whether a number up to 100 is prime'. Suggested methods are provided in the teacher notes for this activity.

Trial and Improvement: I don't see it mentioned specifically in the English National Curriculum for Mathematics, but I do think trial and improvement is an extremely important skill to learn. Let pupils learn by doing the exercises as help is available and there's nothing like learning from mistakes – literally!

Examples and Non-Examples. Over the years, I must have shown my students thousands of examples to illustrate mathematical concepts, but far fewer non-examples. Yet it’s often the non-examples that sharpen understanding and reveal the true essence of an idea. This new activity introduces a drag-and-drop interface to help students distinguish between examples and non-examples. While there are only a few categories so far, I’m keen to expand the collection based on feedback and suggestions.

The Fraction Wall has been on the website for a long time but after a couple of requests to add additional rows, I decided to make the visual aid more interactive. Not only can you now add and remove rows but you can now also easily demonstrate fraction calculations with some ready-made suggestions to get you started.

Michael, a primary school teacher from Sydney, Australia, was kind enough to share some of the ways he used the fraction wall with his Year 5 and Year 6 classes. He inspired me to include some interactive dice to be optionally shown above the wall for whole-class or pair games. Who knew a fraction wall could be so much fun?

🎲 🎲 🎲 🎲 🎲

A new Advanced Starter with no specific question or instruction has been created. It is called Rounding Up or Down and hopefully it will cause students to think hard and discuss:

It was really nice to receive an email from Colette, who teaches in County Clare, Ireland. She wrote "Here at Mullagh NS, we work on the Starter of the Day problem most days. The children wanted to share their construction of a regular hexagon in response to today’s starter, May 13th." She enclosed a photograph of the whole class sitting on the floor grinning with pride and joy (see below - used with permission). They had made a regular hexagon with the classroom desks!

Thursday, 5th June, is World Environment Day which is celebrated to encourage awareness and action for the protection of the environment. It may come as no surprise that Transum has a page containing activity ideas from the deep and meaningful to the "It's a sunny day, let's do some outdoor maths". I am always happy to receive photographs or accounts of your activities that might fit into this category.

🌱 🪴 🌲 🌳 🌴 🌵 🌾 🌿 ☘️ 🍀

Don't forget you can listen to this month's podcast which is the audio version of this newsletter. It's called Transum Mathematics Puzzles.

Finally, the answer to last month's puzzle which was:

Freddie returned a defective Bluetooth speaker to the shop and asked for his money back. By mistake, the shop assistant reversed the pounds and pence in the refund: the amount of pence was given as pounds, and the pounds were given as pence. Freddie did not notice and put the money in his pocket.

On his way home, he used £1.50 from the money in his pocket to buy a drink. When he got home, he counted the money left in his pocket and found he had exactly twice as much as the cost of the speaker.

What was the cost of the speaker?

The answer is:

£48.99

The first five people to send answers to me were Chris, Rick, Iniha, Esther and Clive. Thank you very much for taking part. Iniha's method is shown below.

Did you know the Bluetooth symbol has Viking roots? The logo is actually a combination of two Nordic runes: ᚼ (Hagall) and ᛒ (Bjarkan), which represent the initials H and B. These stand for Harald "Bluetooth" Gormsson, a 10th-century Danish king known for uniting parts of Scandinavia, just as Bluetooth technology unites devices. The name and symbol are a nod to his legacy, blending ancient history with modern wireless connectivity.

Thanks to Chris (the Scottish weekly newsletter and Pi Day legend) for letting me know about that.

That's all for now,

John

P.S. What did the mathematical acorn say when it grew up?

A. Gee I'm a tree (Geometry).

Home :: Previous Newsletters :: Podcast

Do you have any comments? It is always useful to receive feedback on this newsletter and the resources on this website so that they can be made even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.