# Delightfully Divisible

Best wishes for August wherever you may be. I am in the UK and am about to catch a train for Glasgow, a city I’ll be visiting for the first time. The record heat wave in the UK has come to an end and today water is falling from the clouds. I think it is called rain but it has been so long since I saw it that I can’t be sure. Let’s start with a rainy-day puzzle:

Three thousand eight hundred and sixteen is delightfully divisible. The first digit is, of course, divisible by one. The number formed by the first two digits, 38, is divisible by two. The number formed by the first three digits, 381, is divisible by three and the number formed by the first four digits, 3816, is divisible by four.

Can you increase the list of digits to make a nine-digit number which is also delightfully divisible? Your answer should be a pandigital number containing all of the digits one to nine. The answer is at the end of this newsletter.

Talking of Pandigital Numbers, I have just uploaded a brand-new, two-level, self-marking quiz about them which touches on divisibility and, to a lesser extent, place value.

Other activities created in July are based on the ‘arranging the digits 1 to 9’ idea and provide a great environment in which to develop problem-solving strategies. For some the difficulty of the puzzle builds over a number of levels providing a low threshold, high ceiling learning activity. Try them for yourself and please let me have any feedback. They are Multitude, Double Treble and Triside Totals.

Sixteen other Transum activities were updated during last month as part of the Forth Bridge style cycle of keeping all of the content on the website fresh, easy to access and relevant to mathematics learning today. I am always happy to receive comments and suggestions and particularly ideas for new content.

You have probably heard the debate about summer learning loss. Research indicates that by the end of the long summer holidays, pupils perform on average, one month behind where they left off in the spring. It’s not too late to send an email to your pupils with suggestions of Maths activities they can do during the down time. I have put together a list of easy-to-assign activities covering a wide range of topics on the Holiday Activities page. Please let me know if you have any other ideas.

Don’t forget that if ever Transum.org goes offline you can always find the activity you need on one of the mirror sites: Transum.com and Transum.info.

The answer to this month’s puzzle is 381,654,729. Did you enjoy working it out? Would it be a worthwhile challenge for your pupils? Go to the Delightfully Divisible page for an interactive workspace and a link to a list of divisibility tests. Depending on your pupil’s abilities (and the time of day) you may decide to give them a clue as I did to you.

That’s all for now, enjoy the month of August,

John

P.S. Why is a dog with a bad foot like adding 6 and 7?

A. Because he puts down three and carries the one.

# Hot Food and Weather

This is a brief newsletter for the month of July because many of you will have your thoughts focused on the end of term and the holidays. Let’s begin with the puzzle of the month. Can you find five different integers that multiply together to give 12? The answer is at the end of this newsletter.

In the northern hemisphere it’s summer time and here in the UK we are in the middle of an uncharacteristic hot spell. The back garden has become an extension to the house and I am typing this sitting on a plastic chair at a plastic table. The Maths that I think of as I look at the garden is the mathematics of nature. I see Fibonacci numbers in the petals and spirals and remember the great time in the past when pupils have enjoyed the great outdoors doing the Scavenger Hunt and People Maths. This activity suggestion comes with a sun screen and hydration warning!

As I have done a lot of travelling in June there have not been as many new additions to the website as during a typical month but I can tell you about Recipe Ratios, a series of short exercises based on recipes for Thai dishes. They complement the other ratio exercises on the website and come complete with the full method in case you fancied cooking the delicious Siamese food.

Bottles, Boxes and Cans is an activity with two levels. Level one is a drag and drop challenge to match the photograph of a container with its capacity. Level two is a little harder, a more traditional exercise on volume and capacity.

The puzzle of the month is actually the new Starter of The Day for June 12th. It is called Weather Report and puts the puzzle in the context of mean temperatures. The answer is -1, 1, -2, 2, 3.

If this was too easy for you (or your students) there is an extension provided as a new Advanced Starter. What other products of five numbers (less than 100) would have given unique solutions? The answer to that is at the bottom of the Weather Reports page.

I’m off to visit Bletchley Park on Tuesday to see the location of the top-secret codebreaking operation during the Second World War. There is a great amount of mathematics involved in deciphering messages as can be seen in the Code Cracking presentation. I’m sure I’ll have more to say on the topic in next month’s newsletter.

That’s all for now,

John

P.S. Calendars, their days are numbered.