Balancing Balloons while School's Closed

Sunday 1st March 2020

This is the Transum Newsletter for the month of March 2020. It begins, as usual with the puzzle of the month which I heard on Signal Radio.

Jamie and Ben each have some balloons.

Ben said to Jamie "It's not fair, you have three times as many as me", so Jamie gave Ben ten of his balloons.

Ben said "It's still not fair, you still have twice as many as me."

How many more of his balloons must Jamie give to Ben so that they both have the same number of balloons?

The answer is at the end of this newsletter.

I have seen enough maths questions about exponential growth that I think I appreciate the amazing effect this phenomenon can have. The Rice on a Chess Board story springs to mind. It is quite shocking however when I see this rapid growth taking place with the coronavirus. I hope you are managing to stay safe.

This health scare is causing more and more schools to close around the world. Are you able to help your pupils continue their maths learning from home if your school closes?

Here are some bullet points of things to consider when assigning learning activities for pupils to do at home:

Practise using online systems with pupils before the school closes, while they are still in the classroom with you (yes I know, it may be too late for that).

Before school closes make sure pupils take home their textbooks rather than leaving them in their school lockers (it may be too late for that too).

Have your key worksheets scanned into pdf format so that they can be issued to pupils digitally.

Keep parents informed of what systems you are using to communicate with pupils so that they can monitor and support at home.

Be mindful of not overloading pupils with tasks. Keep the expected work time to within normal, school-open limits. Remember they will receive work from other subject areas too.

Assign a longer term project that pupils can be working on even if communication breaks down and you are unable to assign short-term tasks.
Individualised learning plans and differentiation are in many ways easier to administer than in the classroom situation. Most Transum online exercises have a range of 'levels' you might find useful for this reason.

You can read more about continuing mathematics learning when school is closed and find some suggested resources on the new Maths at Home page.

So after digesting that here are some of the key resources added to the Transum website during the last month.

New 'help' videos have been made for the Quadratic equations, Decimal Multiplication and Division, and the Interest online exercises. The videos are found by clicking the help tab while doing those exercises.

Refreshing Revision now has an editable panel. You can type in your own key revision questions to supplement those that are randomly generated.

Voronoi Diagrams will probably be new to you. You probably did not study them when you were at school yet they are a fascinating and colourful topic providing a great way to practise finding coordinates, understanding loci, finding equations of linear graphs, constructing perpendicular bisectors, finding areas and applying Pythagoras' Theorem.

Amortisation and Annuities are words unfamiliar to most pupils but something most adults have to get their heads around. This set of exercises for the older pupil makes great use of spreadsheets or the GDC's financial functions.

This month contains Pi Day on the 14th March. I would like to direct you to some resources that will help make the day memorable. They are all linked from the 14th March Starter of the Day page. The main, fun activity is a memory competition in which pupils work to commit as many digits of pi to memory as possible. Further down that page you will find links to more traditional pi activities involving areas and circumferences of circles. There are also some unexpected facts, videos and jokes on that page.

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

Finally the answer to this month's puzzle:

Let the initial number of balloons Jamie has be J and Ben's be B.

Initially:

J = 3B

After the first act of giving

J - 10 = 2(B+10)

That's two simultaneous equations which can be solved by a number of different methods to give:

3B - 10 = 2B + 20

B = 30, J = 90

After the first act of giving, B=40 and J = 80

Finally Jamie will have to give 20 balloons to Ben if they are to have the same number.

That's all for now,

John

PS. 3.14% of Sailors are PI rates!

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.