A Maths Starter Of The Day

On a full page in the back of your exercise book draw a perfectly regular pentagon.


This image is a work of a U.S. military or Department of Defense employee, taken or made during the course of an employee's official duties.
As a work of the U.S. federal government, the image is in the public domain.


Topics: Starter | Construction | Geometry | Shape

  • Mark Richer, Brockworth Enterprise School, Gloc.
  • I like the construction task.
    However, the origami method does not produce a regular pentagon, but one which is very close.
    The angle formed by the first two folds is in fact 109.47 degrees and not 108. This can be established through the fact that the ratio of sides of A4 paper (or A3, A2 etc) is always 1 to root 2, and similar triangles. Hence the tangent of half of the internal angle is root 2.
    I became suspicious through understanding that it is impossible to construct a regular pentagon without a protractor.
  • Mark Richer, Brockworth Enterprise Scool
  • Following my comment of 9 Dec where I refuted the Origami method of producing a regular pentagon from a sheet of A4 paper, and stated that I did not believe one could be constructed without a protractor, I was delighted to view on your web-page a graphical demonstration of a non-protractor method which showed how a pentagon could be constructed.
    My instinct tells me that this is not possible. I have checked out the method shown, using traditional Pythagorean and Trigonometrical methods, using a standard calculator giving results to 8 or 9 d.p., I found lengths and angles to be within 40 parts per million of the theoretical values, which is well within the bounds of rounding errors in the complex series of calculator processes.
    This leaves me in two minds.
    1. Do I eat ‘humble pie’ and accept that my assumption was wrong? No angle-relationships or other mathematical methods known to me can prove that this construction method is valid.
    2. Just like the Origami method which I know is flawed, could it be that some clever person has come up with another contrived construction method which ‘produces the goods’ in practice, but is flawed in theory?
  • Mr Mark Richer, Brockworth Enterprise School
  • Are comments from teachers on the 'Starter of the Day' website vetted?
    Is there a mechanism by which mathematical statements which are clearly wrong can be deleted so that both pupils and teachers are not misguided?
    I of course refer to the suggestion that a regular pentagon can be constructed.
    I am concerned that for as long as this page shows an incorrect method (or even two), we are not informing learners, but arming them with invalid mathematical ideas.
  • Transum,
  • Mark, thanks so much for your comments. We are just about to leave for the Christmas holidays but when we return will remove the word 'perfect' from the origami film. We will happily take down any of your previous comments if you request us to but they do make an interesting read!

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 2.9 out of 5 based on 242 votes.

Previous Day | This starter is for 13 September | Next Day



If you can't see the images above it may be because you do not have a recent version of the Flash Player installed or that your device (such as the iPad) cannot show Flash diagrams.

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.

Have you read Craig's book yet?

Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more...

"How I wish I’d taught maths' is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it’s a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don’ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics—from primary school to university—this book is for you." Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL.

The Craig Barton Book

Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a gift for a special occasion but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

iPad Air

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

You have to hold iPad Air to believe it. It’s just 7.5 millimeters thin and weighs just one pound. The stunning Retina display sits inside thinner bezels, so all you see is your content. And an incredible amount of power lies inside the sleek enclosure. So you can do so much more. With so much less. more...

Before giving an iPad as a gift you could add a link to iPad Maths to the home screen.

Click the images above to see all the details of these items and to buy them online.

Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.

It is quite easy to draw a perfect pentagon using the repeat command in Logo. Follow the link below for an online version.

It is also possible to fold a kite from an A4 sheet of paper. Follow the link below for more information.

Student Activity



©1997-2018 WWW.TRANSUM.ORG