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 241 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.

Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

Equate board game

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.

Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more...

How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more...

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 Christmas present 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 Christmas 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 Christmas gift you could add a link to iPad Maths to the home screen.

Aristotle's Number Puzzle

It’s a bit of a tradition to give puzzles as Christmas Gifts to nieces and nephews. This puzzle is ideal for the keen puzzle solver who would like a challenge that will continue over the festive period (at least!).

This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

Keep the Maths in Christmaths with this reasonably priced stocking filler. more...

The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more...

Click the images above to see all the details of these gift ideas 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



©1997-2017 WWW.TRANSUM.ORG