Tag Archives: GCSE

5 Resources for Maths GCSE(9-1)

Hello and welcome to the Transum Mathematics newsletter for February 2017. It is being written a little earlier than normal to make up for the fact that there was no January newsletter and that I will be travelling later in the month at the time when I would otherwise be writing this.

This month’s puzzle is about a restrained flea that jumps one foot at a time either north, south, east or west. At how many different places could he end up after 8 jumps?

Flea

While you think about that I would like to tell you of five resources on the Transum website that have been updated recently. Although they are perfect for the UK’s GCSE exam preparation they could also be used in different ways for younger learners.

  1. Weekly Workouts. These question papers (5 more have just been added) are designed for students on the Mathematics GCSE(9-1) Foundation level courses who are hoping to achieve one of the higher grades available. Each Weekly Workout contains 7 exam-style questions. The first six can be answered online but the seventh requires the student to draw something that needs the teacher to check. Each Workout can also be printed onto one A4 page.
  2. Practice Papers. These printable papers are designed to challenge students on the Mathematics GCSE(9-1) Higher level courses. Each question is similar to a question on one of the specimen papers produced by the exam boards for the 2017 exams. Full worked solutions are available for each question for Transum subscribers.
  3. Revision Tips. This is a page of suggestions and links to resources for anyone preparing for a mathematics exam. There are links to self-marking exercises on all the basic school mathematics concepts along with puzzles, games and investigations all designed to support revision.
  4. Syllabus Checklists. This part of the Transum Mathematics website contains a growing list of objective checklists for various common mathematics exams. Students can go through each objective and classify them as easy, OK or help! They can then print the objectives they have classified as requiring help and fill in the space for notes as their understanding develops.
  5. Exam Presentation. Save this for a week before the exam. It contains the tips and tricks that students might find useful when doing their last-minute preparation. You, as a subscriber, can download the PowerPoint version of the presentation so that it can be customised to suit your situation.

In addition to the items mentioned above, many other pages on the Transum Mathematics website have been updated or changed. A Starter called Tindice provides a quick, fun (when you know the answer) Starter to a busy Maths lesson but it can also be used to initiate an investigation into the sum and product of odd and even numbers.

I often help older students with their understanding of significance testing in statistics. In particular the chi-squared test is often clouded with strange precedents and terminology. A very short presentation called Significance has been developed to simplify the concept and to get the student to analyse the data provided by the Optical Illusions survey. As a subscriber you can see the results of the significance testing in real time. The students can use their GDCs to find the connections themselves. The presentation focusses on the big picture idea and leaves you as the teacher to fill in any gaps.

The Transum website was particularly busy in the weeks leading up to Christmas. Some of the ChristMaths activities had been updated and clearly people all over the world were enjoying them. If you missed out this year why don’t you send yourself a time-delated email (to arrive on the 1st December) reminding you of the URL. An email to yourself can be flagged as ‘Delay Delivery’ in many email programmes such as Outlook.

The answer to this month’s puzzle can be found by considering the following:

Think of the flea on a coordinate grid starting at the origin. If the flea only jumps in one direction it would end up at either (0,8), (8,0), (0,-8) or (-8,0).

Now consider the possible points in the first quadrant, (x,y) where x is the number of jumps east minus the number of jumps west and y is the number of jumps north minus the number of jumps south. It is probably a good idea to sketch these points on some graph paper and you will see the pattern created by the locations. Multiply the number of points in the first quadrant by four and add the ‘return-to-origin’ possibility to find the total.

The answer is 81 different places.

That’s all for now

John

P.S. If a got 50 pence for every time I failed a maths exam I’d have about £6.30 now.

October 2016 News

This is the Transum Newsletter for October 2016, the 10th month of the year. Have you ever noticed that the month name begins with the suffix ‘Oct-‘ suggesting eight and not ten. There is a reason for that and a quick internet search will reveal it to you.

Let’s begin with the puzzle for this month which is about three hungry children.

There was a short queue in the school canteen. Ayden was directly in front of Betsy who was directly in front of Carl.

Aden’s age is an even number but Carl’s is odd. Is a person with an even age directly in front of a person with an odd age? The answer is at the end of this newsletter.

652

I am very keen to tell you about some of the new additions to the Transum website that appeared last month. The first is Maths Mind Reader. Absolutely everyone I’ve used it with have been extremely impressed with this clever web page. As a Transum subscriber you will be see the mathematics that makes it work and Secondary pupils should be able to understand and even prove the concept.

A Transum website visitor, Les Page, sent me an addictive little puzzle he has devised called Zygo. He has kindly allowed a Transum interactive version to be created which is now ready to improve the numeracy and problem solving skills of your pupils. Thanks Les.

Pupils quickly learn to recognise and name regular polygons but the new activity called Polygon People may help younger pupils to name irregular polygons too. The activity has three levels and only accepts the correct spellings.

For the older pupils (14+) the Completing the Square and Proof of Circle Theorems activities should support those entered for the higher tier of the GCSE exams (or equivalent).

At times when I have not been creating new content for the website I have had a small amount of time to look at an updated app that I have downloaded to my iPhone. Photomath has been around for a couple of years but I’ve been very impressed with the recent improvements. You point your phone camera at an equation, and it will give you the answer and show you the working. I’m still amazed it can read my handwriting!

Photomath supports arithmetic, integers, fractions, decimal numbers, roots, algebraic expressions, linear equations and inequalities, quadratic equations and inequalities, absolute equations and inequalities, systems of equations, logarithms, trigonometry, exponential and logarithmic functions, derivatives and integrals.

My only reservation against using it with pupils is some of the phrases used to explain the stages of solving an equation. “Move constant to the right side and change its sign. Move variable to the left side and change its sign” is less helpful than the notion of doing the same thing to both sides in my opinion.

The answer to this month’s puzzle is yes. We don’t know Betsy’s age but we do know it is either even or odd. Let’s consider the two possibilities.

If Betsy’s age is odd then Ayden (even) is in front of Betsy (odd) and the answer is yes.

If Betsy’s age is even then Betsy (even) is in front of Carl (odd) and the answer is yes.

So regardless of Betsy’s age, the answer is always yes.

A similar problem was devised by Hector Levesque and it was included in Alex Bellos’ Guardian blog. Unbelievably 72 per cent of the 200,000 people who answered the question got it wrong.

That’s all for this month.

John

P.S. Why do mathematicians think that Halloween and Christmas are the same?

Because 31 OCT = 25 DEC (You need to know about the octal number system to understand this month’s joke 318 = 2510)