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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?
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.
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.
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