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Beginning as usual with a puzzle for the month but this time from Transum Subscriber Nigel Fearn. He contacted me to say how a good puzzle just cropped up the other day and is probable one we are all familiar with in a practical situation. The puzzle comes out of a need to carefully and accurately cut the last piece of a cake into two equal pieces.
Imagine a delicious coffee and walnut cake (my personal favourite) that has almost completely been eaten except for a lonely slice that needs to be cut in two. Rather than cutting the cake in the normal way, from circle centre to the midpoint of the arc (which can be tricky), you decide to cut it in a direction perpendicular to that. So you are not cutting the cake horizontally but vertically so that the centre of the original cake is on one side of your cut and the arc of the remaining slice is on the other.
So the question is where do you make the cut so as two get two equal volumes of mouth-watering cake? The answer can be found at the end of this newsletter.
The most popular lesson Starters (according to the mean of the scores collected on each page) are, in reverse order:
10. Addle (Mental addition)
9. Flabbergasted (Factors and multiples)
8. One Out of Ten (For April Fool’s Day)
7. Ice Cream (Click the buttons on the machine)
6. Mystic Maths (Scroll down the page for the best mind reader)
5. Broken Calculator (A number of versions available)
4. Sum Square (One of many puzzles)
3. 9:50 Puzzle (Just for fun)
2. Maths Crossword (My sense of humour, sorry)
1. How many? [Triangles, Rectangles or Squares)
The most customisable Starter is Refreshing Revision.
March was a busy month with many hours given to updating the website. In addition to the pages that were improved, the following is a description of the new features:
Iteration is an online exercise requiring learners to find approximate solutions to equations numerically using a looping or repeating process. There are a number of levels including one which focusses on the use of a flowchart to show the steps required.
The Brackets online exercise has been around for a long time but now a tenth level has been added for those wanting to practice multiplying three binomials and simplifying the result.
Both Circle Equations and the equations of the tangents are included in this new online exercise.
These aforementioned topics are new for this year’s Higher GCSE(9-1) so are particularly useful for students who have been using past papers to revise as they won’t have seen those topics represented.
Superior and Nevertheless are variations on the ever-popular Great Expectation activity. Guaranteed to create excitement while thinking mathematically. Try one of them during the last ten minutes of your next Maths lesson.
A completely new Cumulative Frequency exercise is now live including grouped data with exam-style questions.
The suite of Pairs programs are always useful for providing variety in the Maths lesson, or, for those individual tutors out there, great for one-to-one tutorials. Three new topics have been added: Units Pairs (both metric and imperial), Fill Graphs Pairs (Great to use after doing the Desmos Waterline simulation) and, inspired by the differences in American and British English, Math vs Maths Pairs.
As April begins it would be remiss not to remind you that there are 20 Weekly Workouts and 20 Practice Papers available on the Transum website for your students taking the GCSE exams soon to use. The Weekly Workouts focus on the higher grades of the Foundation tier while the Practice Papers are strictly for the Higher Tier candidates. As a subscriber you have access to worked solutions for the Higher Tier questions.
For future reference there are two ‘mirror’ sites that contain all the Transum Starters and activities. They are at www.transum.com and www.transum.info The only difference is that they don’t contain the details of your Transum subscription account so you won’t be able to log in there. If it looks like Transum.org will be offline for a long time then I will transfer the database containing your details to Transum.com so you will eventually be able to log in there too.
The answer to the puzzle is that the position of the cut depends on the angle between the straight horizontal edges of the slice of cake. The maximum ratio is:
1 : √2 − 1
You can see the working here.
That’s all for this month,
John
P.S. If you are asked to subtract five squared from the square root of six hundred and twenty five, say nothing and you'll be correct!
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