You are reading the Transum Newsletter for the month of February 2020; a month with 29 days due to the fact that this year is a leap year. On the 2nd February the date will be palindromic, it reads the same forwards as backwards when written in the short format
Now let's move on to the puzzle of the month.
The number 57 came up as the answer to a worked example on the board. One of my Secondary school pupils, Carl, mentioned that this was the product of his parents' ages divided by the double of his age. He also threw in the fact that his father was five years older than his Mother.
How old was Carl?
While you think about that here are some of the key resources added to the Transum website during the last month.
Awe-Sum This puzzle is more difficult than I thought. I uploaded it confident that the logic of my method was correct but no – the correct solution eluded me until after I had uploaded it. Can you find the largest Awe-Sum? I bet you used the same (incorrect) strategy that I initially did – let me know.
This puzzle is a great teaching resource. It really makes pupils think of the relevance of place value when devising a strategy. It reinforces the algorithm for adding three digit numbers but goes much deeper than mere drill and practice. Give your pupils the clue to consider the effect on the result of putting a number into each cell of the grid. It's surprising, amazing and makes learning mathematics exciting, enjoyable and rewarding. [Can you tell I really like this resource?]
I have made a new help video for the Changing The Subject exercises which will hopefully make the resource more useful as a homework assignment. The video is not intended to teach rearranging formulae from scratch but it should be a helpful reminder for those who have learnt and forgotten.
I have just finished designing the Perfect Magic Square puzzles. There are nine levels of difficulty determined by the number of clues given (numbers already in the correct position). It never ceases to amaze me the complexity of a four by four perfect (pandiagonal) magic square. There are so many groups of four numbers that sum to the magic total that makes partially completed puzzles easy to complete.
In addition to the fun of developing a solving strategy there is such a lot of opportunity to practise mental methods for addition and subtraction. This makes this resource a great alternative to a traditional numeracy exercise for children of all ages.
I managed to get an emergency exit row seat on my long flight at the beginning of January which meant I could use my laptop to develop the Flabbergasted Starter into a game. A shout out to the dentist who sat next to me during the flight and was talked into being the first to play the completed Flabbergasted Game despite the fact that he beat me!
The puzzle that inspired my next creation involved the numbers one to six. I adapted the whole numbers to be twelfths, expressed them in their lowest terms and then viola - Circumfraction was born!
There then followed a whole collection of number placing puzzles that came flowing out of my computer: Goal Products, Triangled Hexagram, Hexagram Star and Octagram Star each have their own character but are all variations on a theme. It is hoped that strategies developed on one puzzle will transfer to another. I think my next job will be to draw up a grid comparing the difficulties of each level of each puzzle (degrees of freedom perhaps) so that a suggested order ensuring progression can be deduced.
This time last year I was writing in the newsletter about the Remainder Race being mentioned on the Frank Skinner radio programme. I still think it is an excellent game and for all of you who are private tutors, a fun way to spend the last ten minutes of your one-to-one tutorial.
Don't forget you can listen to this month's podcast which is the audio version of this Newsletter. You can find it on Stitcher or Apple Podcasts. You can follow Transum on Twitter and 'like' Transum on Facebook.
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.
Valentine’s Day falls in February and if you want to prove that you are a real trendy teacher you could surprise your pupils with one of two Valentine-themed Starters on the 14th: Valentine’s Puzzle and Love Maths.
And now the solution of the puzzle of the month. First of all let me make it clear that this situation is totally fictitious. Only in the imaginary world of maths problems do pupils come up with such statements. I named the imaginary pupil Carl as a nod to the mathematician Carl Friedrich Gauss.
I began by letting Carl's age be c which is an integer (between 10 and 18 because he is at Secondary school).
Product of patents' ages ÷ 2c = 57
Aha, one equation and two unknowns. I need to be a little creative here:
Product of patents' ages = 114c
Product of patents' ages = 2 x 3 x 19 x c
I looked for ways of pairing these factors to give two numbers that differ by 5 and that had c between 10 and 18. I came up with:
2 x 19 as one number and 3c as the other. So either:
38 = 3c – 5 [no integer solution] or
38 = 3c + 5 which gives c = 11
My solution is that Carl's age is 11. His parents are 38 and 33.
I checked my solution by doing a 'brute force' check of all possible father's ages using a spreadsheet.
That's all for now,
PS. Are monsters good at mathematics?
Not unless you Count Dracula.
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