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This is the Transum Newsletter for the month of November. The name November comes from the Latin word novem, meaning nine. In the original Roman calendar, November was the ninth month of the year before January and February were added.
And now, without further ado, the puzzle of the month.
There are four fictional planets orbiting the fictional star Vesperion:
How many moons does Nymeria have?
If you get an answer I'd love to hear how you or your students solved the puzzle. Fire off an email to gro.musnarT@rettelsweN
While you think about that here are some of the key resources added to the Transum website during the last month.
Pictograms has ten levels. The first seven levels require the student to answer questions about pictograms while the last three levels require students to draw their own. While the computer can award trophies for the self-marking exercises you as the teacher and subscriber can award trophies if you think the student's pictograms are good enough.
Some Sums and Products was suggested to me by subscriber Sarah. She was "...wondering if there is an exercise already, or if one could be made available. Sum/product. Where learners have to find a pair of numbers that add to make something and times to make something else.". She then went on to say that she would use it as pre-task for factorising quadratics. So here it is ... and the last level, with negative numbers, practises the skill that young, budding quadratic factorisers need!
Name That Graph is another variation on the graph recognition set of exercises. Recognising algebraic graphs equips students with essential skills. Understanding how a graph shifts, stretches, or reflects based on transformations enhances students' grasp of algebraic manipulation. This reinforces the idea that equations and their graphs are two sides of the same coin.
Two-Step Percentages is, as the name suggests, a new set of exercises that requires a deeper understanding of percentages. Talking of which, I wonder if you have seen the Percentages Debate? Leave a comment on your thoughts on something even the text books disagree on.
Odd Scatter Out challenges students to get a 'feel' for the summary statistics ..... Based on Anscombe's Quartet this activity is aimed at your senior students. I find it so amazing that four of the five scatter graphs have the same regression lines and standard deviations.
I received some nice feedback from Helen and Mikey Moore in Australia. Their comment was about The Column Method for Addition page. They wrote "My son struggles with writing, forming numbers, and putting them onto paper. He struggles to write numbers underneath each other in correct columns, even though he knows exactly which column they belong in. This has led to a struggle with completing sums, even though I know he can do them. Now that he can do them on the screen and type the number in, he is flying. This is brilliant for him and for me (his mum), thank you so much for this!".
The percentage of Trophies awarded for each level for a typical 5-level set of exercises such as Reading Graphs and Charts is roughly: y = 67 x^{-1.87} where y is the number of trophies and x is the level (a positive integer) :: Surely the nerdiest fact ever to have been mentioned in this Newsletter.
Do you need an interesting story to tell when teaching Rounding? I read in The Times last month that "There was some hand-wringing at MI5 in 2010 when the government admitted that 'a formatting fault on an electronic spreadsheet' had led the Security Service and the Serious Organised Crime Agency to tap 134 incorrect telephone numbers. A user had told the program to round up the numbers so that it changed the last three digits to zeros."
This month's reflection on artificial intelligence is a positive one because it has genuinely taught me something new. Just yesterday, I learnt that there are actually four different methods for calculating the quartiles of a data set. (please don't tell me I'm the only Maths teacher who didn't know that!) When I received different answers from Wolfram Alpha and ChatGPT; I decided to investigate further, leading me to the Wikipedia page on quartiles. To my great surprise, for discrete data, it turns out that there is no universal agreement on how to determine quartile values.
For example, consider the ordered data set: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49.
Here are the lower quartiles calculated using four different methods:
| Method | Lower Quartile |
|---|---|
| Method 1 | 15 |
| Method 2 | 25.5 |
| Method 3 | 20.25 |
| Method 4 | 15 |
This variation in results highlights the nuances in statistical definitions that we often overlook. It's fascinating (and humbling) to realise that even concepts we thought were straightforward can be approached in multiple ways, depending on the methodology used. Perhaps it's a good reminder for all of us, as teachers, to maintain curiosity and be ready for unexpected surprises—even in areas we think we know well.
Dates this month with maths-themed links:
2nd November George Boole's birthday
5th November: Bonfire Night
16th November: World Heritage Day
23rd November is considered to be Fibonacci Day as the date, in the mm/dd format, is 11 23.
Finally, the answer to last month's puzzle, which was:
Vesper bought a number of pumpkins in one shop at the rate of 4 for £20.
He then buys the same number of pumpkins in another shop at a rate of 6 for £20.
What was the mean number of pumpkins bought for each £20 spent?
Imagine Vesper buys 12 pumpkins in each shop. He would spend £60 in shop 1, and £40 in shop 2. In total he has spent £100 and has 24 pumpkins. For each £20 spent, he has thus bought 24/5, or 4.8 pumpkins.
[Adapted with a Halloween theme from a puzzle published in The Guardian on 27 May 2024]
The first five correct answers were received from Rick, Kevin, Mala, Chris and Shreyak. Many thanks to all those who took part and shared their answers and methods. Very much appreciated.
That's all for now,
John
P.S. My nephew Ben took a geometry test at school last week.
I've had a serious word with him. He's promised me he will stop stealing things.
Do you have any comments? It is always useful to receive feedback on this newsletter and the resources on this website so that they can be made even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.
Kevin,
Tuesday, October 1, 2024
"4x pumpkins bought for $20x
6y pumpkins bought for $20y
4x = 6y so x = 1.5y
Total pumpkins bought = 4x + 6y = 6y + 6y = 12y
Total cost = 20x + 20y = 20(x + y) = 20(1.5y + y) = 20(2.5y)
12y pumpkins cost $20(2.5y)
$20 buys (on average) 12y/2.5y = 4.8 pumpkins "
Chris,
Tuesday, October 1, 2024
"The way I read the puzzle, Vesper buys a number of pumpkins that is a multiple of 4 and a multiple of 6 (my solution can be tweaked if that’s not the case…). That means that the number of pumpkins purchased in each shop must also be a multiple of 12, so let’s call that number 12a, where a is a positive integer.
In the first shop Vesper buys 12a pumpkins at a price of 20/4 each. So it cost him 12a * 20/4 = 60a altogether.
In the second shop Vesper buys 12a pumpkins at a price of 20/6 each. So this cost him 12a * 20/6 = 40a.
Vesper bought 24a pumpkins for £100a.
£100a = 24a pumpkins.
if we divide both sides of this by 5a we get the answer to the puzzle:
£20 = 4.8 pumpkins
The mean number of pumpkins bought for £20 is 4.8 pumpkins. "