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This is the one hundredth Transum Newsletter and it is for the month of March 2023. Did you know that 100 is the sum of the first nine prime numbers (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 100) and also the sum of the first four cubes (1³ + 2³ + 3³ + 4³ = 100)?
That's put me in the mood for the puzzle of the month. Can you make 100 from four sevens and a zero? You are allowed to use any of the mathematical symbols in the scene above. Please let me know if you succeed and my answer will be in next month's Newsletter.
There are plenty of activities on the Transum website related to the number one hundred. They include: Centexpression, One Digit 100, Calc-a-Hundred and Sums with Hundreds.
Refreshing Revision has for a long time been a very popular Starter. Because it is so customisable, teachers find they can adjust the settings to make the activity just right for their class. During this last month I have been creating a sister application called Advanced Refreshing Revision. I am hoping it will be useful to teachers of older students taking A Levels or IB Diploma courses.
When you encounter an exercise labelled as Level 0, it may not always signify an afterthought or a task created after the more challenging levels have already been established. However, in some instances, that is exactly what it represents. However Pythagoras Theorem Level 0 was suggested by a fan of Transum, Paul. Unlike the more conventional Pythagorean Theorem exercises, it serves as an introduction to the concept by gradually building up to the routine. This exercise emphasizes the idea of squares on the sides and features questions with integer side lengths and solutions.
Sharon wrote to say "We are currently looking at solving equations and inequalities with our year 8s and our diagnostic test at the start of the unit showed that for my class (a top set) they have a lot of fluency already but made mistakes when the answer was a fraction. The question we asked was 2x+7=4x+2 and some students wrote the reciprocal of the correct answer. I was looking for similar style problems to help students build fluency." So may I present Solve To Find Fractions.
Ann suggested the new Three Unknowns exercise. She told me that AQA Level 2 GCSE Further Maths requires students to solve simultaneous equations in three unknowns. I don’t recommend that people attempt Level 3 without the use of technology though as it's excruciatingly tedious.
An old French woman was caught trying to bring a hand grenade through airport security (according to the urban myth!).
“But I always take it with me on every flight,” she protested. “I figured that the probability of there being two bombs on the same plane was very low, so I feel much safer in the air.”
Was the old lady correct in her understanding of probability?
This is the latest Advanced Lesson Starter and is to promote a better understanding of conditional probability. I have called it Airport Security
Three special dates coming up this month:
Teacher trick: Get one up on those crafty students who paste their homework equations into Wolfram Alpha to get the solutions without much thinking. Instead of using x and y as the variables use e and i instead. My version of Wolfram Alpha treats these letters as Euler’s number and an imaginary number respectively and won’t give them the result they expected. Smart teacher one, crafty student nil.
Occasionally I will remember that the word data is pleural and say things like “The data were collected by various researchers.” This has never sounded right to me though I understand that the singular form of the word is datum (I studied Latin for three years at school). I am now pleased to hear that using data as a singular noun has now been accepted as being correct. In fact, the Financial Times has updated it’s style guide to reflect this change in their use of the English language and I have now updated the Transum Style Guide. I am now in the 4:1 majority of English speakers and my next paragraph will be much easier to write:
The data stored on the Transum website shows that a total of 631,369 learners have created virtual trophy cabinets since the beginning of time.
Don't forget you can listen to this month's podcast which is the audio version of this newsletter. You can find it on Spotify, Stitcher or Apple Podcasts. You can follow Transum on Twitter and 'like' Transum on Facebook. If you have any comments about this podcast please contact me at podcast@transum.org.
Finally the answer to last month's puzzle which was: Mr Wheeler was on a long drive when he noticed that his odometer showed 15951 miles which is a palindromic number. The next time he saw a palindromic number on his odometer was exactly two hours later. What was his average speed during those two hours?
The answer is 55mph (as the next palindromic number is 16061) and the puzzle was adapted from one in The Moscow Puzzles by Boris A Kordemsky.
That's all for now,
John
P.S. Always wear glasses to Maths lessons. They help with division!
