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You are reading the Transum Newsletter for the month of May 2024. What better way to start than with the puzzle of the month:
I insist that members of my class bring certain items to the lesson. Today 90% remembered to bring a pen, 85% brought a pencil, 80% brought a calculator and 65% brought a ruler: what percentage, at least, must have brought all four items to the lesson?
If you get an answer I'd love to hear how you solved the puzzle (or your students solved it). Send 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.
Coins and Notes is a new, quite basic, exercise on recognising British coins and notes. It was prompted by a statement in the Functional Skills curriculum and the fact that new bank notes will be released in the UK next month featuring the image of King Charles.
The set of exercises on Geometric Sequences has been expanded, and a new help video has been included. This video is designed for revision and, although it is not intended as a first introduction to the topic, it does cover all the important points. It could be useful for a teacher, especially for the graphics and examples. New levels have been added including one addressing the sums of convergent geometric series. I'm guessing it will be of use for your older students on courses where this is required.
When I was training to be a Maths teacher in the early 1980s, the mantra was TOTAAT. This mnemonic stood for "Teach One Thing at a Time," which, I suppose, was our approach before the concept of cognitive load was more widely understood.
I was reminded of this yesterday while listening to the Mr. Barton podcast. He offered many excellent suggestions for carefully choosing examples and discussed the problem of starting with an example where there is too much included. Here is one of his examples:
"When you do that first example you want to focus on the core concept and don't weave in anything else. So I watched a lesson a while ago which was on angles on a straight line and the first example the teacher gave was find this missing angle next to an angle of 92 degrees. The problem was the kids' arithmetic skills weren't at the point where they could immediately do the 180 subtract 92. So all their attention or a big chunk of their attention was on doing that calculation. So therefore, whenever it then came to little twists with this, they hadn't been thinking hard enough about the actual concept of angles on a straight line, all their attention had been on the arithmetic. So keep the arithmetic as simple as possible and don't weave in anything else at first"
I highly recommend the Mr. Barton podcasts.
During an online tutorial last week my student pointed out the Zoom AI Companion. It's designed to "enhance collaboration and productivity for users" and it does this by remembering everything that is said during a session. During meetings, participants can ask AI Companion questions based on the meeting transcript. It uses AI technology to provide quick answers.
The interface contains a button labelled 'Catch Me Up' and we decided that we could use this at the end of the tutorial to summarise the learning that had taken place. This is what we got:
The tutorial of the day, led by John, focused on improving Sally's understanding of prime numbers and trigonometry. They started with prime numbers, discussing how to identify prime numbers and their relationship to factors. They then moved on to trigonometry, explaining how to find angles in a right-angled triangle using the cosine, sine, and tangent ratios. John also showed Sally how to use a calculator to simplify the calculations. They practiced finding angles in various triangles, with Sally gradually gaining confidence in applying the concepts.
So I think the system is best suited to give summaries of meetings rather than maths tutorials so I'm not sure how useful the paragraph is to us. The funny thing is that the student's name is Josh but he was using his mother's laptop to run the Zoom software, and her name is Sally!
Don't miss the forthcoming special dates.
Looking for last minute revision resources?
IB Exam-style questions – You probably already know that there are many questions similar, but not exactly the same as those that have appeared on past IB Standard and Higher level papers. They are designed for you to try in these last few days before the final exam. Sorted by syllabus statement:
(I)GCSE Higher/Extended Exam-style questions – Here are collections of (I)GCSE Higher/Extended question which can be accessed individually but are also presented in sets of 5 which can be printed on A4 double-sided paper.
(I)GCSE Foundation/Core Exam-style questions – For teachers of students working towards (I)GCSE Foundation/Core exams; These collections each contain six questions that can be answered online for instant feedback and one question requiring pencil and paper. You could assign a workout per day
Don't forget you can listen to this month's podcast which is the audio version of this newsletter. You can find it on all good podcast services.
Finally the answer to last month's puzzle which was:
A - 3B + 5C = 37
3A + 7B - C = 47
A + B + C = D
What is the value of D?
D is the sum of A, B and C which is 21.
Out of interest, when I was making up this puzzle, A = 7, B = 5 and C = 9, but there is no way you could have worked that out from the information given and that is not what the puzzle is asking for. The focus is on the value of D which has to be 21.
The first five correct solutions were received from Kevin, Chris, Mala, Rick and Wil. You can see some of the logic used to solve the problem below.
That's all for now, I'm looking forward to receiving your solutions to this month's puzzle so may the fourth be with you!
John
P.S. I love Maths but what seems odd to me are integers not divisible by two.
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, Yeppoon, Australia
Monday, April 1, 2024
"Adding the equations gives
4A + 4B + 4C = 84
Dividing by 4
A + B + C = 21 = D."
Chris Smith, Scotland
Monday, April 1, 2024
"First thing to notice is that there must be some devious trickery going on because three equations wouldn’t usually be enough to find four variables…but thankfully we’re not asked for the individual values of A,B,C but for their sum and I think I’ve spotted something. Adding the first two equations gives
$$4A + 4B + 4C = 84$$
Dividing this by 4 gives
$$A + B + C = 21 $$
And since A + B + C = D we now know that
$$D = 21$$
Lovely puzzle. If the sum of the two equations were tweaked like this then we’d get the kind of numbers my students expect to appear now and again (once in the question and once in the solution 😉):
$$A - 3B + 5C = 3141$$ $$3A + 7B - C = 4955$$ $$A + B + C = D$$
Thanks for all your excellent resources, John! "
Rick, Waiting To Board A Flight To Paris
Monday, April 1, 2024
"Subtracting the third equation from equation one and three times equation three from equation two yields:
$$-4b+4c=37-d$$ $$4b-4c=47-3d$$
Adding these two equations yield:
$$0=84-4d$$
Solving for d yields
$$d=21$$"
Leonard Pomrehn, United States
Tuesday, April 2, 2024
"Greetings John,
I was listening to the April puzzle this morning, and decided to give it a try.
With pencil and paper, I started with
$$(i) A – 3B + 5C = 37 \text{ and } $$ $$(ii) 3A + 7B – C = 47 $$
I next computed,
$$7(i) + 3(ii) \text{ to be } A + 2C = 25 \text{ and } $$ $$1(i) + 5(ii) \text{ to be } A + 2B = 17. $$
Adding the above two equations then yields \(2A + 2B + 2C = 42\), so that \(A + B + C = 21\).
I hope that is correct.
Love the website. "
Pauline Perkins, Liverpool
Tuesday, April 2, 2024
"Happy Easter...
I think I have the answer D=21
$$A=15, B=1 \text{ and } C= 5$$
Thanks again for the site. I am loving the Functional skills input. A lot of my students are using the site. I have to give them a link to the topics first. "
Candice Wilson, United States
Tuesday, April 2, 2024
"I used elimination twice, to eliminat the A variables, leaving two equations with B and C variables. D was treated as a part of the constant value. I was prepared to try eliminating all the B and C variables separately but they both cancelled out at once! Is D=21? "
Cecy Kemp, St. Andrews Prep
Tuesday, April 2, 2024
"I would make D = 21
I added both equations together and divided by 4.
Thank you for all you do with your website. It is much appreciated and we use your site daily at school. "