As regular readers will know, and have been ignoring, we’ve been steadily working through ACARA’s new mathematics curriculum, compiling the annoying-or-way-worse 1-liner content descriptions and elaborations. No one is reading it of course, because that would be nuts. Or, it would cause the reader to go nuts. But, we’ll continue. In for a penny, in for a pounding. Continue reading “The Awfullest Australian Curriculum Number Lines”
Tag: arithmetic
PoSWW 29: Cut Down in One’s Prime
As part of writing our WWW article, we forced ourselves, finally, to look at ACARA’s new Mathematics Curriculum. Jesus, it’s bad. Like village idiot bad.
We’ll start a post in the near future,* compiling the various nonsenses, new and old, and including aspects readers have already pointed out on this post. One new piece of stupidity, however, seems worthy of special mention.
WitCH 83: A Viral MAS Question
8 ÷ 2(2 + 2) = ?
This is really a PoSWW. Except, there are a lot of words.
Above is one of those stupid BODMAS things, which appear in the media about once a month. Except, this one has just been sorted by a couple of Canadian Maths Ed professors, in a Conversation article titled The Simple Reason a Viral Math Question Stumped the Internet. Regular readers will be aware of our method of resolving such questions, but we think there are aspects of the Conversation article that warrant specific whacks.
Have fun.
PoSWW 27: That Does Not Compete
This one’s from AMT‘s 2007 upper primary Australian Mathematics Competition. Yes, it’s a while ago, and we are not aware that such BODMAS nonsense has appeared since on the AMC, and of course such BODMAS nonsense is endemic elsewhere. But we hold, or at least held, AMT to a higher standard.
NotCH 6: Not Abbott’s and Not Costello’s Mulsification
We have the bigger projects (AC, ITE, SD) in the works, plus an FOI appeal to do, plus 2000 words for a lefty magazine due in a couple weeks. We’re kinda busy. But, we’ll try to keep the general posts ticking along. This one is some fun, plus some history and a couple of puzzles.
One of the all-time great maths scenes is Abbott and Costello’s famous bit, where Lou Costello proves that 7 x 13 = 28:
Continue reading “NotCH 6: Not Abbott’s and Not Costello’s Mulsification”
Another Fraction Question
OK, following up on our previous post, we have another fraction question. This one is not new, has appeared in the comments of a previous post, and many readers will have heard us bang on about it. Nonetheless, given the discussion on the previous question, and given the possibility that some new readers might not have yet read Marty’s Collected Sermons, it seems worthwhile giving the question its own post. Here it is:
![\[\color{Mulberry}\boldsymbol{(-1)^\frac26 \overset{?}{=} (-1)^\frac13}\]](https://mathematicalcrap.com/wp-content/ql-cache/quicklatex.com-8d4371e618bad3139eabb80461f1772a_l3.svg "Rendered by QuickLaTeX.com")
NotCH 3: The Love of Learning
It’s amazing the things one finds while scavenging.
ACARA Hates Algorithms
Yep, ACARA hates algorithms. That may come as a surprise, since ACARA evidently loves the word “algorithm”; it appears fifty-seven times in the draft curriculum. They love something. But it’s not algorithms.
Mr. McRae’s Triple Gift
This is a story from long, long ago. It is about Mr. McRae, who was our grade 4 teacher, at Macleod State School. We have written about Macleod before, and we have written, briefly, about Mr. McRae before, in regard to the moon landing:
I still have vivid-grainy memories of watching Armstrong’s first steps. A random few students from each class in Macleod State School were selected to go to the library to watch the event on the school’s one TV. I was not one of the lucky few. But Mr. Macrae, our wonderful Grade 4 teacher, just declared “Bugger it!”, determined which student in our class lived closest to the school, and sent out a posse to haul back the kid’s 2-ton TV. We then all watched the moon landing, enthralled and eternally grateful to Mr. Macrae.
He was that kind of guy. No-nonsense and intelligent and cultured.
The year he taught us, Mr. McRae was new to Macleod. He had just appeared on the playground before the first class of the year, tall and commanding. Rumour had it that he had played Under 19s for the Richmond Football Club, making Mr. McRae just shy of a Greek god. (The actual Greek god was, of course, Carl Ditterich.) He was a standard and excellent teacher. Firm, disciplined and disciplining, but kind, and with a calm and intelligent air of bemusement. He was the boss, but a thoughtful and unpredictable boss. Hence, our class getting to watch the moon landing. And, how else to explain the boxing match?
One day, Mr. McRae inadvertently started a harmless play-scuffle between two students. He then decided the dispute should be settled by a proper boxing match in front of the class. Once, of course, a kid had been sent home to fetch a couple pairs of boxing gloves. We can’t remember whether we lost, although we remember we didn’t win. In any case, neither of us had a clue how to box, and so the match was followed by Mr. McRae giving the class an impromptu lesson on technique. This was, to explain it a little, the era of Lionel Rose and Johnny Famechon and TV Ringside.
That’s all by way of background. The story we want to tell is of a mathematics lesson.
One Friday afternoon, Mr. McRae introduced his grade 4 class to Pythagoras’s theorem. Or, at least, to Pythagorean triples; we can’t specifically remember the triangles, or anything, but undoubtedly 
made an appearance. Why he showed us this, God only knows, but Mr. McRae ended the class with a challenge: find more triples. Our memory is that the specific challenge was to find a certain number of triples, maybe three, maybe five.
We have no idea what Mr. McRae hoped to achieve with this challenge, but we remember pondering, aimlessly, hoping to find triples. Eventually, by smart persistence and dumb luck, we stumbled upon the trick: doubling a triple gives a new triple. So, 
, and so on. With this kid-Eureka insight, we then happily spent the week-end doubling away.
Come Monday morning, Mr. McRae asked for the class’s triples. We proudly went to the blackboard and wrote up our largest creation. By memory, it was something in the millions. So,
![\[\boldsymbol{1572864^2 + 2096152^2 = 2621440^2}\]](https://mathematicalcrap.com/wp-content/ql-cache/quicklatex.com-e71dd4bbb3c3495f57d48a7da8bd0770_l3.svg "Rendered by QuickLaTeX.com")
or thereabouts. And then Mr. McRae uttered the fateful words:
“Let’s check it!”
There were the inevitable groans from the class, and the little Archimedes hero of the story was more popular than ever. But, Mr. McRae was the boss, and so we all set down to multiplying, including Mr. McRae himself. And, ten or so minutes later, the class collectively started to conclude … the equation was wrong. Yep, Little Archimedes had stuffed up. Which led to more fateful words:
“Let’s find the mistake!”
More groans, more multiplying, and eventually the error was found. By memory, after quite a few doubles, somewhere in the mid thousands. And, satisfied, Mr. McRae led the class on to whatever he had been planned for that day.
What is the moral? We have a reason for telling the story, beyond a simple tribute to a great, memorable teacher. We think there are morals there. We’ll leave it for the reader to ponder.
2019 TIMSS Sample Items
While we’re working away on ACARA, here’s another post to keep readers occupied. Below are released “benchmark” test items from TIMSS 2019. (Further details about the benchmarking can be found in the full report (pp 35-59, 172-198).