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The 10 Dumbest Maths Questions

March 21, 2010

This post could be called the 10 Most Annoying Maths Questions. It began when Sarah Ebner, who runs the fabulous Edu Blog for the Times (UK) Schoolgate asked me to comment on her daughter’s maths homework.

Here is the question:

This week we have been working on addition and subtraction linked to money. The children have been using skills relating to mental strategies such as bridging through a multiple of 10, number bonds, partitioning, doubling and near doubles, counting on or back in 10s, using what they know to look at patterns or use the inverse, using imaginary number lines or 100 square in their heads. They have also been using the idea of the difference when doing some subtraction sums or when giving change

Homework task: 

Using the appropriate strategies, complete the attached worksheet. Show your workings. Buying a balloon. Lolla bought a balloon at the circus. She gave the clown six coins to pay for it.

What could Lolla have paid for the balloon? Which of your answers seems a reasonable amount to pay for a balloon?

Key questions: 

What is the largest amount of money we could make? What is the smallest amount of money we could make? How will we know when we have all the possibilities?”

Now keep in mind this HOMEWORK has been set for an 8 year old. The complexity of this maths is ASTOUNDING, obviously, for an 8 year old. This question fits the heading ‘Permutations & Combinations’ which introduces Statistics. The language is over-the-top. It is in Australia too. Why can’t kids just DO maths? I was helping my 10 year old neighbour do his maths homework on Thursday. He was doing short division. ‘You have to know the algorithm’ he explained. “You mean you have to know the way to do the maths?’ I asked. His 8 year old sister did a pig drawing for me. I think she’s captured the moment, really without prompting.

PARENTS who do not do maths must feel totally intimidated. As an ex-maths teacher married to an engineer our kids were not blessed either. We tried, on occasion, to help them out. But it was TOO MUCH information. It might explain why both of my children grew up to be arty. One of my kids was bored witless in maths and would fall asleep on his notes. The other one did maths like SUDOKU to fill in time between art classes. Their experience, in part, is why I’ve created Mathspig. They’re not alone. Australian students are dropping advanced maths in droves. The statistic shown was published in The Australian yesterday (20th March, 2010) 

I went and read a number of maths books lying around the house – collecting dust – and I found there was a real pattern to Dumb Questions.

When I returned to maths – as a hobby, always lerved it – after 25 years in the media I found texts books often read like THE ANCIENT RED SEA SCROLLS. What area does a goat graze???? A GOAT!!! Why not ‘what area does your computer mouse need to move at different lengths?’ Good maths students will tackle anything. Teachers face greater challenges. This blog is aimed at finding ways of grabbing the attention of ALL students.

Please send me any DUMB MATHS QUESTIONS you stumble across and I might give an award at the end of the year to the dumbest. The questions below are from a Year 7 TEXT book unless specified. It was quite a good text but well…..

Here are the 10 Dumbest Maths Questions;

1.SO FAKE

These are the questions where maths teachers (Text book writers are usually maths teachers) want to say ‘Look! See maths is important. You can use this particular maths to solve real problems. But the questions are so FAKE they’re laughable. Some boil down to the three men walked into a bar type model … others are just weird. Check out the Names in Q (below) and the Year 12 Q. What is the likelihood of hitting the bird? -Um, absurd!!!!!! 


2. ONLY AN IDIOT

Once again trying to show students that maths is useful questions are asked that only an idiot would try to solve using maths.

IN the Year 11 Q2  (Below) if you had any relationship with a sheep or a goat – I’m thinking goat farmer – you don’t calculate the area grazed. You move the goat. In Q1 how could your friend remember all of those details, but forget the actual number of your house!!!!!!

 

3. THE MORAL TO THIS MATHS

In the first question check out the punishment for not doing maths!! That’s about as subtle as being hit on the head with a Maths Landing Vehicle.

In the second question the mathematicians die!!!!! Mind you, the idea might cheer up the class. look how much homeowrk the kid does in the last Q? Year 7.



4.MAKE THE MATHS WAY MORE COMPLICATED

In the first Year 11 Q you do not use matrices to score cricket statistics. In the second Q if you want to know the names of your friends, um, ask them.

 

5. REIGN OF TERROR

or Fear and Loathing in the Loungeroom. This is when the maths set is way beyond the resources or standard of the students involved. If these questions are then sent home as homework – as with the Q that started this whole discussion – then the pain is transferred others. Sometimes you suspect that teachers offload the questions they can’t answer to parents!!!! Here are some more. The Q1  is doable but it will be hours of fun and games for all the family. Q2, um, Wha?





6. CLUELESS

The students are studying fractions, say. Then they are given a task that involves maths they have not learnt yet. The problem is that the question looks reasonable but isn’t. These sorts of questions produce the whining lament of young students … ‘I can’t do maths!!!’

7. WE ARE FUNNY GUYS. WE MATHEMATICIANS. HA! HA!

When maths teachers make jokes they are often lame. Check out the Question below. It’s just bad PR. Who would want to grow up to be such a nerd.

 

8. IMPOSSIBLE

Either the question is impossible to solve. These often come from typos like ‘find the square root -4’ in Year 8. Or the question is just all wrong. Could you cut a cloth into 1mm strips…. without a laser cutter?

 

9. WHY BOTHER?

There is no point to doing the question. Who would count the legs to find out how many beetles are involved? So why do it?

 

You could go to all the trouble to work out the surface area of your dog and then calculate how many hairs Rufus had, but why? Is Rufus worried he’s going bald?

10. THERE’S NO ANSWER YOU B*&#*#!S

This has made me rethink mathspig. I’ll add more answers. There is nothing more frustrating that doing all the hard work and there is no answer at the back of the book. You want to throw the book at them. The following is a Year 12 Q but, alas, no answers at the back of the book. 

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35 comments

  1. Kerry,
    An interesting post, I certainly agree that the problem posed in Sarah Ebner’s post is just odd for an 8-yr-old.

    But I have to disagree on just about every other example you’ve given of ‘dumb’ maths questions. I do hope you’re being ironic, but I’ll assume you’re not.

    First off, do you really think that maths problems have to be given convincing real-world scenarios in order to be motivating for students? That would be condescending, and utterly boring. A child doesn’t need to cut fabric into tiny strips, but nor might a child give a monkeys about calculating compound interest in a savings account. To the student the ‘adult’ world of applied maths is just as abstract as the sometimes absurd world of maths problems.

    It’s also fatuous to point out that there are multiple ways of solving problems – that using a matrix for a cricket calculation, or simply asking for kids’ names and ages. Of course there are multiple ways of solving problems, it goes without saying that the most efficient method is not necessarily the one we want to be teaching – otherwise we may as well give every child a link to wikipedia, a pocket calculator, and teach them intellectual passivity.

    It seems you’re wilfully missing the point of maths problem-solving – it’s about investigating and using maths in unexpected ways, and in scenarios that you wouldn’t expect to see described in mathematical terms.

    If kids leave school believing that the only applications of maths are practical ones, they’ll fail to use maths creatively and instead rely on it only for shopping, tax returns, and the like.

    I don’t need to know how many leaves are on a particular gum, but it can be a challenge, a mental tickler, to calculate a decent estimate. In fact, questions like that are exactly the kind that certain top companies pose to ambitious graduates to see how well they can problem-solve.

    The dog-hair question is another such example, and I think it’s a great idea. A child will be prompted to think of their pet in abstract terms that reveal pointless facts that are sometimes fun just knowing. But, as any scientist will tell you, investigating the world in novel ways can reveal unexpected truths – this is something we have to teach children. How many times have you heard a child revel in a particularly obscure statistic – “did you know a mouse eats its own body-weight in a day?”?

    I’ve often wondered, in daydreaming moments, how long all the (now very short) hairs on my head would be, laid end to end. This information is utterly useless to me, but it’s like those facts that children hoover up – the surface area of a pair of lungs covering a tennis court, etc.

    I’d agree that some of these questions are clumsy, or overly hard (I can’t comment on #6), but if they give students even the slightest sense that there is a mathematical world that helps us describe the real one, then the teachers will have done their job.

    Thanks for listening!


    • Hi Duncan,
      Thanks so much for your comment. Justify yourself is the gist of it. Fair enough too.

      I agree with nearly all of your comments except the ‘most efficient method is not necessarily the one we want to be teaching?’ Why not? As a maths student I would have tackled all these problems and more. I loved maths. Loved. Loved. Loved it. Ditto when I taught maths. But I have been working in the media for over 25 years and I’ve come back with a different world view.

      The maths you are describing is Novelty Maths for Nerds. They are the sort of questions that the good maths students, like yourself, love. But that is not the world in which teachers or parents operate. Kids are bored or afraid of maths at school. The groan and complain. They need a portal into the maths. Teachers have to get their attention first then draw them into the more complex maths. The questions I sighted aren’t horrific. (I’ll collect more. Send some if you can.) they were the questions I had at hand. Coming back to maths after a long break it was like reading the old sea scrolls. What are they on about? Moving goats. What kid has anything to do with goats? Why not what is the arc moved by your computer mouse? I’m not excluding goats but read on.

      In the media you capture the readers attention in the first line. The headline is like a flag ,the first line is the deal maker! This blog sets up maths topics that flag their attention and then grabs them. You want to do logs… How about vampires? You want to do quadratic functions? Here is a real murder solved by a graph of a parabola!!!!

      Your website looks fun. It seems to me that you are using fun to teach maths too.

      Keep going.
      Mathspig
      aka Kerry Cue


      • Kerry,

        Thanks for the detailed reply!

        I had a bit more of a browse around your blog after reading this post, and I see more what you’re getting at. In fact, I was thinking about it yesterday, whether introducing problems like dodging bullets (rather than circling goats!) would engage kids, or simply pander to them.

        There’s a fine line between cool and condescension, and there’s often nothing worse than a maths teacher trying too hard. With a few culture-savvy writers books and exams could certainly be improved. But what we’ve tried to do at Maths-Whizz is create scenarios (admittedly for younger kids) that are less bound by culture – nothing looks dated like yesterday’s fashion.

        I’ll admit that the lessons I remember most vividly from school are those that engaged me emotionally, or shocked me into paying attention. But they didn’t necessarily feature contemporary elements, rather I was drawn more thoroughly into that lesson’s ‘narrative’, if you will. If that narrative was about out-running zombies I don’t doubt I would have paid attention!

        We’ve implicitly recognised this by trying to create scenarios and characters that are emotionally engaging without having to be ‘cool’. The older the student is the harder it is to do convincingly.

        And whilst it’s good of you to assume I’m a mathematician, I’m not very confident with advanced methods, but I somehow enjoy puzzle-solving, which is likely a side-effect of good teaching in other disciplines, as my maths teachers were rather dull. So I agree that more engaging books will help bridge the gap between those middling teachers and switched-off students.

        Your remarks have got me thinking. The dog-hair and dripping tap questions engaged me because I could see the science behind them – investigating the real world, reporting accurately, and discovering hidden mathematical facts about it.

        Scientific thinking is crucial to maths, but we rarely get the opportunity to measure zombie running speed or vampire dietary requirements.

        Even so, I love the thinking behind some recent novelty papers that have analysed the statistics behind a zombie outbreak, or the sustainability of vampire populations (i.e. testing whether vampires are impossible because we’d all become vampires in due course).

        thanks for making me think a little more about this and for adding context to your original post.

        If you want to check us out in more detail, or even review Maths-Whizz, do ask.


  2. Thank you for this Kerry. I have mentioned it today on the blog….


  3. what a pathetic article.

    why do students do these problems? because they are fun, and they equip them with skills to progress to more complex and inevitably more useful mathematics.

    the writer has such a short-sighted, petty, world view that I pity them.


    • Thanks for your comments. I have an engineering background. Novelty Maths for Nerds can be fun but it has limited appeal. This is a plea to maths teachers to make maths relevant to all students …. mathspig.


  4. and what on earth is impossible about Q8???

    if you’re actually complaining about the physical difficulty of cutting cloth that fine, that is ridiculously pedantic.

    Abstraction and maths for maths sake are core to its study.


    • Hi Shaun, this question looks as antique as the Shroud of Turin. Novel but why bother? Cheers Mathspig


  5. “How many leaves ona typical gum tree?”

    Zero.
    Life begins at conception ( the Pope says so and we know it must be true because he’s infallible).
    Fertilised gum tree seeds have no leaves.
    The number of fertilised seeds vastly outweighs the number of mature gum trees.

    (However I agree it’s more of an Oxford interview question).


    • Hi Malcolm,
      Thanks for your thoughts. I love your Zen like response and the fact you’ve come up with a comment outside the answer box. Moreover your reply suggests the answer is blowing in the wind.
      cheers mathspig


      • If were an oxford question, it would make sense. The answer would depend where the tree was. In the northern hemisphere, it would have no leaves, as the oxford interviews are in December 😉


      • Hi Ben,
        I’m assuming the tree is an Aussie gum tree and if so it is an evergreen. It would lose leaves all year round and that would, now that I come to think of it, really upset the calculations!!! cheers mathspig


  6. Most of these questions are very sensible, although they do vary greatly in their level of difficulty. However, the pedant in me always gets hung up on ambiguities.

    Take Q11 for example, as the nature of the fence is not specified, the answer could be anything from 100.pi m^2 (the fence is in a circle surrounding the stake with radius 10m, movement is limited only by the fence and so the area is that of a 10m radius circle) to 400.pi m^2 (a straight fence heading directly to the stake which comes to a halt 10m from the stake – this does not impede the sheep at all and so the area is defined by the rope, i.e. the area of a circle of 20m radius).

    The interesting bit (presumably what they were after) is if the fence is straight, of infinite length and passes by the stake at a closest distance of 10m. The solution involves integrating the square root of (c-x^2) which is not for the faint hearted (I’d say it’s at the level of 17-18 yr olds studying maths).

    Even more complicated would be, say, a 20m length of straight fence that passes by the stake at a closest distance of 10m. The sheep would be able to pass by the fence and access some ground ‘behind’ the fence… now that really would get the braincells working!

    Finally, maths problems, especially more advance maths, are through necessity made of ‘impossible’ circumstances just because real life is too complicated. Light=zero mass, strong=unbreakable, etc. etc.


    • Thanks Bob,

      Lerv, lerv your comment. I lerv your thoroughness and that you could see more possibilities. And you also understand what I’m on about. Kids moan in class ‘Why do we need maths?’ This question would not convince any kid that maths counts. I recognise the need for ‘impossible’ scenarios …. but they can still have meaning. I used many assumptions to calculate the speed of hailstones, for instance, in an earlier entry.
      Cheers
      mathspig


    • Bob, there is no need for integration to solve the goat grazing problem. By about Year 10, many students will have seen these formulae in geometry or trig:
      http://en.wikipedia.org/wiki/Circular_segment


      • HI David,
        Mathspig loves a debate. I think it depends on how the question is asked whether the answer requires simple trig eg. graze quarter circle or complex integration. Cheers Mathspig


  7. Maths is a process required in every day life. You dont need to pander to lids not engage them in Maths classes. Your comments are in line with the general approach today that everything has to be sugar coated. The kids cant stand up to the pace of life. Your article, as someone has already commented, is pathetic and shows a complete non understanding of Maths, or for that matter, what he tester was trying to achieve.


    • Hi Geoff,
      I don’t think these are bad, bad maths questions just annoying. Meanwhile there is a maths crisis in Australia. HIgh school students are dropping maths. Last week the chief scientist of NSW suggested universities should take students into engineering degrees with NO maths. Ahhh! Students must build up their maths skills. But I argue that at some stage kids should be shown that maths is relevant to their lives and that it can solve problems that concern them!!!! Do you have any other ideas re: how to interest students in maths? mathspig


  8. Hi mathspig,

    I really agree with your sentiments about school maths questions – they’re irrelevant and uninspiring. I remember lots of similarly contrived and dull questions from my school days, which were not so long ago actually.

    But I always blamed bureaucratic politicians rather than maths teachers. In the UK, all maths lessons and textbooks have to fit tightly to the national curriculum. for example, here are the 99-page guidelines for what to teach 7-11 year olds in maths:

    http://curriculum.qca.org.uk/uploads/Mathematics%201999%20programme%20of%20study_tcm8-12059.pdf

    This detailed prescription homogenises maths teaching between schools, but makes for very formulaic teaching with little time to waste on interesting and open-ended diversions that would actually inspire kids. Any teacher at a state-funded school with an independent streak who wants to ignore the curriculum will find their students fall foul of SATS exams, hence the controversy now:
    http://news.bbc.co.uk/1/hi/education/default.stm

    I love your blog posts about real world maths, and I wish there could be more of that in schools. But I particularly sympathise with teachers and find it hard to blame them, because their jobs are not exactly coveted – pay is low, and the kids’ discipline can be pretty poor owing to recent British social trends. You used to be a teacher; can you relate to this or are teachers more valued as important public servants in Aus?

    Also, I notice that Australia is preparing a national curriculum too. Be afraid!

    Best,

    mpatter

    PS. In the interest of full disclosure, I’m a young male academic with no children. Part of my motivation for writing this was that I don’t like academic-types getting stereotyped as arrogant and detached from reality. It’s only half-true…


    • HI mpatter,
      Thanks for your very informative and interesting comment. I’ll follow up on the links. I agree with you. Maths teachers in Australia are under pressure to meet NAPLAN (National Assessment Program for Literacy and Numeracy) standards. They have no time for being creative… but they do have data projectors in nearly every classroom so they could use blogs like mine to make the maths real.

      On the other hand, in australia, Macdonalds has put the entire maths curriculum online for free!!!!!

      https://mathspig.wordpress.com/2009/07/17/what-are-maths-teachers-for-sir/

      So the way we teach maths is changing. Maybe all maths teachers will have to do in future is make it exciting!!!

      Good to see an academic getting his teeth into the whole maths debate. Many thanks Mathspig


  9. Dear Bob
    What are examples of better maths problems, please?


    • Hi Amark,
      Kerry here. This blog offers some suggestions. But I’m open to all ideas that help promote maths. mathspig


  10. Hmmm – there is just so much here that merits comment that I am overwhelmed. Many years ago I read Mechanical Engineering and subsequently Operational Research & Systems Analysis so I feel I was reasonably proficient in mathematics (before I forgot most of it!).

    I do not think that mathemetics should be exclusively practical but I do believe it should be interesting, stimulating and stretching – lets take the plug out of the bath! Why does the water always swirl in one particular direction in our hemisphere?
    But….
    We all need to be able to master the mathematical techniques appropriate to the circumstances.
    Also….
    Where does comprehension play a part and where should it stop? Are conducting an exercise in comprehension or assessing mathematical technique? Or both?
    And another thing…
    The jargon! I think this has been mentioned before but “bridging”, “number bonds”, “partitioning” and so on – I have no idea what these terms mean and I question the value they may have in teaching mathematics. If an implement is a spade then call it a spade – we do not need pretentious drivel!
    I believe that homework should reinforce and consolidate what is being taught in class but perhaps this is being old fashioned and I am out of touch.

    Incidently, talking of 6 coins from eight, are these just 8 types? Can we have selection with replacement? I think my attention is wandering and I am getting bored with maths….ooops!


    • HI Tony, thanks so much for your comment. I taught maths for 10 years then went into the media.I see maths differently now. I think kids have to practice skills but they must see that maths can solve real problems or why bother. Any other thoughts welcome. And if you do come across some awful maths questions pass them on. Cheers Mathspig


  11. […] The rather good Mathspig blog was brought to my attention in a recent Google subject alert which pointed to a list of the ‘10 Dumbest Maths Questions‘. […]


  12. I was a Maths teacher, with a degree in Applied Mathematics including Astrophysics, and, much to my surprise, when I started teaching, I enjoyed teaching the less gifted far more than the clever ones. The clever ones, like I had before them, could do it from books. (Good books, I mean, not NEW MATHS type books.

    But with the less able, you could make it fun and relevant. The problem with all your examples are that the teacher is trying to show how clever SHE is, because she knows how to solve these abstract absurdities! One of my colleagues was obsessed with Cricket, so all HIS examples had no meaning at all to any of the children in that working class school where Cricket wasn’t even played!

    I strongly believe that Mathematics is often confused for Calculation. You can have good calculators (darts players for instance) who have no mathematical ability at all, and good Mathematicians who can’t count to save their lives! Likewise – good writers don’t have to be good spellers, not does spelling well make you a good writer!

    Here’s a good idiotic question – ‘If One Man and One Woman can produce one baby in 9 months, How Quickly can 9 men and 9 women produce one baby?’


    • HI Sion,
      Thanks for your thoughtful comments. Needless to say, I agree with you. It is difficult today for maths teachers today to be creative because of the huge administrative workloads. Then again blogs like this help. I’m very interested in your thoughts on calculation. I would argue a computer calculates, a mathematician thinks!
      As for you final question…. aren’t 8 of those males actually redundant? Cheers Mathspig


  13. 6: “I looked under a slice of onion” But again, a vegetarian does not really need the stake at all :-DDD


    • Hi Vegi,
      Did I write steak again!!!! I salute all vegies and this includes members of my own family. You make meat eaters more honest. Cheers Mathspig
      PS: One of the great deceits of our culture, as you know, is to make cute and cuddly cartoon characters for kidslike my mathspig logo while hiding the brutal and bloody truth about pigs et al.


  14. Smart questions, just the quality of the scans, especially the large versions, is “loss of reality” 😀

    Fixed:


    • Thanks Ann,
      I’ll see what I can do. They’re OK on my computer. But that doesn’t mean a lot. Cheers Mathspig


  15. If my teachers at school were able to demonstrate to me when I was going to be using a particular skill I would endeavour to learn all about it. If they could not, I dismissed it as irrelevant.

    My new work requires somewhat basic mathematical skills (arithmetic, algebra, etc). I felt I was lacking in this area, and so got my mathematical ability assessed. Initially the assessor could make very little sense of my results, some areas I excelled in, others I failed to grasp even the most basic applications.
    Exploring this further, it became apparent that each of the areas I had excelled in, I had been given a “reason” to learn it. It would appear the areas I struggled in I had not had a reason for learning them initially, so had never committed the skill set to memory.

    So, this is just my support of making maths relevant when it is initially being taught!


    • Hi Baby-paramedic,
      Thanks sooooo much for your comment. You’re experience supports the whole philosophy of this blog. Nerdy kids will do maths for the academic challenge. But most kids need a context. Otherwise, maths equates with learning a dead language. The good thing is that you haven’t been put off maths forever. When you need maths for a job, say, you can if motivated pick it up in no time. cheers and thanks Mathspig


  16. I have enjoyed reading these comments they are all just so interesting. I cant really contribute to ‘awful’ maths problems – I try not to remember them – but I can comment. I think I must be, in part, a nerd cos I liked (mostly) maths – I looked upon it as problem solving (but in those days that was’nt the way I would have described it).

    At school experience was varied but I wanted to do better than the guy in the next desk – I wanted to be top – mostly this translated to being in the top 5 (there was always some other so-and-so who did better). At Uni I had a really good Maths experience – it was just so interesting, not always related to practical applications but just so interesting in the way it was presented and in its own right – problem solving (I really must be a nerd!)The problem with the goat and the fence is that it is not uniquely defined.

    I have 2 maths books I really like – ‘What is Mathematics’ Courant & Robbins pub 1941, OUP (no, I wasn’t alive when it was published)and ‘The Language of Mathematics’ Frank Land pub 1960, John Murray – but I guess these days we all need to fit into the current straight jacket of education!


  17. For the coins problem, it should be possible for an 8 year old to do it. It’s not asking how many combinations there are, it’s asking what’s the highest and lowest amounts that the balloon might cost, if you use 6 coins. If they’re 6 pennies, the balloon will cost $0.06. If they’re 6 dollar coins, the balloon will cost $6. If they’re 6 quarters, the balloon will cost $1.50.



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