jtsimmons108 wrote:
Agreed on question 8b. No need for calculus. Throw the equation into a graphing calculator and find the minimum. Easy to find...
Wait, so having a calculator find the answer for you is the same as solving it yourself?!? With these types of rules I believe that I could solve every math problem ever solved.
Step 1: Find someone else' correct solution
Step 2: Problem solved
What the What wrote:
jtsimmons108 wrote:Agreed on question 8b. No need for calculus. Throw the equation into a graphing calculator and find the minimum. Easy to find...
Wait, so having a calculator find the answer for you is the same as solving it yourself?!? With these types of rules I believe that I could solve every math problem ever solved.
Step 1: Find someone else' correct solution
Step 2: Problem solved
I don't understand the opposition. The problem said to find the x value that minimizes the value of the function. If I understand that the graph will have a minimum point, and I can calculate that minimum point with technology, why waste my time calculating it by hand. I have to know what I'm looking for when I graph it and interpret what values the calculator gives me back.
If calculators are allowed on the exam, then you should work efficiently to solve the problem. If you want the person to have to find the minimum by using calculus and doing optimization, then don't allow calculators or make the answer not come out to an integer and ask for the exact value.
depends on the exam. Multiple choice, you can just plug the answers in to the calculator to find the minimizing one. No difference with graphing.
If you have to show your work and you just put the answer from your graphing calc, you'll probably get 1 point of 5.
thanks for this thread. liked it. refreshed my calculus too. I tried to do it in my head, but got stuck and brought out the pen... A+
No high school student would be expected to solve the croc question without calculus. It's just straightforward derivation. There might be some kind of dirty trick you can pull with a trig substitution but to expect that would be cruel.
The frog/toad thing requires only precalculus though you have to recognize the geometric series modeling the increase in height. That's why you have to give kids word problems. And why you should never allow calculators on a math test (science is ok).
The only thing impossible for me to understand about all of this is why so many people call it a "maths" question. It's "math", short for mathematics
Graphical calculators are not allowed in the exam, for good reason.
For anyone that thinks it is hard to do 8b without calculus, or a graphical calculator then:
You have found values for x=0 and x=20.
The question states that the optimal value is somewhere in between. Simply use trial and error, starting with x=10 as a sensible point to start with. If you next try x=11 you will see the total time increase. The next logical step is to try numbers lower than 10 and see how things go. You will quickly see that x=8 is the correct value.
The question could have seemed confusing to some kids if they didn't follow properly what they did in part a or didn't listen in class.
Metric Miler wrote:
Graphical calculators are not allowed in the exam, for good reason.
For anyone that thinks it is hard to do 8b without calculus, or a graphical calculator then:
You have found values for x=0 and x=20.
The question states that the optimal value is somewhere in between. Simply use trial and error, starting with x=10 as a sensible point to start with. If you next try x=11 you will see the total time increase. The next logical step is to try numbers lower than 10 and see how things go. You will quickly see that x=8 is the correct value.
The question could have seemed confusing to some kids if they didn't follow properly what they did in part a or didn't listen in class.
This makes sense if you know ahead of time that the answer is going to be a whole number, but if the answer turns out to be 7.346, guess and check is going to be a pain.
The problem with this question is not the math. The problem is that the context represents a kind of microaggression against Scottish students relative to certain recent immigrants.
Clearly there are no crocodiles hunting zebras in Scotland. This lack of familiarity with the paradigm is likely to penalize native students relative to students from Africa.
The resulting increase in time necessary to answer the question (as well as the emotional distress that accrues) may be responsible for what I am going to call the Scottish "achievement gap".
adfasdfdfa wrote:
ventolin^3 wrote:http://www.telegraph.co.uk/education/educationnews/11921671/Can-you-answer-the-tricky-crocodile-maths-question-that-left-students-in-tears.htmlnow, i woud like to hear american 17y/18y oles on how "hard" this problem is & how long it took them to solve 8b
( note : no "grown-ups" disparage efforts of youngsters, as it shoudn't take to solve 8b, more than the 1'39.9 that Ryun '67 was capable of on a '70s synthetic off perfect drafting to bell
i managed 8b in about 1'00 but i'm doing some maths teaching to young relatives & have been read "dummies" on precalculus / calculus 1 / calculus 2, so am "trained up", so that 1'00 is unfair to ask for most "grown-ups" )
Should be very straightforward for anyone in HS taking AB/BC calc. Just differentiate and solve for a zero of the deriv, then plug back in.
Without calculus is trickier...
Yeah it is like the most basic calculus question ever...I'm not 17 anymore but I certainly would have solved it in well under a minute then. What the hell are they (not) teaching in Scotland? I taught calc in grad school and I would have flipped out if a student whined about how hard that was.
I think they made it a little too easy. It's been years since my high school calculus class, but I had problems like this all the time, except that I was told that the crocodile could swim at 5m/s, walk on land at 4 m/s, and the river was 6m wide and was expected to come up with the time formula myself.
I honestly don't think I would have blinked if this question had appeared on an exam. If the GCSE is supposed to test calculus then it looks to me to be a very fair question.
However, I'm way out of practice doing differentiation, so I'm not going to crunch the math on 8b.
kartelite wrote:
Yeah it is like the most basic calculus question ever...I'm not 17 anymore but I certainly would have solved it in well under a minute then. What the hell are they (not) teaching in Scotland? I taught calc in grad school and I would have flipped out if a student whined about how hard that was.
I think the issue is probably that more and more kids are taking calc. When I was in high school, only the really advanced math students took calc. Most of us just went through precalc, then took calc in college. Now, calc seems to be pretty much a standard part of the curriculum for any college bound student. More students taking calc => poorer quality of calc students and watering down of material.
Tangentially, the push to get more high school kids into calc doesn't really seem to be doing much good. Lots of kids who had high school calc really seem to have no clue what they're doing when they get to college calc.
It's minimization of a quadatric equation (which those kids have had drilled into their heads a thousand times) dressed up with a confusing picture and a confusing description of the problem. Ignore the diagram and the verbal description and most of them sail right through.
It's more a crude (and cruel) psych experiment than a math problem. No wonder so many students are put off math.
8ai) 10.44 sec
8aii) 11.0 sec
8b) 9.8 seconds
If this was a question given to students in United States who take AP Calculus AB or BC, they would be expected to be able to answer this. I'ts by no means a challenging question for AP Calculus AB or BC. Optimization is maybe the 3rd or 4th chapter. If they can't answer this, I doubt they'd be able to pass the AP Exam (maybe they could sneak by with a 3 without being able to do this, not sure).
If kids in Scotland are whining about the difficulty of this question, my guess is they were never taught how to do it. I'd also say it's a pretty hard/unfair question if nobody ever taught you how to do it.
All of you are wrong. A croc will not run in a straight line. Neither will the zebra. Running straight lines is not how prey and predator works.
straightintimidation wrote:
It's minimization of a quadatric equation (which those kids have had drilled into their heads a thousand times) dressed up with a confusing picture and a confusing description of the problem. Ignore the diagram and the verbal description and most of them sail right through.
It's more a crude (and cruel) psych experiment than a math problem. No wonder so many students are put off math.
Totally and completely disagree.
It was an awesome question in my opinion. If you can't do word problems, you can't apply math in real life. This is what math is all about. Math is more than crunching numbers in your calculator. You can't have everything spoon fed to you. Except maybe they expect that today, which is embarassing in itself. Word problems are great and this was a good fair one, IMO.
Background: Took Math IB and this exam would have been an easy ace for all students in our class. Square both sides and apply the quadratic minimization if you haven't done calculus. Easy.
straightintimidation wrote:
It's minimization of a quadatric equation
It's not quadratic.
Kids in advanced algrebra, and definitely in pre-calc would be able to solve this easily with a graphing calculator
Btw, was it multiple choice? If so, anyone who has taken pre-algebra (6th grade?) should be able to plug the choices in and see which one yields the lowest result.
that's a classic precalculus question, those scottish kids need to learn math better.