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Caroline bought a school bag, a pair of shoes and a jacket for her son. She paid a total of $\$170$. The pair of shoes cost $\$23$ more than the school and $\$16$ less than the jacket How much did Caroline pay for the jacket?

lulu
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Joseph liew
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    Please edit to include your efforts. And to explain why you want to avoid Algebra. After all, Algebra was invented to solve problems like this one. – lulu Jul 09 '21 at 11:18
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    @lulu I can shed some light on that. It's one of those idiotic aspects of the "modern" Singapore primary school math curriculum, where they want students to use "models" rather than symbols to solve problems. They claim not to penalise students who learn algebra on their own and use it, but they often do penalise these poor kids. – Deepak Jul 09 '21 at 11:23
  • @Deepak Thank you for that explanation. I'd be interested to see what a "model" would look like here. Have you got a link to an example handy? – lulu Jul 09 '21 at 11:29
  • @Deepak Oh, I see you posted an answer here. I'll read that. Thanks agan. – lulu Jul 09 '21 at 11:29
  • Are the schoolchildren required to collapse their compass when making a model? https://en.wikipedia.org/wiki/Compass_equivalence_theorem – DanielV Jul 09 '21 at 11:33
  • @lulu For example here (a pdf download link, don't be alarmed): https://www.hmhco.com/~/media/sites/home/education/global/pdf/white-papers/mathematics/elementary/math-in-focus/mif_model_drawing_lr.pdf For what it's worth, I'm not sold on the whole nonsensical models thing, so I may not have given a very "model" answer (no pun intended). – Deepak Jul 09 '21 at 11:35
  • @Deepak Thanks. I think I've got the notion. For very simple problems, like the one in this post, I can even see some value. But I can't imagine doing it for more elaborate problems. – lulu Jul 09 '21 at 11:39
  • @lulu Ah, there's the rub. They actually expect you to use it for problems with varying proportions etc. It's the most pointless mind-bending I've ever had to do! Let me dig around and find a ridiculous example for you. – Deepak Jul 09 '21 at 11:40
  • @lulu For example, (an actual question) Allan had 60 stamps more than Becky. They each gave away some stamps. Becky gave away 2/5 of the number Allan had at first. Allan gave away 2/3 of the number Becky had at first. Both had an equal number of stamps left. How many stamps did Allan have at first? – Deepak Jul 09 '21 at 11:44
  • @lulu Another gem.

    A,B,C and D each have some money.

    A has 1/3 of the total B, C and D have.

    B has 1/4 of the total A, C and D have

    C has 1/5 of the total A, B and D have.

    D has $92.

    How much do they have in total?

     – Deepak Jul 09 '21 at 11:45
  • @lulu The last one for now, to avoid spamming the comments: There were 500 beads in 4 jars P Q R and S. If the number of beads in P was halved, the number of beads in Q was increased by 18, the number of beads in R was tripled and the number of beads in S was decreased by 24, they would all have the same number of beads. What was the difference in the number of beads between P and Q at first? – Deepak Jul 09 '21 at 11:49
  • @lulu There are even more twisted problems out there the misguided Singapore educators expect kids to solve with "models" and not "letters". But I'll stop with those. – Deepak Jul 09 '21 at 11:50
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    @Deepak There's a frustrating phenomenon out there in which (some) math educators find what they regard as an intuitive approach to some problem, or class of problems, and then elevate it to Dogma. In some instances the intuitive method is even useful and worth describing. But I don't understand the impulse to then force the method into an unconvincing universality. – lulu Jul 09 '21 at 11:58
  • @lulu Very well said. – Deepak Jul 09 '21 at 12:04
  • Are you going to accept any of the answers? – jjagmath Jul 23 '21 at 21:20

2 Answers2

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Since the (idiotic, in my view) Singapore system wants you to avoid algebra (by which they seem to mean letters representing variables), draw a block to represent a school bag, the cheapest item. The shoes are a block plus $23$ dollars. The jacket is a block plus $23+16 = 39$ dollars.

The sum of all the three items is $170$. If you clip away the excess of $39$ and $23$ from the two more expensive items, you get three blocks. Three blocks will add up to $170 - 39 - 23 = 108$. One block will be $36$. That's the price of the school bag. So the price of the jacket is $39$ more, or $75$ dollars. Done.

Deepak
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    A more charitable interpretation would probably be that what the the school system or teachers in question want to discourage is mindless symbol churning. While algebra is a wonderful invention and can help keep track of computations that are much too complex to keep in one's head, students also need to develop familiarity with the concrete calculation that the algebra stands for. Otherwise they might end up considering The Rules of symbolic manipulation to be just magic which works not because anything, but simply because authority says so. (...) – Troposphere Jul 09 '21 at 11:57
  • (...) From a mathematics education perspective that's just as bad as not learning symbolic algebra at all. Of course, this can be implemented too heavy-handed; bad math teachers an make everything impossible. But if you're teaching two views that are both necessary, it's not a priori "idiotic" to set exercises that are supposed to train one view even though the other would give the same result. – Troposphere Jul 09 '21 at 11:57
  • The relation of the sign to the thing signified is being destroyed, the game of exchanges between signs is being multiplied of itself and for itself. And the increasing complication demands that there should be signs for signs. . . . – fonzane Dec 30 '22 at 10:13
  • As collective thought cannot exist as thought, it passes into things (signs, machines . . .). Hence the paradox: it is the thing which thinks and the man who is reduced to the state of a thing. – fonzane Dec 30 '22 at 10:13
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Imagine you are about to pay for the three items. The cashier says it's 170. Then you say: I changed my mind, instead of the school bag I'll take another pair of shoes. Then the cashier says: it's 23 more for a total of 193. Then you change your mind again: instead of the jacket I'll take another pair of shoes. The cashier says: Then it's 16 less, the total is now 177 for three pairs of shoes. Now you know that each pair of shoes is 177/3=59, so the school bag is 59-23=36 and the jacket is 59+16=75.

jjagmath
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