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commutative and associative

Discussion in 'Mathematics' started by adelady, Dec 31, 2010.

  1. Associative - food maybe?
    Whether a meal is served on one plate per person or each item is served on its own platter with adequate quantities which each person gathers onto the plate for themselves. Not wonderful for your purpose but it might stimulate someone else to think of something better. (It's actually very good for something I've been putting together myself, now that I think of it)
     
  2. Off the top of my head [​IMG]
    You need to pick the kids up from school 3 days a week, your partner does the other 2
    You can do Monday and Tuesday in a row and then Thursday or you can do Wednesday, Thursday and Friday in one hit (or numerous other combinations
    You can decide which ones you do together (ie a wed and a thurs) but you can't pick them on on Friday in between Tuesday and Thursday
    So you dont pick the order you do them in just which you do together, this is an example of them being associative yet not commutative
    Does that work or am I losing it?
     
  3. bombaysapphire

    bombaysapphire Star commenter

    For the associative law could you do something with sweets in packets. You have a packet of 2,3 and 4. You cannot open the packets or change the order. How many sweets could you give as a present if you give away 2 packets?
    You could give away 2+3 = 5 and 3+4 = 7 because they are associative.
    Not great but it might inspire improvements.
     
  4. Think of an old-fashioned train, with the brakes in the guard car at the end. Now if it's on the flat, coupling and uncoupling is associative. If it's on an incline, it is not.

     
  5. thanks - i like that!!!
    i think i may use socks/shoes and shoes/gloves for commutative too - no nakedness involved! [​IMG]
     
  6. Great Idea.
    Let's take some kids around 10-11 years old, introduce commutative and associative, which alone are fairly big words and new math concepts and then to assist learning, use the idea of a train 'coupling' and 'uncoupling' which of course is second nature to them.
    Im amazed at some of the ideas teachers come up with these days......oh but......ah of course.
    "today year 3 we are going to learn about being nice to our class mates and what it means to be good person"
    kids look gone out
    "oh come on, its little more than philanthropy in the micro sphere of the classroom"
     
  7. beta - this is a particularly sparky, sciency and general-knowledgy y6 gat class, so i think it will work for me
    erm - i do a y3/4 pfk module on 'what is a friend?' too [​IMG] - and it has thrown up stuff that has brought tears to my eyes
    and yeah - i do know i'm spoilt with the kids i get to teach
     
  8. Yep - this is worrying.
    Dice can also be problematic. A couple of years ago I was worried when I saw a Yr 8 pupil roll two dice and count the spots to add 5 to 3. I thought he couldn't do 5 + 3 = 8 mentally. In fact, he didn't recognise the numbers on the dice, so what he was actually doing was counting the spots to discover that one was a '5' and then counting spots to discover the other was a '3'. He then added them mentally to get 8.
    This lack of familiarity with dice is only compounded (IMO) by interactive whiteboard "dice" that magically give the numbers up on screen and mobile phone apps that do similar things.
    Then there are exam questions that go something like: "Natasha spins a spinner. The probability she gets red is twice the probability she gets yellow. There are 6 sections on the spinner and all of them are coloured either red or yellow. Which of these could be Natasha's spinner ... ?"
    What is a spinner? Where do children ever use them (*) ?
    (*in a maths classroom, presumably?)
     
  9. I am embarrassed to report that my kids believe that custard is only available in little pots with foil lids - we don't even go to all the trouble (!) of boiling milk and stirring custard powder and sugar together.
     
  10. ah - but my daughter is allergic to eggs, so i'm excused!

     
  11. sorry - pressed wrong button - i do do the milk-and-custard-powder bit occasionally tho
     
  12. oh wow! [​IMG]
     
  13. "Eggs-cused", surely?
     

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