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Teaching multiplication

Discussion in 'Primary' started by Ramjam, Jan 2, 2012.

  1. Ramjam

    Ramjam New commenter

    This is a problem - and teaching multiplication by arrays and understanding multiplication as repeated addition is the easiest way round it. I know what the primary Strategy says, but when children are saying tables to help ingrain them, saying three twos are six, five eights are forty means exactly that. Even my poorest children can get out the correct Numicon shapes if I say five fours. Perhaps the National strategy needs amending.
     
  2. minnieminx

    minnieminx New commenter

    No way should we have a curriculum that prescribes exactly HOW we should teach. I know having all kinds of odd things is tricky for supply teachers (been there and done that) but the alternative is unthinkable. Teachers have to be free to teach the best methods for their class.

    The strategy isn't compulsory and so many teacher just ignore the bits that are nonsense.
     
  3. tafkam

    tafkam Occasional commenter

    No! That's the last thing we need.
    The fact is that in real life, people might write 3x2 to mean either of those things, and children need most importantly to learn that the order of the numbers doesn't matter in such a calculation... 3 lots of 2 is the same as 2 lots of 3.
     
  4. While the numerical total for 3 lots of 2 is the same as the numerical total for 2 lots of 3 what it actually means is NOT the same, and that is entirely my dilema. Surely if on supply cover I expalin 2 x 3 to a class as 2, 3 times ie 2 + 2 + 2 and show this using diagrams) then the class teacher when returns and tells the children 2x3 means 3 lots of 2 this would need different groupings in her diagrams; whilst the net <u>numerical result</u> is the same , the meaning of the X symbol is not.
    I am also aware that by teaching by arrays one can show the numerical result of 2x3 is the same as the <u>numerical result</u> of 3x2, but the groupings are swapped arround ; they do not actually mean or represent the same situation .
    All Primary Maths text books I have seen in schools prior to the Primary Strategy have given one meaning whilst those post Primary Strategy seem to give the other explanation. Why was this explanation changed?
    If I teach muliplication in a school on supply cover I always feel I need to check first which <u>meaning </u>they attach to the "X" symbol ; I think it would be confusing to explain it one way only to find the class teacher returning & expalining the meaning the other way around.
     
  5. I know - isn't maths fun? Same as 18 divided by 3. Is it 18 into 3 groups or 18 into groups of 3?
    I have 5 boxes of jaffa cakes with 12 cakes in each box. What would you naturally write in a sum?
    5 x 12 or 12 x 5? I know that in primary we often say 5 lots of 12. Is this the same as 5 x 12?
    Technically the answer is the same and that's useful to know. But what does the x symbol mean - or what does 5 times 12 mean?
     
  6. minnieminx

    minnieminx New commenter

    Any good teacher will be teaching both ways anyway, so it won't matter much.
    Understanding the commutative law of multiplication begins at level 2 maths, so year 1/2 for most children. If the schools follows the framework, then year 1 won't really do multiplication. Year 2 will and will start to understand the commutativity and anyone older will know either is fine. So teach whichever you feel happy with if you aren't told.
     
  7. tafkam

    tafkam Occasional commenter

    But the point is that when it comes to abstract multiplication, it doesn't matter which way round it is. The key point of learning multiplication should be that the rules of commutativity can help us. For example, when buying 75 screws at 3p each, it is academic that that calculation I need to do is 75 lots of 3. What is useful is to know that 75x3 is equivalent to 3x75, and thus that I can simply add 75 three times.
    We shouldn't waste our time on technical niceties unless they serve a purpose.
    As Stanley Gudder says:
     
  8. though i do thing 3 x 2 = 3 lots of 2 works better with tables - where you have 1 lot of 2, 2 lots of 2, 3 lots of 2 and so on
    and if children did learn their tables, they wouldn't need to do bombays's (i think) switching 5 x 7 to 7 x 5 because counting in 5's in easier
    (hah! no, i don't know how to make children learn tables, either)

     
  9. I dont get the dilemma. They need to know both representations. All you are saying is that you can read the calculation 3 x 2, in two different ways. Yes you can, but you can also swap the numbers around and read it in two more different ways. Surely children need to know all those different ways?
    When beginning to teach multiplication, I read the X symbol as "Lots of" so 3 x 2 we represent as 3 groups of two. As soon as the basics of multiplication are understood, I do LOTS of varied vocabulary work, say it different ways, represent it different ways, make sure they know they can do it both ways around, work on looking for the 'easiest' way of solving a calculation etc.
    My class therefore, presented with the problem 7 x 5, will (hopefully!) recognise that they can count in 5s seven times to find the solution. If I asked them what else they could do, they might suggest creating 7 groups of 5, or 5 groups of 7. The most important thing is that they understand WHAT multiplication is, and to always look for the quickest/simplest way of solving a calculation. I dont see why consistency across schools is necessary as long as schools are teaching to fill the gaps for their children.
    If its tricky as a supply teacher, Im afraid thats the way its going to be - there must be hundreds of examples of times when you teach things differently to the way the classteacher would. I dont think it hurts the children to have it explained in different ways.
     

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