Level 6 Question from CGP

[NorthLondonMummy]

Simplify

2m - 3n + n + 3m - 4m + 3n + 6m


A step by step explanation may help, explaining to my DD.

Thank you in advance.

[Okanagan]

As it is all addition and subtraction then the order of the operations isn't relevant. So you could start by regrouping it to put all the m's together and all the n's together (once she is used to this she'll be able to do it mentally)

==> 2m + 3m - 4m + 6m - 3n + n + 3n

It might help to avoid confusion if the negatives are moved to the end of each group, and single instances are given the number 1

==> 2m + 3m + 6m - 4m + 1n + 3n- 3n

Then convert to
==> (2+3+6-4)m +(1+3-3)n

So
==> 7m + 1n (or just n)

Taking it a step further she might start to spot where it can cancel - so -3n and +3n can just be crossed out and ignored.

Try explaining it as objects instead of letters which makes it less abstract - mangos and nectarines are easier to visualise than m's and n's for example.

So your original question would become
2 mangos - 3 nectarines + 1 nectarine + 3 mangos - 4 mangos + 3 nectarines + 6 mangos

With practice it gets easier to use the letters.

[Guest55]

Please no 'fruit salad' algebra - what does m squared represent?!

Letters in algebra represent numbers or values not fruit ...

[parent2013]

I agree (with Guest55 not Okanagan). Ages back I was taught algebra the same way that .....assume x means apple and I could never figure is out what x square would stand for.

I would do this question by adding "likes" with likes.

Would also suggest that you get this concept right by using some numbers.

m + m = 2m
m + n = n + m
m x m = m square
m x n = mn

[Okanagan]

Well yes of course you don't continue with the analogy. By the time you are looking at algebra with squares etc it would be long gone and probably forgotten. But in this context of introducing it for the very first time - when you are not even trying to solve it, just to simplify, then restating it in less abstract terms can make it understandable for those who don't instantly grasp the concept. Then you can move on from if you can do it with objects you can do it with letters. And then introduce the idea that the letters actually represent numbers and we can work out what those numbers are or substitute particular values to get an answer.

[Guest55]

Okanagan - I have to disagree - fruit salad analogy should never be used.

[stevew61]

I liked the fruit salad recall seeing it used previously elsewhere to introduce the concept of balancing equations. Anything that helps introduce abstract concepts is a bonus in my book.

Right now I would like three eights of a pizza, please.

[Guest55]

Only 3/8 ths

I know it 'appears' to help but it does not in the long run - in fact it hinders understanding.

[stevew61]

In the long run we are all..........

KS2 and 11+ DIY parents sometimes have to improvise to overcome educational gaps, oh let's not go there.

[southbucks3]

Well I stupidly bought 4 really scrummy looking pies in a bag from Morrison's and there are five of us...I don't think there is a sum that equates to 3 boys + 1 daddy - 1 mummy = martyr.

By the way, before anyone suggests it, chopping each pie into 5ths and giving everyone 4/5ths = big mess.