Year 3 Math Division - circles and dots?

[debs227]

My DD was doing her homework last night and when working an answer our for division, lets say 112 divided by 6 she would start with drawing 6 circles and then putting a dot in each until she reaches 112.
It seems quite a long process for large numbers?

It is a really long process and am sure that this will be the only time she does it like that. However, it is a good way of emphasing what division actually is and getting children to understand that it is about grouping and sharing (and is the opposite of multiplication). Many children don't really "get" this and then struggle with word problems or applying division later on. I'm sure that she will move on to quicker methods next time.

I would let her do it her way with dots and groups, but once she has reached the answer going by her method, then I would try and explain quicker way:
12:6=2 groups of six
120:6=20 groups of six
Now she doesn't start with 120, but let her start with 120 and let her reduce groups of 6 going from 120 backwards, so 20 groups in 120, 19 groups in 114 and finally 18 in 108, 18 is her answer with 4 remaining which she can not group, hope this makes sense.
18x6=108+4=112

Hi debs277

I think strictlovingmum is on to something - but have found with both DDs counting up is somehow an easier concept to counting back.

If your DD is the same - you may want to try and treat it as 'chunking'

so 112 divided by 6

What's a big number you could think of that is a multiple of 6?

60 (6 x 10)

112- 60 = 52

Can you think of a multiple of 6 near 52? 6x9 = 54 -too big but
6x8 = 48 works.

48 (6 x 8)

and that leaves

4 left over (52 - 48).

so go back and look at what you multiplied 6 by:

10 and 8.

10 + 8 = 18
with four left over

18 R 4 is the answer.

HTH

Maybe it's long and tedious on purpose? So that when shown a standard method next, it definitely seems superior.

Yes, I too found that mine got so fed up with dots and circles that their dots morphed into dashes which eventually overlapped and made it impossible to count correctly thus having to do it all over again....pretty quickly they'd devised much easier division methods without any further input needed.

How about asking your DD what she would really do when faced with 112 objects to be divided between 6 people?

She would probably come up with something like 'I'd start off by giving them out in 10s' (so write 10 in each circle).

'How many do you have left? Can you give everyone 10 more?'

'112-60 = 52, so no'

'Can you give them out in smaller groups - what would be another multiple you know well?'

'5s might be good' (so write 5 in each circle)

'How many left? 52 - 30 = 22'

The remaining 22 could be given out in 2s or as 1s.

It is a tedious stage, and hopefully they'll get through it quickly, but it is an important visual step for some children to understand about division being about sharing. Giving out in larger groups is a really good first step to the 'chunking' method (which just formalises the above discussion).

Have never come across anything that hard in Y3 yet.

My dd started with circles and dots. I think it helps to visually imprint the grouping/sharing in the brain before moving on to quicker methods.