Seeing a 5 year old learn about division of thousands, hundreds, tens and units

Can a 5 year old learn division?


It turns out that division is really all about sharing – as we see here when a 5 year old Montessori student divides 9,257  by 4. He starts by using The Golden Bead material to physically represent the number 9,257. These are materials he is already used to working with to represent units, tens, hundreds and thousands having previously learnt about addition, subtraction and multiplication.

His learning takes place as he, working on his own, goes through the process of sharing the 9 thousands, 2 hundreds, 5 tens and 7 units equally 4 times. Let us watch as he works:

He has gathered and stacked the 9 thousands, below, and the 2 hundreds.

9 thousand blocks from the golden bead material


Next he starts sharing the 9 thousand blocks amongst 4 green skittles.

Sharing 9 thousand blocks 4 times


Having shared 8 blocks equally he has 1 thousand block left over which he ‘exchanges’ for 10 hundreds.

Now he is exchanging 1 thousand block for 10 hundreds



The 10 hundreds he has just counted out in exchange for 1 thousand block.

Having 2 original hundreds and 10 new ones he starts sharing them out.

Starting to share the hundred blocks equally amongst 4 skittles.


Almost finished with the hundreds – we see 3 hundreds in three stacks and one more to go


He has shared the tens and is left with 1 ten bead which he cannot share equally yet.

Sharing the tens equally he finds 1 ten bead strip left over


He has exchanged 1 ten bead for 10 more units ready to complete the sharing process with all the unit beads


Counting up how many beads there are for a skittle

He finds that 9257 shared out 4 times means that each skittle has 2 thousands, 3 hundreds, 1 ten and 4 units which he writes in the correct columns in his book.

Each skittle has 2 thousands, 3 hundreds, 1 ten and 4 units…

He also knows that he has one unit bead left over! Its at the bottom of the picture towards the left.


Remainder 1 unit bead


Thus our 5 year old Montessori student is already learning about division having shared out 9257 beads 4 times. He is also finding out that sharing is not always perfect and he can be left with extra beads called remainders.


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