Understanding written division

Last week we moved from mental strategies and understanding the concept of division to using written methods. I remember last year, going through the motions of teaching chunking - first on a number line and then vertically.

This year I decided to try out something different and to build up to chunking bit by bit. I found a great website https://desertdesigned.me/2015/10/23/teaching-division-with-area-models/ that showed how to use the area model when dividing. This seemed to be a more visual way to begin. Rather than recording horizontally on the side though, we did all of our recording within the rectangles.

I think this was a really clear picture for the children as it carried on from last week's idea that division is about trying to get as close to 0 as possible.  They all seemed to be on board with this which was great.









The following day we looked at using the same method but recording our subtracting on the right hand side, using a vertical method.

The final stage was to not use the rectangles at all, but to
record using the chunking method recording vertically. Some children were happy to move onto using this, but some wanted to stay with the area model. At this stage I am not worried about which method they use, but the fact that they have understood what they are doing - taking away 'chunks' each time to get as near as possible to 0, and using known table facts to help them do this.

They also came across some sums where there was a remainder and it was not possible to get to 0. This led to a great discussion of what we would do with that leftover number.

What does division mean?

As I am aiming to get the children to have a deeper understanding of concepts in Maths I am trying to take a few steps backwards before racing on with the Year 4 objectives. So we started this week by discussing what division means to them and using the Frayer Model to help guide us with our thoughts.

The Frayer Model was introduced to Paul and I at the workshop we went to on Conceptual Maths. It is a graphic organiser that requires learners to understand not only definitions but also the more complex concepts. It will hopefully promote a higher level of thinking and can also be used to assess deep understanding of the mathematical concept. It will take a bit of modelling but once the children get the hang of it, I believe it will be a really useful tool - not just for Maths.

The children came up with ideas that division was about grouping and sharing. We discussed the term 'equally' and trying to make groups in order to get 0 - or as near as possible. The week was taken up with different strategies we can use in order to help us solve division problems (not using a formal written method). That included using manipulatives as well.

At the end of the week I gave them a sheet where they had to solve various 'mastery' questions. This was the first time they had been exposed to these type of questions. Could they apply the strategies and use of manipulatives independently?

A mix response! One student broke down in tears - not quite what I was hoping for! But at least half of them, independently took what manipulatives they needed and started working on the questions. There was one question where they had to round up after dividing, which was a new concept. But by drawing groups they were able to visualise why they needed to round up, and not have a remainder.

They then blogged one explanation of how they solved the problem.

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