Decimals - 'adding a 0 when you multiply by 10'...

The mastery scheme makes great connections between the units. We are moving from fractions to decimals without too much of a gap and the children have been able to refer back to previous learning on fractions and relate it to their decimal understanding.

Followed the ideas here and used the base 10 blocks.

http://corkboardconnections.blogspot.com/2013/09/placevalue.html

Had to get the children to rethink previous experiences with the manipulatives and think about the 100 block as one whole, rather than one hundred etc.

Using a place value chart on the carpet helped too as they were able to physically move blocks or number cards.

Lots of work on building decimals and relating them back to fractions and vice versa before we delved deeper.

One interesting moment was when we reviewed what happens when we multiply a number by 10. I gave the children a pre-assessment sheet and the results were quite surprising.

A lot of children had obviously learnt that when we multiply by 10, you add just need to add a zero. I think this is what I was taught at school too! It is really important for us to stop doing this and show the children that actually it is about each digit getting 10 times bigger and thus moving one place to the left. Reviewing that our number system is based on the base 10 system. A great video from maths antics explains this to the children in a clearer way.

http://mathantics.com/section/lesson-video/decimal-place-value

Hoping to see better results when we come to do this as a post assessment...

Maths Mastery Article

Great article here that has been developed by a school in UK on 'maths mastery'. Lots of great ideas and advice on progression of maths and calculations throughout the whole school. The visuals are brilliant for conceptual awareness, moving from concrete to the abstract.

https://drive.google.com/file/d/0B913yUciLy8YZEExNDk4RU5Tb28/view

23 Years of Teaching Time The Wrong Way!

Teaching Time...teacher and kid's nightmare! Groans from Mairead and Alf when I said this was coming up! But found a couple of great articles.

One of which informed us that we had been teaching time the wrong way, and when we all read it we agreed that it made a lot of sense.

http://ainsleelabs.com/avoid-the-biggest-mistake-teachers-make-when-teaching-time/

So instead of talking about where the hour hand is pointing to, we describe it as what room the hour hand is in. The class have really got behind this and I think it has helped in stopping making those common errors for times such as 2:50, 4:55 etc.

Also a great idea for looking at minutes came from http://maccss.ncdpi.wikispaces.net/file/view/Taking+Time+to+Understand+Time.pdf 
which I found on the following blog: http://www.teachingspecialthinkers.com/2013/01/telling-time-is-easy-peasy.html


Again, using the manipulatives of unifix cubes, having the children count in 5s and visual tools has really helped them in their understanding of the concept of hours and minutes. We have also only looked at minutes past the hour as this seems more logically when moving on to digital and 24 hour clocks the following week.

Fractions and the Bar Model

Trying to approach fractions with a more hands-on approach this time round.

Looking at what fractions mean, using lots of manipulatives and visuals. Found an interesting article on Singapore Maths using the bar model and this has proved a really effective way for children to find fractions of different amounts.

http://www.greatmathsteachingideas.com/2014/12/26/bar-modelling-a-powerful-visual-approach-for-introducing-number-topics/

Most of the children have been able to use this bar model in order to solve fraction problems. They have seen the link to division and having a visual to rely on has made what is normally a pretty hard concept, a much easier one for them.

Finding fractions of colours in a bag of 'skittles' provided some 'real life' explorations too.

Unplanned Perimeter of Compound Shapes

After searching on pinterest for ideas of how to approach area and perimeter conceptually I came across this website:

http://www.theteacherstudio.com/2016/03/area-and-perimeter-studies-deep-thinking.html

Again moving away from my 'norm' of teacher talk at the start of a new topic the class were asked to use 12 tiles to make as many different rectangles as possible. The only input they had was the pre-assessment which showed none of them were secure with the concepts of area or perimeter. Through this hands-on task they were able to use the language needed for the week as well as skills of measuring. Nathalie was the first one able to see the connection between multiplication and area. It was a great introductory lesson.

The following day we moved to the 'cooperation' challenge found further in the teacherstudio website:
http://www.theteacherstudio.com/2014/03/perimeter-and-area-problems-cooperation.html?utm_source=feedburner&utm_medium=email&utm_campaign=Feed:+FourthGradeStudioLearningThinkingCreating+%28Fourth+Grade+S

A definite challenge, but I could really see a much deeper level of thinking. What I didn't think about though was the fact that this would lead them to thinking about perimeter of compound shapes. Not a year 4 objective. It was my 'a-ha' moment as I realised that through these type of investigations learning can happen accidentally, but naturally. And there I have been for most of my maths lessons standing at the front of the class 'teaching' concepts...

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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