Fascinating Fractions

Fractions is never an easy subject to teach. I remember it was always the one topic that I dreaded teaching when I was in year 3. No matter how I tried to deliver it, some of the children remained confused.

This mornings lesson really needed to go well as we were being visited by one of the numeracy consultants from the LA as part of my MaST course. It wasn’t encouraging when two of my boys announced that ‘I don’t get fractions!’ When I pursued that, they both felt that fractions were hard and that they generally didn’t understand lessons involving them.

We were looking at comparing fractions eg which is bigger 2/3 or 4/5. I was quite surprised by how many children had no idea of where to place a selection of fractions on a 0-1 number line. We spent quite a long time discussing where each one would go and using the fractions ITP to help.

Then I introduced them to the idea of an array and asked how a 3 x 5 grid could help them decide which fraction was bigger. They quickly spotted how it could be used and felt that it was clearer and easier than a number line.

Then I really pushed them and asked which was the larger out of 4/5 or 7/9. They each had a piece of paper and had to fold it into fifths one way and ninths the other way to create a folded grid of 45 squares. This was an incredibly difficult task. How often do we ask children to fold anything other than halves or quarters I wonder? Not being able to start by folding in half made it a real challenge for most of them.

What was really interesting was the level and perseverance. Not one child wanted to give up, they were all determined to fold their paper accurately. They shared their ideas about how they could find fifths and ninths and tried different ways to see which worked best. The two boys who said that they didn’t get fractions produced a very accurately folded sheet and could quite easily see which fraction was the largest. And could tell me that the difference between them was 1/45.

I need another lesson to develop that and actually do more work on folding the paper into different fractions which I think was a really useful activity. It gave the children a real feel for how big a certain fraction was compared to another.

The consultant was impressed with the amount of discussion being done and the level of language being used. I felt that every child had developed their knowledge of fractions and maybe most importantly, they enjoyed doing it.

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Measuring Outside.

Finding angles outside

 

Today was the day of my outdoor maths challenge. I had it all set up carefully with each challenge carefully written up and all the equipment ready. I had a back up plan in case it rained but the sun was shining brightly so everything was looking good. I explained to the children what they were going to do and outlined each of the challenges to them. Then the heavens opened and it began to pour with rain!

I put the back up plan into operation and the children settled down to work. The shower stopped and so we finally all went outside.

The children were excited about doing something different but they were mainly on task. The task choices were interesting. Overwhelmingly they chose to measure trees and find the differences. Only 6 children opted for one of the other 5 tasks.

The lesson was a qualified success I think. Some of the children worked really well and did some useful maths. Some others didn’t really focus on what they were doing and didn’t really complete any of the challenges successfully.

Part of the problem might have been that my explanations weren’t clear. I tried to set the task out as clearly as possible but the explanations were misunderstood by quite a few children. A major problem with the children being scattered around a large area is that it is difficult to intervene and help each group so misconceptions were hard to address until they came to show me their work.

I wanted it to be as much of a free choice as possible but maybe I needed to have fewer options for them to choose from? There certainly needed to be more direct teaching input about a couple of the tasks before we started them. Finding the total surface of a brick stumped everyone and yet we have covered area several times. Taking it out into a different context seemed to make it seem like a different idea altogether.

A good idea I think and one that I want to pursue. Maybe I tried to do too much at one time? Giving the children lots of choices and using the outdoor environment could have been one distraction too many.

I certainly want to do more work on both of these things but probably not at the same time.

Proportionality

This morning was very early for a Saturday as I had a MaST session at NTU so had to get up well before 8 0 clock!

The session was on the 4th big idea ‘Proportionality’. This is probably the part of the course that inspires me least for some reason. All the sessions are interesting and this one was no exception but the idea of proportionality doesn’t seem to inspire me in the same way as the others. Maybe it’s because there seems to be less direct relevance to my classroom experience. I love to be spoon fed and love the way that I take away so many ideas that I can use from this course. Proportionality doesn’t seem to work in the same way. A lot of the ideas seem to be aimed at year 6 or higher. I know that getting a bank of teaching ideas is not the primary aim of the MaST course but relevance to my own teaching and that of my colleagues is one of the things that makes me so enthusiastic about other sessions.

We looked at fractions and discussed the idea that maybe we focus too much on finding parts of a whole eg find a quarter of this number. Do we put enough emphasis on the whole? We looked at the idea of giving students a given shape which is a certain fraction and asking them what the whole shape could be.

Most of the session was looking at the idea of scaling and proportionality and we looked at 2 lessons which were aimed at addressing this idea. It was interesting that the more open ended approach was a japanese lesson where the teacher never really told the children what the correct answer was but let them work it out from each other’s work.

Apparently, children often try to solve proportion problems by addition strategies rather than mulitplication so we need to look at how we can address this misconception. I need to think about how I can look into this and address this issue in my lessons.

The rest of the morning was taken up with looking at our next assignment. At the moment I’m guilty of taking the ostrich approach. I’m putting my head in the sand so that I can’t see it, or just avoiding it in the hope that it goes away. I have the horrible feeling that it really isn’t going to and I am going to have to get some serious work done.

 

Be Proud to be a Teacher!

“I’ve come to the frightening conclusion that I am the decisive element in the classroom. It’s my daily mood that makes the weather. As a teacher, I possess a tremendous power to make a child’s life miserable or joyous. I can be a tool of torture or an instrument of inspiration. I can humiliate or humour, hurt or heal. In all situations, it is my response that decides whether a crisis will be escalated or de-escalated and a child humanized or de-humanized.”
Haim Ginot

This was the opening to our inset session tonight. I’m sure that it is familiar to many people. We were given a presentation by the Head and Deputy of our local high school who together call themselves ‘The decisive Element’ and this quotation set the theme.

Part of the focus of the presentation was that all children are improveable and we looked at the research regarding What’s the difference between a first violinist in the Berlin Phil and an also ran?  Answer – 10 000 hours practice.

The head actually said that he had come to the conclusion that there is no scuh thing as a gifted and talented child. He said that he has come to the conclusion that our gifted and talented children are simply those who have been encouraged to try things and practice them.

I’m not sure that I agree with this. I agree that a lot of our more able children are those who have been encouraged and helped by their parents early in their lives. However I still think that there are children who do display a natural talent for certain things which cannot simply be explained by their background.

The point though is that any child can get better at something and that is something that I wholeheartedly agree with. We should never label a child as unteachable or say that they can never do something. It might take longer for them than others but they well get there in the end.

We also discussed who inspired us as teachers and what we loved about our jobs. They talked about how easy it is to get ground down by everything around us. There was a brief look at work done by Andy Cope (author of Spydog) on happiness and the number of people who are generally happy and look forward to life.

http://www.artofbrilliance.co.uk/

We watched Pig of Happiness

You can decide to be happy and if you decide to be positive then that will spread to others around you. The 4 minute rule is supposed to be that if you can be positive and upbeat for the first 4 minutes then that will set the mood for the next hour. Well it can’t be that hard to be happy for 4 minutes of each lesson surely?

The end message was that we have the best, most important job in the world and we should ‘Be Proud to be a Teacher’

Outdoor maths challenge

I want to use our outside environment more, especially for maths and I have been getting my thoughts together for a maths challenge morning. As it’s nearly the end of term and we haven’t covered anywhere the things that I wanted to, it needs to cover elements of Block D of the new framework. So I’ve decided to base it as much as possible around measurement.

I’ve come up with the following activities so far and the children can choose which ones they want to do. I might have some sort of points system for each one so that they can be a bit competitive (as my group is mainly boys!).

So far I have:

1. Measuring the circumference of 5 different trees and finding the biggest possible difference between them and the smallest possible.
2. Choosing 5 different features and estimating how far away they are in metres and then measuring
3. Finding the area and perimeter of the ball court and then trying to work out how many tennis balls would cover the surface ( I did something similar with snowballs a couple of years ago)
4. Measuring all the edges of a brick. What are the surface areas? What is the volume of a single brick?
5. Use sticks to make triangles as per the nrich challenge
6. Go on an angle hunt and find and measure 2 acute, 2 obtuse and 2 right angles.

That’s all I’ve come up with for now. Any thoughts or comments would be very welcome.