### January 31 - Fractions, free-play and 3 part lessons

I was sitting around enjoying some playtime with my son over the weekend, when he picked up his Melissa and Doug cutting foods and started playing.  I knew I was starting a unit on Fractions the next day, so I packed them up and stole them.  I know, I am a terrible father.

I got some apple juice and some wooden knives and we had a tea party.  I tried not to give any instructions, just to let them have free play with the toys (even though it was quite comical to us all that a bunch of grade 5's were playing with a little baby toy).

As the tea party started, several problems arose.  First, they was obviously not enough food for everybody to have a piece of everything.  This led to arguments over who got what (mostly the watermelon and the baguette were the popular items).  So, once a fair consensuses was reached (paper rock scissors) they started cutting and sharing.  They poured themselves REAL apple juice, and pretended to eat their wooden food.

Once everybody was full up, I asked them to reflect in their math journals on a couple of simple questions.

How much of the baguette did you eat?

How much watermelon did you get?

How many pieces of food did you and the person to your right eat in total?

How many pieces of food were on the table?

Some of them reflected in fractions, while some of them just used whole number strategy.  After the reflection time was finished, asked them to try and express the answers to the questions using fractions.  I used this as my diagnostic assessment for the unit.

Tomorrow we will start our first lesson of the unit.  I am going to try and stick to a three part lesson strategy for the entirety of this unit.

1) Developing the Context - This is where the teacher sets the stage for the problem.  A good problem is a situation - realistic or fictional - that students can imagine and visualize.  This is done as a whole class.  I like to use oral stories that I make up off the top of my head, but that is just my style.  Picture books, poems, images and other art is useful here as well.  This is also a good place to review what we have studied in past lessons, and how it may help us in today's problem.

2) The Investigation - After the context is set up and a problem has been introduced - and hopefully the children are excited about the problem - we break off into small groups and try and figure it out.  The role of the teacher here is just circulate, perhaps ask some pointed questions or encourage students to explain their thinking to you.  It is important here to keep everything based on the context of the problem, and to let them make their own mistakes. Usually this step finishes with the children preparing some kind of poster explaining their work.  Give them time to discuss how they will present it to the class.

3) Math Congress - This is where we meet as a class and discuss out strategies.  Using math talk to is essential here.  A math word wall is a great resource.  The children can explain their thinking and see the thinking of others.  The key point here is to ask them to reflect on their methods, and to notice if there is a more efficient way of doing it.  The teachers job is to use the childrens work, and try to present it in a way that introduces the main concepts or big ideas and lets everybody reflect on the process of mathematical thinking.