Parts of a Whole: Modeling Fractions & Creating a Portfolio

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Objective

Students will be able to create a folder to organize their fraction work and explore parts of a whole with fraction circles.

Big Idea

Fraction organization or a piece of it!

Introduction

I always start out a new math concept by having my students create a folder portfolio.  I recently went to a NGSS professional development day and was shown a new way to create a science folder.  I wish I had this information earlier in the year or I would have used it for my fraction unit.  I am going to be using this format for math, reading and science – I used it last year with my novel study units and loved it.  I have created a folder as an example and I will share it with you.  I am really excited to use this format next year for all subject areas!  It is for geometry but you will get the idea. 

Your students may be in 5th grade but they have been developing their understanding of fractions since they were little – and it is incomplete or misguided.  

I’ll share half of my cookie with you.  Your half is bigger!

Look at the quarter moon! (This one causes misconceptions with science also.)

The laundry basket is less than half full.  I don’t have to do laundry.

Since classroom instruction should scaffold on children’s previous experiences teaching about fractions means correcting some misconceptions and giving a lot of opportunities through exploring, modeling and a lot of vocabulary development. 

Creating the Portfolio Folder

20 minutes

Start with giving your students a large piece of construction paper to create a Journal Cover, some lined paper and three pages of blank paper.  Fold the construction paper in half and have your students title it with the concept you are teaching – for this lesson it should be fractions.  Have your students stack the paper with one blank page on top, then the lined papers and lastly the left over blank pages.  You can take a look at the pictures to see how they are labeled.  The blank page in front is a Personal Page, the lined pages are for Student Notes or doing work and the Index is for the vocabulary words and the pages they are on. 

I’ve always wondered which way was the best way to teach vocabulary.  Give the words and definitions first and then do the work, or give the words while working?  This PD I went to emphasized research that states when learning new vocabulary it should be taught within the context of the work, not in isolation.  As you give your geometry vocabulary, have students write the word in the index with the page number from the notes where the definitions and examples should be.  This also gives a great test practice page for kids to quiz each other from.  

Introducing and Modeling Parts of a Whole

25 minutes

Before you begin, keep in mind that there are two different kinds of fractions -- parts of a whole or parts of a collection.  Parts of a whole is dividing a pie into sections, while parts of a collection is one soda out of a 6-pack. 

Bear in mind that as you teach fractions, use different materials so that your students don’t link the fraction concept to only fraction circles or fraction bars. There is research out there that gives reasons to not use fraction circles to teach fractions for one reason or another but fraction circles can be related to pizza and that is one thing that every student has had and can relate to.  Remember you are scaffolding their learning so I start with the basic and build to the complex. 

This activity I’ve modified from About Teaching Mathematics by Marilyn Burns.  The book suggest bringing a 6-pack of soda to school but I prefer to find something healthier such as juice boxes – I also bring enough for the entire class to have during our “brain break” or snack time. I have a range of income levels in my class, from very low and struggling to extremely high, and whenever I use food as an example I make sure I have enough to share with the kids because it wouldn’t be fair to use food as an example when some may not be getting dinner when they get home.  

Take one of the juice boxes and say “If I drink this juice box what fraction can I write that shows what part of the six-pack I drank?”   The answer is 1/6.

Ask these questions next to get them thinking about parts of a set fractions.

What do you think the 6 means?

What do you think the 1 means?

Why does this make sense mathematically?

What fraction should I write to show what the fractional part of the juice boxes I didn’t drink? 

Make sure you probe further with any student who gives a short answer – ask “Why do you think that?”  “How do you know?”

Once you have had a few students answer these questions, walk them through removing another can or box from the part of a set, and then another using similar questions through 3/6, 4/6, 5/6, 6/6.  Pointing out that 3/6 = ½ of the set and 6/6 is equal to one whole. 

While we are working on this I tell my students they can be illustrating the math on their math folders – it decorates the folders and reinforces math through their drawings – art.  You may have some students who do not want to do the drawings and this typically will be your highly gifted students – I have found they typically do not want to put in the time or effort into anything that uses fine motor skills.  Because I am developing the whole child I encourage them to do this because it does build a weakness they have. 

The next part of this activity gets kids really excited and continues to reinforce parts of a set.  Call a group of 6-8 students to go to the front of the room.  Ask questions to the audience such as – What fractional part of our group are girls/boys? Wearing a jacket?  Wearing short sleeves?  While you are going through these examples, use these questions again and have your students explain the fractions:

What do you think the number (in the denominator place) means?

What do you think the (in the numerator place) means?

Why does this make sense mathematically?

What fraction should I write to show what the fractional part of the (short sleeves) I didn’t call on? 

In the next part you are going to pass the questions over to your students but you need to model it first. Have the students give the fraction examples and ask the questions.

Student Reflection

5 minutes

Because I have my students reflect after every lesson this time I am having them reflect by drawing on their folders.  I have told them to decorate their folders but they must have the words, definitions and pictures of numerator, denominator, parts of a whole and parts of a set. You can see this in this Student Work example.