Introduction to Parts of a Whole

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Objective

SWBAT explain fraction names and notation through an understanding of parts of a whole.

Big Idea

Students build upon their knowledge of partitioning circles and rectangles to discuss and explore what happens when one or more sections of the whole are taken away.

Introduction to New Material

10 minutes

I start class by laying out a fraction circle divided into fourths on the carpet or underneath the document camera (if you do not have access to fraction circles, you can simply draw a circle and cut it into fourths).

How many pieces have we divided this circle into?

Students will easily identify that the circle has been divided into four pieces. 

What do we call it when we divide a whole into four pieces?

Some students may remember that we call this fourths. If not, it's a good vocabulary reminder. 

Now, we know that this circle is a whole. None of it has been taken away.  We have one full circle here. Let's imagine that this is a pie.  I eat one fourth of the pie.  

I take one fourth of the pie away. 

How much do I have left?  Turn to your partner and explain how many pieces I have left. 

As students share, I circulate to listen to student conversation. 

When finished, I ask two or three students to share.   Some students might say "you have three pieces left" or "three of the four pieces are left". 

Before I took this one piece away the pie had four pieces--I had evenly divided it into fourths.  When we talk about wholes and parts of wholes we use the language ______ out of _______. 

So, when we took one away from this pie, we had three pieces left.  We had three out of four pieces left.  We can also call this three fourths or 3/4.  

As I say these terms, I write them on the board so that students will have a visual. 

Let's look at another example to practice this way of talking about parts of a whole. 

I set a fraction circle of thirds on the carpet or underneath the document camera.

Let's say that I divide this pie into three pieces.  ________ comes and eats one piece.  How many pieces do I have left? Turn to your partner and share using the  the same language we used before. 

I allow students to share for 1-2 minutes.  When I am finished, I cold call a student or partner to share his/her idea. 

If students are struggling I ask them the following questions:

How many pieces did I have to begin with?

How many pieces did I take away?

How can we use the same terms that we used to talk about the first pie? (_____ out of _____)

Guided Practice

10 minutes

During guided practice I divide students into groups of two or three. I give each group a large piece of chart paper or construction paper with a circle drawn on it and tell them to divide it into fifths using a pencil. (They are allowed to trace over in marker once they have divided the circle correctly) I allow students 2-3 minutes to divide their circle.  I then tell them to shade in two parts of their circle using a marker or a pencil. 

I allow students two or three minutes to work.  Then, I have students discuss in their groups what part of the shape they have shaded using the language we used during the independent practice.  I ask them to write the fraction underneath their circle. 

When finished, I have each group of students hold their poster in the air so that I can see it. I ask two groups to share their work explaining how they divided their circle and how they determined what fraction was shaded. 

Independent Practice

10 minutes

During the independent practice, I divide students into groups of two or three. Students work together to divide circles and squares into equal pieces and then to take one piece away and determine how many they have left.

If student understanding was shaky during the guided practice, I model the first guided practice problem (or have a student model the first guided practice problem) before releasing students to work. 

During the independent practice, I walk around and listen to student conversation stopping to help correct any misunderstandings or work with groups who are struggling with any part of the problem. 

I give students who have shown clear mastery of this subject during the introduction to new material and guided practice an extra "challenge" worksheet to complete during independent practice as well.  I determine which students to give this extra work to based on whether they had any difficulty during the earlier sections of the lesson. 

Closing

5 minutes

After the majority of the students have finished their work, I bring the students back together and using my document camera or the board, go over the problems with them, having students explain their thinking for each part of the problem.