Partitioning Circles

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SWBAT partition circles into halves, thirds, fourths, fifths, and sixths.

Big Idea

Students learn the vocabulary halves, thirds, fourths, fifths, and sixths and then work to divide circles into equal pieces.

Introduction to New Material

10 minutes

For the last few days we have been working on dividing squares and rectangles into equal parts.  Today we are going to work on dividing circles into equal parts.

I hand each of my students the worksheet attached which has five circles printed on it.

Using your pencil, I want you to divide circle A into two equal pieces. 

I allow students to divide their circle into two equal pieces.  Then, I ask them to share their work with  a partner, explaining how they know each section of their circle is equal.

When we divide a whole into two pieces, we call it halves.  You can see the word halves written underneath circle A.

Now, I want you to divide circle B into three equal parts with you partner.  Draw lightly so you can erase if your circle is not divided equally.

(Note: students might have a difficult time dividing their circle into thirds.  I allow them to work with their partner and reason through this problem, stopping only to ask guiding questions:  Are the pieces of your circle even? How do you know?  How else could you draw the lines to divide your circle equally?  It looks like you have _____ equal pieces / _________ unequal pieces.  How could we change our lines to divide our circle evenly? )

After giving students time to puzzle through this work, I have at least one group share out their work explaining their process for figuring it out.

When we divide a whole into three pieces we call it “thirds”.  You can see the word “thirds” written beneath circle B. 

Guided Practice

20 minutes

You are going to work in groups of two or three to complete the rest of this worksheet.  Use the word in teach box (fourths, fifths, and sixths) to determine how many pieces each circle should be cut into.   As you work, make sure that you are being accurate and that your circles are divided evenly.

As students work, I circulate, checking in to make sure that students understand how many equal pieces they are supposed to divide their circles into. 

When finished, I hand each student a piece of tape and have them hang up their worksheet on the board or around the room.  I bring students back together and explain that we are going to do a gallery walk:

During the gallery walk you are going to look at your teammates' work and the ways that they divided their circles.  As you walk around you are going to think about the following questions ( I write these questions on the board)

--Are the pieces even?

--Did this person divide his/her circles differently or similarly to mine?  How so?

I allow the students 2-4 minutes to walk around and look at each others' work.  As they walk, I also walk around observing the work and asking students the questions I outlined above. 

When finished, I bring the class back together and give each student a reflection sheet.  I have students work independently to fill out their reflection using the information they gleaned from the gallery walk to influence their answers. 

Independent Practice

20 minutes

During the independent practice, students work independently (or in partners) to make a poster.  I start by handing every student a large piece of construction paper and asking them to divide it into two columns and three rows.  We then write halves, thirds, fourths, fifths, and sixths in each box (see Poster for more detail).  Students then cut out circles and paste them in the appropriate box.  

As students work I circulate and support students who are struggling and ask guiding questions:

1) How do you know this circle has ______ equal parts?

2) How are these circles similar/ different?


10 minutes

During the closing, I have students bring their completed posters to the rug.  In partners, they share their work explaining the differences between halves, thirds, fourths, fifths, and sixths.  When finished, I pick 2-3 students to share their work to the class while other students listen.