6th Grade Math : Unit #4 - Fraction Operations : Lesson #3

What Fraction of the Section Does Each Person Own?

Objective: SWBAT: • Determine fractions that represent portions of land • Develop strategies for combining fractions
Standards: 5.NF.A.1 5.NF.A.2 MP1 MP3 MP4
Subject(s): Math
60 minutes
1 Do Now - 7 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to start thinking about strategies to find a fraction that represents a portion of a shape.  These rectangles are taken from Investigation 2 of Bits and Pieces II in Connected Mathematics 2.  

Some students may break number one into sixths.  Other students may recognize that 2 and 3 each represent 1/3.    

Students participate in a Think Pair Share.  I call on students to share out their thinking.  For problem 1 I declare, “I think number 1 represents ¼ because it is one of 4 pieces of the rectangle.  I want students to articulate that yes, there are 4 pieces of the rectangle, but they are not equal.  I ask students, “If the whole rectangle represented a cake, and I cut myself section 2 and gave you section 1, would you be satisfied?”

I also ask students who is correct for problem one if one student says section 2 represents 1/3 of the rectangle and another person says it represents 2/6.  I want students to apply their knowledge of equivalent fractions and recognize that they are equal.  


2 What fraction of a section does each person own? - 5 minutes


  • I use the data from the Fractions Pretest to Create Homogeneous Groups.
  • Each student gets 2 different colored markers.  They use one marker to trace over the boundaries of a section.  This way they can clearly see the boundaries when they are splitting up the land.
  • I have rulers ready if students request them.  I also make extra copies of the Land Sections sheet in case students need to start over.


I have students move into their groups.  I have a volunteer read about Tupelo Township.  This problem comes from Connected Mathematics 2's Bits and Pieces II Investigation 2.  I read students their job and I show them a copy of the Land Sections sheet under the document camera.

I ask students the following questions:

  • How many sections of land are being talked about in this problem?
  • How many acres are in one section?
  • Does anyone own an entire section?
  • Who do you think owns the largest piece of a section?
  • What fraction of a section does Lapp own?

 With these questions I am ensuring that students understand what a section is and what they know about each section.  I want students to recognize that Lapp owns ¼ of a section.  I have volunteers pass out the Group Work Rubric and the Land Sections sheets.  

3 Group Work - 38 minutes

As students work, I walk around and monitor student progress and behavior.  I make sure that groups check in with me when they have answers to problem 1, before moving on to the other problems.  Students are engaging in MP1: Make sense of problems and persevere in solving them and MP4: Model with mathematics

Some students may struggle in finding a common denominator.  If this is the case, I have them return to the do now problems.  What did you do for these problems?  Why?  How can you apply that to the land sections?  Some students may struggle with combining fractions.  For problem 2, I ask students to explain what they need to do.  Why?  What do you know about combining fractions?  I want students to recognize that they must have common denominators in order to combine Fuentes’ land with Theule’s land.

If groups successfully complete the questions they can move on to the challenge questions.

Creating Equal-Sized Pieces

In this lesson I was surprised at which students were able to create equal-sized pieces and which students struggled.  The students who figured out a strategy quickly were students who have typically struggled in my class.  I had these students share and explain their work during the closure.

Section 18:

Many students struggled to initially break up Section 18.  I counted up the 8 different land owners and asked whether each owner owned 1/8 of the section.  Students were able to express that the different pieces were not the same size, so each section did not represent 1/8 of the section.  Then, I had students return to the do now to see what strategies they could use.  Other students were able to recognize that the Lapp family owned ¼ of section 18 and that the Bouck and Fuentes family owned 1/16 of the section.  They then had to find another strategy to figure out the other landowners.

32nds:Unit 4.2 Section 18 Horizontal 32nds.jpg Unit 4.2 Section 18 Vertical and Horizontal 32nds.jpg

One strategy included splitting section 18 into 32 equal-sized pieces.  Some students had 32nds that were all horizontal, which other students had 32 equal-sized pieces but some were vertical and some were horizontal.

64ths:Unit 4.2 Section 18 64ths.jpg

Other students split the sections into 64 equal pieces.  When students presented this strategy I asked other students whether the correct answer was 64ths or 32nds.  Students were able to see that 8/32 and 16/32 were equivalent.

Section 19:

Unit 4.2 Section 19 Part 1.MOV

Unit 4.2 Section 19 Part 2.MOV

At first, this particular student started to create horizontal 32nds to Section 19.  When I came back to her, she was able to see that her partner’s strategy of creating 16ths wasn’t working because of the boundary between Burg and Walker.  She decided to split up the pieces even further.  By the end of class she had split Section 19 into 64 equal pieces.

Another student experienced the same difficulty with the Burg and Walker boundary.  Her strategy was to create a four vertical 32nds around the boundary.  Unit 4.2 Section 19 Vertical and Horizontal 32nds.jpg  She was able to show me that she first drew in the horizontal lines and then erased them to create the vertical pieces.  She was also able to show me how the vertical pieces were equivalent to the horizontal pieces.

4 Closure and Homework - 10 minutes

 For Closure I ask students, I ask groups to share out their strategies for finding a fraction that represented the amount of a section each person owned.  If two groups present different fractions for the same person, I ask students which group is correct and why.  In many cases the fractions will be equivalent, making both groups right.

Then I ask students how they combined fractions for problem 2.  I have different groups share out their strategies and I ask students to comment on whether they think the group’s strategy is reasonable.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others

Instead of giving a ticket to go, I collect students’ work to look at.  Then I pass out the HW What fraction of the section does each person own.