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# What Fraction of the Section Does Each Person Own?

Lesson 3 of 19

## Objective: SWBAT: • Determine fractions that represent portions of land • Develop strategies for combining fractions

## Big Idea: What fraction of the section of land does each person own? Students use an area model of farmland to determine how much land each person owns.

*60 minutes*

#### Do Now

*7 min*

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.

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Notes:

- 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.

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#### Group Work

*38 min*

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.

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#### Closure and Homework

*10 min*

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.**

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*Responding to Kim Haber*

Hi Kim! I can definitely relate to your dilemma. I know that sometimes when I'm teaching I realize that I will need another block to have kids wrap up their learning. I think the TTGs are really important because without them I have a hunch about what kids can do, but sometimes I'm wrong. Sometimes I'll teach a lesson and give the ticket to go and it's clear that kids still need more time to master the skill. I'll mark up the TTGs and during the next block I'll split them up into homogeneous groups to correct their TTGs and continue working on the problems (they almost never finish the packet :)). Do you have that kind of flexibility? Also, do you have a remediation block built into your schedule? Once a week I have a block where I have the benefit of a couple other math teacher adults coming into my room and we run small groups based on targeted skills that we know students have to master, but haven't yet. Feel free to ask me more questions!

| 2 years ago | Reply*Responding to Maleeta Kitchen*

Hi Maleeta! The pdf for section 18 and 19 is a resource in the "Group Work" section of the lesson.

| 2 years ago | Reply

I really love your lessons Andrea and I am using them frequently. I am wondering if you have any thought for me as I frequently run out of time (my classes are 55 minutes but I think my issue is bigger than that) and as a result, I rarely get to use the TTG and sometimes have to cut some of the classwork. I'm finding I struggle with when to move on especially when kids are engaged in meaningful discussions/questions etc. during the lesson (e.g. Do Now). I also think I need to get more comfortable with moving along before 100% of my kids are finished with a classwork activity etc. Do you struggle with this? Any thoughts?

Thanks!

| 2 years ago | Reply*Responding to Jennifer Coalter*

Hello Barb and Jennifer. Unfortunately, I do not post the answer keys for my lessons. For this particular lesson you can cut each land section into smaller, equivalent pieces so that each land owner's piece will have a common denominator. Thanks for your feedback!

| 3 years ago | Reply

Do you have your answers for this? I want to be sure that I have done this correctly before doing this with my students.

Thanks!

| 3 years ago | Reply*expand comments*

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- UNIT 1: Intro to 6th Grade Math & Number Characteristics
- UNIT 2: The College Project - Working with Decimals
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Fraction Operations
- UNIT 5: Proportional Reasoning: Ratios and Rates
- UNIT 6: Expressions, Equations, & Inequalities
- UNIT 7: Geometry
- UNIT 8: Geometry
- UNIT 9: Statistics
- UNIT 10: Review Unit

- LESSON 1: Pretest
- LESSON 2: Many Names for Fractions
- LESSON 3: What Fraction of the Section Does Each Person Own?
- LESSON 4: Which Fraction is Greater?
- LESSON 5: Adding and Subtracting Fractions Day 1
- LESSON 6: Adding and Subtracting Fractions Day 2
- LESSON 7: Looking for Patterns + Show What You Know
- LESSON 8: Representing Fraction Multiplication
- LESSON 9: Representing Fraction Multiplication Day 2
- LESSON 10: Mixed Number Multiplication
- LESSON 11: The Multiplying Game
- LESSON 12: Connecting Multiplication and Division
- LESSON 13: Dividing Whole Numbers by Fractions
- LESSON 14: Dividing Fractions by Fractions
- LESSON 15: Strategies for Dividing Fractions
- LESSON 16: Strategies for Dividing Fractions Day 2 + Show What You Know
- LESSON 17: Unit Review
- LESSON 18: Unit Closure
- LESSON 19: Unit Test