Exploring Unit Fractions 1/5, 1/6, 1/7

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Objective

SWBAT show and explain how many unit fractions are in a whole.

Big Idea

By partitioning and adding unit fractions, students will gain a deeper understanding of the meaning of fractions.

Opening

20 minutes

Today's Number Talk

For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I am encouraging students to represent their thinking using a number line model. For each task today, students shared their strategies with peers (sometimes within their group, sometimes with someone across the room). It was great to see students inspiring others to try new methods and it was equally as great to see students examining each other work for possible mistakes!

Getting Started

Prior to the lesson, I placed magnetic money and fractions on the board to help students conceptualize our number talk today. 

I invited students to join me on the front carpet with their number lines. I then drew a number line on the board and marked 0, 1, and 2 on the line. I asked students to do the same on their own number lines.

Tasks

Next, I gave students each of the following numbers and asked students to identify where each number would be located on the line. After students had time to place each number, I asked students to turn and talk about their thinking. I also asked for a student volunteer to explain to the class where the number would be placed and why. At this point, I didn't need to ask students to place corresponding decimals. They automatically explained, "1/100 is located here because 1/100 is equal to one penny, $0.01!"

  • 100/100
  • 200/100
  • 50/100
  • 1/100
  • 90/100
  • 120/100

Although I didn't capture pictures of this particular number talk, here are a couple pictures of a similar class number line, Class Number Line, and a similar student number line, Student Number Line

Teacher Demonstration

30 minutes

Vocabulary Posters

Although I didn't specifically review each of the following vocabulary posters, students referred to them throughout this math period. Once in a while, I'd ask questions like: What is unit fraction again? Other times, students would refer to the posters and say, "That's a mixed number!" 

 

Lesson Preparation: Google Presentations

For today's lesson, I created three Google Presentations for representing Examples of 1/5Examples of 1/6, and Examples of 1/7. I wanted to continue providing students with an avenue to share their thinking and an opportunity to collaborate and comment on each other's work.

After creating the above presentations, I shared each of them with students. Here's further information on How to Create a Google Presentation for Student Practice. Sometimes I have students copy the presentations in order to make them their own. However, for today's lesson, I wanted all students to collaborate and work together on the same presentation (all at one time).  

Prior to today's lesson, I assigned each student a slide number in order to provide each child with a workspace. For example, Student A was assigned the first blank slide, #4. Student B was assigned slide #5. Students used the same slide with each presentation. In order to communicate assigned numbers quickly, I created and shared the following Google document with students: Student Numbers.

Ultimately, the goal was for students to follow this process:

1. Represent unit fractions (such as 1/5) by choosing appropriate tools.

2. Take a picture of their representation using their computers.

3. Insert the picture on their assigned slide.

4. Use arrows and text boxes to show how many 1/5 units are equal to one whole. 

5. Collaborate with other students to make their work better. 

Goal & Introduction

Once students had opened all the shared documents, I asked them to join me on the front carpet. 

To begin, I reviewed our math GoalYesterday, you investigated how to represent the unit fractions, 1/2, 1/3, and 1/4. Today, we are going to continue working toward the same goal: I can show and explain how many unit fractions are in a whole. Only this time, we are going to move on to representing unit fractions with larger denominators, 1/5, 1/6, and 1/7. 

Just like yesterday, we will all be working on the same presentations. Each of you will continue using your assigned slide number found in the Student Numbers document. 
I referred to the pictures drawn below the Goal to review the individual tasks to complete for each unit fraction presentation:
1. Show: the unit fraction, such as 1/5, by choosing an appropriate tool, representing the unit fraction, taking a picture, and inserting the picture on your slide of the class presentation.

2. Explain: your representation by labeling the unit fraction and using an equation to show how many of this unit fraction equals a whole.

3. Make Comments: on other student work that are mathematical, thoughtful, respectful, and helpful. 

4. Respond to Comments: and clarify your thinking so that others can understand your work better. 

Math Tool Ideas

In order to review the variety of tools that students could choose from to represent fractions. I showed the Math Tool Ideas slide of the first presentation (Examples of 1/5) and pointed to some available tools (Tools on Counter). 

To engage students in Math Practice 4 (Model with mathematics), I also brought some real-world tools from home: Oatmeal BoxRootbeer 12 PackApple PackagingPizza Box, and my Coffee Creamer. I called these "challenge items" as each item contained a number of parts greater than the unit fraction denominators (5, 6, and 7). This way, students who felt comfortable could go beyond showing 1/5 of 5 tiles and, instead, represent 1/5 of the 10 packages of oatmeal in a whole box.

Choosing Math Tools

I also wanted to encourage students to represent fractions by strategically choosing appropriate tools (Math Practice 5). So I reviewed the following anchor chart, introduced during yesterday's lesson: Appropriate Tools Anchor Chart.

Just like yesterday, I selected a student to watch for and eventually celebrate a student choosing appropriate tools by giving the Outstanding Tool Selection Award. Here's a copy of the Tool Awards

Mathematical Comments

Next, I encouraged student engagement in Math Practice 3 (Construct viable arguments and critique the reasoning of others), by reviewing how to insert comments on other students' slides. I referred to the Math Talk Anchor Chart to model the expectations with commenting.

Once again, I selected a student to watch for and eventually celebrate a student making mathematical, thoughtful, respectful, and helpful comments by giving the Exceptional Collaborator Award. Here's a copy of the Exceptional Collaborator Award

In addition to commenting on others' work, I also encouraged students to go back and respond to comments on their own slides. (Prior to this lesson, I commented on almost every slide, often asking questions to push student thinking.) I wanted to make sure students took the time to respond to both my comments and student comments and to truly participate in a collaborative process. 

Modeling with Student Examples

Finally, before moving on to student practice time, I showed work examples of students meeting expectations with appropriate tool choice, labeling, equations, and commenting. Not only did I want to recognize amazing student work, but I also knew that this would inspire other students to try new tools and strategies! 

Student Practice

50 minutes

Math Partners

Students continued working with the same math partners as yesterday. Even though students were working on their own slides, they'd often check with their partner before taking a picture of their representation. Also, some students needed their partner's support to take a picture. One student would hold up the computer or fraction model while the other student took a picture.  

Different Starting Points

While many students were ready to begin representing fractions using the 1/5, 1/6, and 1/7 presentations, others were still finishing up their representations of fractions from yesterday (1/2, 1/3, and 1/4). That's what was so great about this lesson... students were able to advance when they were ready! 

Monitoring Student Understanding

Once students began working, I conferenced with every student. My goal was to support students by providing them with the opportunity to explain their thinking and by asking guiding questions. I also wanted to encourage students to construct viable arguments by using evidence to support their thinking (Math Practice 3). 

  1. How did you choose this tool?
  2. Is this tool working out for you?
  3. Have you run into any problems with this tool? 
  4. Can you show me 1/5? 
  5. How many units of 1/7 will it take to get to a whole? 
  6. How do you know? 
  7. Where is one whole? 
  8. Can you explain your thinking? 
  9. Which comment was the most helpful? Why? 

Conferences

While conferencing with this student, 1:4 Creamer, I asked: How much is one whole? (64 ounces) How much is 1/4? (16 ounces) How do you know? (Because 64 divided by 4 equals 16.) I loved watching students using their understanding of division to represent fractions!

Another student represented 1/4 with the twelve pack of root beer: 1:4 Rootbeer 12 Pack. He explained, "If there are 12 cans, then 1/4 is 3 cans because 12 divided by 4 equals 3."

One of my absolute favorite moments during today's lesson was when this student showed 1/5 on a digital timer: 1:5 Digital Timer. After today's lesson, I commented: I wonder what 4/5 of a minute would be. Eventually, this student was able to explain, "4/5 of a minute = 48 seconds because 60 - 12 = 48." I was so proud of him! 

Completed Work

Here are a few examples of student representations of 1/5:

Here are a few examples of student representations of 1/6:

 

Here are a few examples of student representations of 1/7: