Fractions On A Number Line (Mixed, Improper)

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Objective

SWBAT represent the conversion of improper fractions to mixed numbers and mixed numbers to improper fractions using models.

Big Idea

Students work in groups to challenge a difficult, complex task involving number lines, mixed numbers, and improper fractions.

Warm-up

5 minutes

Prior to this lesson, students will have learned how to convert fractions to mixed numbers and mixed numbers to improper fractions using models.

The warm- up is open ended, it is intended to allow students some choice while remaining rigorous because they have to perform on the spot. 

Journal Entry:

Think about a time in your life when you encountered improper fractions or mixed numbers. Write about this in your journal.  Then, use a model to show how this number could be represented as a fraction or a mixed number. 

Open-ended journaling may appear to be an unconventional activity for starting a lesson, however, I use this approach often in my class.  Over time, students have become more comfortable with this approach to expressing themselves and making connections between the math we are working on in school and their own lives. 

For me, the task of journaling is a low-risk, highly challenging task.  I expect the students to try something.  They can express their thinking in words or pictures or both. The level of complexity varies for students depending on the the prompt is asking.  

Frequent journaling allows the students to develop skills needed for the mathematical practice of making a viable argument and critiquing others, because the students work on defending their own thoughts with examples, pictures, and words.

Launch

10 minutes

The focus of this lesson will be on using models (fraction tiles and number lines) to represent improper fractions and mixed numbers.  To start this lesson, I draw a number line on the board and label 0, 1 and 2.  

I invite students to come up and place a mark between each of the numbers on the board, then ask the class to consider what fraction is represented by each of these marks.  

I call on students to share their thinking and explain their reasoning. (It is important that students include their reasoning when responding.)  Once a fraction is labeled, I prompt students to also label it a different way (so there will be an improper fraction and a mixed number). 

I use this number line experience to serve as a quick review of using models to convert between mixed numbers and improper fractions. Students will need this approach in the lesson today.

Guided Practice

20 minutes

For the guided practice, I provide students with a copy of the number line I will be using so they can participate from their seats.  

1 2/6

4 2/3

14/7

3 1/2

(I choose these fractions because they can all be placed on a number line with either 6 or 12 segments between whole numbers, I added in 14/7 as a challenge, because even though the 7 doesn't have 12 as a common multiple, it represents the whole number 2).

First, I ask students to brainstorm all of the "fraction skills" that we have been using through the year.  These skills serve as building blocks that are essential in solving more complex fraction problems.  Fractions are like a tower of blocks, if you remove one of the blocks, the tower can not stand up.  Visually connecting the "blocks" helps students metacognitive process.  They are able to see how each skill builds on a prior learning. 

I had prepared a second set of fractions to work on together, but the students are ready to move on.  I let them get to work sooner than I had intended. 

This is the second set that I was planning to use in case your students need a little more support.

7/5

16/10

9/3

Throughout the guided practice, I connect each of the skills used to place or locate a number on the number line back to the "building blocks" that students have been working to master.

Independent Practice

20 minutes

Students will move to their color groups. These groups are homogenous. I have them working in color groups so I can control the level of complexity of each set of fractions and mixed numbers. 

For this lesson, students have to create the number line themselves. It is important that the know how to create the strategic math tools they need to solve.

In their groups, students work on placing, then locating fractions on a number line.  

The red group has fractions with a common denominator of 16.  Within the set, one of the fractions needs to be reduced to determine this.  

The orange group has fractions with a common denominator of 12.  It includes numbers between 1 and 4.  This group is working on organization.  The challenge they face is how to create the number line.

The yellow group has a fraction set with a common denominator of 15.  This are challenged to represent on a number line too.

The gray group has problems working with the common denominator 6.  They work on mastering the models for converting between mixed numbers and improper fractions.  So I do not want the number line set up to become a distraction.

I have attached the hand outs for each of the color groups.  These hand outs outline the assignment.

I provide the prompt for our group share about five minutes before we wrap up independent work, so students have an opportunity to prepare. 

What challenges did you find?

How did you work as a group to over come them?

What would you like the class to focus on when they look at your work?

Direct students attention to this prompt and allow them time to prepare as they complete the task.  

Group Share

10 minutes

Before one student from each group shares out, I let the students in on a little secret.  All groups have been working away on the same task, but with different fraction sets.  Knowing that everyone has done something different makes the sharing more authentic and meaningful. 

Students share their thoughts about the lesson using the prompts as a guide.

What challenges did you find? How did you work as a group to over come them?

What would you like the class to focus on when they look at your work?

To wrap up, students place their completed work on the desks to make a Math Museum.  After all groups have presented, the students walk around to see how other groups completed the same task using different numbers and facing different obstacles. 

Ticket Out

5 minutes

When students have seen the rest of the groups' work, they head to their desk and reflect on the lesson.  To do this, they write something that stuck with them from the lesson.  Students post their responses on a chart paper as they pack up for lunch.