Large Number Lines

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Objective

SWBAT order fractions on a number line, create models of unit fractions, and identify equivalent fractions.

Big Idea

Using large number lines provides an opportunity to use a large strip of paper to represent the whole amount and conceptualize how fractional amounts changed based on the size of the whole amount.

Warm-Up

5 minutes

Our class has been focusing on fractions for the last few weeks, and the students being most days with practicing counting fractions on a number line.  Today, I mark zero and one on opposite ends of the blank classroom number line.  I then mark 12 tick marks on the number line but without any fractions.  

I ask the students, "Where do we begin counting today?"  Previously when we began this activity, I would have some of the fractions marked on the number line such as 1/4, or 3/8.  This information provided the students with the denominator (or close equivalent).  Quickly one of the students realizes we were going to be putting all the fractions, no matter what the denominator, for halves, thirds, fourths, sixths, and eighths on the number line. 

Ordering fractions has been practiced in different formats during our fraction unit, and this lesson provides the students with using a different representation of one using a long strip of butcher paper about 6 feet in length and approximately 12 inches wide. 

Group Practice

30 minutes

Ordering fractions has been practiced in different formats during our fraction unit. This lesson provides the students with using a different representation of a number line using a long strip of butcher paper, about 6 feet in length and approximately 12 inches wide. Students will also need fraction strips for this lesson (made from construction paper cut to 2" by 12"). The students work collaboratively in teams of four students. Because workspace is critical to this activity, the desks are grouped into 4s as well.

This number line is not to scale, because the lesson focuses on ordering fractions and finding equivalencies for halves, thirds, fourths, sixths, and eighths. Because of the large size of the paper, there are some material management aspects that challenge the students.  I left my students to problem solve the problem - you might want to consider the frustration level of your class, or individual students. My students determine the best way to manage the paper is to begin on the left end of the paper. The length is folded into halves so there are approximately 16 different sections. The students begin with unfolding the length of the paper and allowing it to drape over the sides of their desks onto the floor.  The students can now slide the paper to the next section without opening and unfolding to find the next section. 

First, I have them write a large zero on the first section.  Using their fractions strips, I ask the students to determine the smallest fraction they have by looking at their fraction strips. I check for understanding, since this is a visual task that doesn't necessarily require understanding. On the number line, which number would the smallest fraction be closest to? (zero).  After they determine 1/8 is the smallest fraction, we write on the fraction strip the fraction, draw a model, and a sentence. We do this to describe each fraction. 

The students slide their number strip to the next section, and I ask, "Which fraction would be next on the number line?" The students use their fraction strips and compare to discover that 1/6 would be next. They record the fraction, draw a model, and and create a sentence to describe the fraction.  This process continues with the fraction 1/4.  Because the Common Core standard requires students to explain equivalent fractions, I ask the students, "Are there any fractions that are the same as 1/4?" to cue them to look for equivalent fractions.

This process continues for fractions of 1/3 and 1/2 including looking for equivalent fractions including questions to check for equivalent fractions with sixths, eighths, and fourths.  Each section of the number line includes a model and a sentence about the fraction. The students use their fraction strip models to compare.  This same activity could be completed with Cuiseinaire Rods if available. 

Try It Yourself

20 minutes

Working with the student sitting next to them, the class continues to complete the number line from 1/2 to 1 using the fraction strips. The students benefit from having reminders to build fraction models using fraction strips first with eighths, sixths, fourths, and thirds, in order, because they are sequencing the fractions from smallest to largest.  

Students in my classroom record the order of the fractions first on a number line drawn on a whiteboard, before putting it on the large number line so they have opportunity for feedback/revision by comparing with a partner, and so I could also check their understanding. 

Wrap Up

5 minutes

To wrap up this lesson, students record a number line in their math journal using colors to match their fraction strips.  For example, the thirds are recorded in blue and fourths in orange. Using color allows the students to identify the equivalent fractions, and which do not have any equivalent fractions.