Fraction Counting

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Objective

SWBAT count using fraction intervals using a number line.

Big Idea

Students develop their understanding of fractions through counting unit fractions on a number line.

Warm-Up

5 minutes

Because students will be counting fractions on a number line, I review counting on a number line using counting by ones, twos, fives, and tens. I ask the students to identify the number line in the classroom, and create their own number lines using a whiteboard.  The students write number lines on their individual whiteboards, and then they write two in their math journals.  I also have students create number lines, beginning at non-benchmark numbers.  For example, one student began a number line at 42, and another began a number line at 409 because it is our room number. 

I then ask the students to write in their journals why we use number lines in math.  Their answers varied from counting, to writing numbers in order, and adding numbers. 

The Fraction Number Line

20 minutes

Because the number line is such an important part of standards in the Common Core, I created a number line using blue painters tape on my whiteboard to use throughout the school year.  This low tack tape does not damage the whiteboard and removes easily.  I leave mine up all year, and its use changes as each lesson and unit changes.  

In creating a fraction number line, I marked zero on the far left end of the number line, and at the far right side of the number line I marked one.  I then compared the traditional number line on the wall of the classroom.  The wall number line is displayed from -10 to 100, and the numbers are very close together.  The fraction number line that is on my whiteboard is approximately 8 feet wide in order for students to gain an understanding that they will be learning about the numbers that exist between zero and one. 

I begin with counting fourths, and I mark them on the number line.  We begin counting chorally at 0 and count 1/4, 2/4, 3/4, 4/4.  I write these one the number line and I put 4/4 under the number 1.  I then have the students practice counting on their own as I touch each fraction.  Next, I have the students count backwards from 4/4 to zero. 

I erase the numbers, and start over with eighths, and repeat the process of counting together, students counting, and then students counting backwards.  

Next, I have the students return to their desks to write in their journals.  They are to create number lines in their journal of equal size and write number lines for fourths and eighths. The eighths number line is still displayed on the whiteboard, and the students use this one as a reference.  Their challenge is to recreate the one with fourths.  I remind them the tape number line on the whiteboard has not changed size and each number line should be the same length with zero and one in the same spot on each number line.  I assist students with this as needed, and I ask them to compare the number lines they have in their journal to see if they see any fractions that are at the same place on the number line. 

I call the students back to the carpet and repeat for halves, thirds, and sixths.  The students then create two more number lines in their journals.  I leave the number line for sixths displayed for them to reference for their journal.  Students work together in groups to create the number lines in their journals.  Students also have the option of using their fraction strips to complete their number lines.

 

Wrap Up

5 minutes

I create a traditional number line on the board, beginning with zero and ending with ten.  I write a tick mark on the number line halfway between zero and one, and I ask the students to use their whiteboard to write a fraction that represents the fraction that is shown by that tick mark.  

There is not a specific answer I am looking for except that it is one of the fractions they just recorded on their number line.  As they are sitting on the carpet, it may affect their perception of where the tick mark is located, and each student may think differently about the fraction amount.  This is just a quick observational assessment about their understanding of fractions on a number line.