To begin the lesson today, I put a length of masking tape on the floor and ask the students to sit behind and to the side of it. I have a student volunteer join me at the front of the room and announce to the students that this "line" is a jumping line. During today's lesson they will all get a chance to see how far they could jump along the line.
I propose this question: If I want to be sure I could get to the end, and I had to make equal distance jumps, how many jumps would it take me? Many think I could do it in one jump, and because I am a kid myself, I try…and fail to the applause and laughs of my class. Then someone suggests jumping halfway first.
Now the teaching begins! The children turn and discuss how to show where "halfway" is and how to mark it. We settle on eye-balling the mid point and labeling it 1/2.
I then introduce the term INTERVAL, or equal distances on a line. Next, we discuss a way to come up with a way to mark 1/4, 1/8, and 1/3 intervals, just in case I couldn't make it!
This video is of the turn and talk partners discussing strategies to create 1/8. Notice the boy in the blue shirt is just randomly sectioning the line. When the partners are done discussing, I will be sure to remind everyone that, with fractions, all partitions must be equal.
This video demonstrates my assistant marking the hash mark tape lines and the class discussing what 3/3 and 4/4 have in common.
For our active engagement, I gave teams a length of yarn. I then asked them to use the people in the group as the hash marks and the yarn as the number line. I explained that the yarn represented a number line from 0 to 2 and asked them to mark exactly where 1 would be. After everyone found where one would be, I asked them to find 1/2. This turned out to be a trick task.
These girls were "testing and revising" as a strategy. They were having a hard time understanding that 1/2 would be before their 1 hash mark because they were looking at the string as one whole, rather than two whole numbers. This is great information for me.
A few of the groups were challenged by the task of locating 1/2, so when this group got it, I assembled the class around them and let the students explain their strategy.
As a wrap up, I have students share what they learned today with a partner and then as a class we discuss the strategies of "guess and check", "folding", and measuring for finding the locations of the fractions on the yarn.
For home practice, I give the students a large, open number line with a 0 at one endpoint, and a 2 at the other. I ask them to write 1, 1/2, 1 1/2, 3/4, 7/8 and 1 3/4 on the back of the number line.
Their assignment is to locate and label the number line with these fractions.