To begin this lesson, I review counting fractions on a number line. Using a large number line on the whiteboard, I mark zero and one at the ends of the number line, and then I mark off lines for the fractions of eighths. Because my students have been practicing this, I mark the third tick mark with 3/8, and ask the students to figure out the other fractions that should be on the number line.
Some of the students choose to recreate the number line on their own whiteboard, and other students work from the large number line. Because the students have different needs, they use different means to find the missing fractions. At this early stage of developing a concept of fraction units, students show diverse entry points with ordering fractions on a number line and understanding denominators.
Students will be using precut pieces of white paper cut into six inch squares. The size in not critical to the lesson. It does allow for students to fold the paper into the different unit fractions easily.
The students have been working fraction strips as models of the different fraction units. In this activity the students see how the units can change shape based on the whole changes. I begin with showing the students folding the piece of paper in half precisely to create the unit fraction of 1/2. I also demonstrate for the students how to fold the square of paper into thirds. Because the students are not working with measurement tools, I demonstrate for the students how to overlap each side of the square to create even thirds. I chose these two units to demonstrate because all other fractions can be created from these two samples.
There is an emphasis on precision in this lesson (Mathematical Practice 6, Attend to Precision). This precision is in the creation of the units, as well as precision in the choice/use of appropriate vocabulary. To assist students if needed, you can provide lines or fold marks for the fractions to also meet this math practice. The students also are addressing MP5 - Use appropriate tools strategically.
Groups of three or four students work together to create squares folded into halves, thirds, fourths, sixths, and eighths. Using the same size piece of paper provides students with a concrete, comparative, model which helps to conceptualize how unit fractions size changes while the size and shape of the whole remains the same.
While students are creating the models, I am checking for precision in their folding. As each model is achieved, the unit fractions are marked and written in each section with 1/6 or 1/8 or 1/4. The students then glue their squares onto a piece of 12 x 18 construction paper to create a poster for their team.
To close this lesson, I have the students share their strategies, challenges, and successes for folding to show the different unit fractions. I have a whole class discussion for this closure.
I ask the students to compare the number of folds they made to create the fractions. "How does the number of folds made for fourths, thirds, and sixths compare to each other?"
Students respond to this question in their journals, and I'm looking for them to realize the number of folds for fourths and thirds requires two folds, and sixths requires three folds.