Each of the three days of this lesson, my students practice counting fractions and finding missing fractions on a number line. This process is repeated using different unit fractions and now extends beyond the number one to include mixed numbers such as 1 1/2, 2 1/4. These are also written in improper fraction form such as 3/2, 7/4, 8/3.
Each day the practice of counting fractions on the number line is also connected to some aspect of my students' "real world". I find that it is easy for students to make these connections to foods. Many of the students in my class play sports as well, so this is also a topic I use to connect to the fractions including half games or half of a field/court.
I use the large number line I have on my whiteboard for counting fractions each day. This large display also allows students to make visual comparisons to how the amount between zero and one as the whole amount changes.
Students order fractions on a number line using fraction cards. Prior to this lesson the students have been ordering fractions with the use of fraction strips and models. This lesson requires them to order fractions based on denominators.
The mini lesson each day is based on identifying the smallest unit fraction to determine which fraction is "first" on the number line. I include halves in all three days of the lessons because it is an important benchmark for students to use when comparing fractions, and it is a quantity most students readily understand and can identify. I want them to be continuously using this as a benchmark when they work with fractions.
Day 1 - halves, fourths, eighths
Day 2 - halves, thirds, sixths
Day 3 - halves, thirds, fourths, sixths, eighths
In partners, or in small groups of no more than four, students plan how to order the fraction cards from zero to one. (A tip - have the student groups highlight the edges of their cards, using different colors in case their cards get mixed with another group as they work on this task.) Students glue the fractions onto strips of paper cut from construction paper, butcher paper, or adding machine tape.
During this task I remind students to use the denominator to order the fractions. I want the students to start with a benchmark fraction such as 1/2, or identify the smallest unit fraction such as 1/8.
At the beginning of this task, it is important students try to reason about the size of the fractions before they use a manipulative or model. The attempt to order the fractions before using these supports is a productive struggle, that I believe helps my students to realize what they understand, and what that do not yet know. The manipulatives are important as a fall back if a student is stuck.
By the third day, the students' confidence builds and improves and requires less supports. Their rich discussions about math show evidence of their understanding of the abstract quantities represented by fractions.
To close the lesson each day, the students record in their journals the strategy they used for ordering the fractions. I ask them to include which fraction they placed first and why they chose that fraction. I also ask them to identify where they struggle and needed to use their fraction strips or a manipulative to help them complete the task. The students also record in their journal the number line and the order of their fractions they created with their partners.