• The idea that a fraction represents a part of a whole.
• The concept that all of the pieces within a fraction are equal. Some fractions are greater than other fractions: 2/3 is greater than 1/3. Some students may still struggle with deciding which fraction represents the greater amount, which is the focus of this lesson.

• Some may be frustrated if they do not understand how to use a certain manipulative to figure out the questions provided. For this reason, at least two manipulatives should be provided for each center in the hopes of minimizing this response.
• If students are working in groups, some may sit back while others dominate the activity. Learning may still be taking place, but if this becomes a concern, it may be wise if the teacher directs students to the centers so that partners may be matched intentionally.
• Students will likely become frustrated with the process of explaining why they are selecting their fractions, especially if they have not been asked to try this before. However, it is important that they develop this ability, and only practice will help them understand.
• Some students may want to visually represent their process. While it is strongly suggested that students attempt to write out their solutions, allowing students to tell a visual story is an adaptation that may need to be considered. The goal is for the teacher to form a better understanding of their thought process.
• While comparing numbers such as 3/8 and 5/8, students may choose the latter because “5 is bigger than 3.” This is the correct answer, but the reasoning demonstrates a lack of mathematical understanding. Students who provide this response may not understand how to compare fractions where the denominators are not identical.
• While comparing numbers such as 3/4 and 3/7, students may decide that the latter number is the greater fraction, because 7 is larger than 4. Watch for this. Students may try to cross-multiply and divide in order to find the largest fraction; however, this lesson is an attempt to move students away from this process.

• Share their strategies with their small groups and with the class as to how to solve the problem of ordering fractions.
• Work cooperatively in their small group settings, by assisting their partners when possible and by sharing their manipulatives.
• Reflect on the process by writing in their math journal.

• The worksheet provided is created for the purpose of assessment. By encouraging students to describe and record their thought processes regarding fraction comparisons, the teacher will gain valuable insight into their answers, and form a better understanding as to what to work on. This may be especially valuable for “easier” comparisons that share the same denominator, as students will often come to the correct answer without considering the implications of the numbers involved.
• If students are practicing with a math journal, they may be able to write up some of their memories and learnings from this lesson. The worksheet provided contains the following prompt for the journal:

1. Was it difficult to explain your decision about which fraction is greater? Do you think that it is important to be able to write out why you chose your answers? Why or why not?

• How are you using that manipulative?
• I wonder what would happen if... [Try to suggest, without sounding like you are “correcting” the student, alternative ways of exploring with their objects.]