There are two kinds of activities here: in the first, students use manipulatives to demonstrate for themselves some concepts and operations with fractions, and in the second, students work in groups at the board. The ideas in one set practice and reinforce the ideas in the other set; there is a lot of practice and review involved in each, and a measured but quite quick movement towards more complex mathematical ideas. I have used both these sets of activities successfully for many years, but would refer the reader to the discussions of student resistance and of group work in Chapters 2 and 5 to ensure a secure underpinning for these activities.
The activities on the following pages require students to use math tools (manipulatives) to demonstrate their understanding of fractions and to show their answers are correct. Some students will find the answers to the questions first by using math notation and algorithms they know; when they go to demonstrate that their answer is correct, they may find that, indeed, it is not correct, and may then be in a position to rethink their algorithm, or to come to a clearer understanding of what the abstraction of the algorithm conceals. The manipulatives give them a chance to correct their mistake before it gets marked wrong by the instructor. Correcting their own errors and showing they are right increases confidence and understanding.
Other students, who do not know the algorithms, or who have less faith in their memory of them, will go directly to finding the answers simply by manipulatives. As they learn the algorithms from their texts or in class, they will begin to combine the two methods, with the learning from the experience with manipulatives helping them remember and understand the algorithms.
The checkmark symbol 
next to a question reminds the student that the answer must be demonstrated with the tools. As students work on the activities, the instructor can circulate and sign off demonstrations as students get them ready. Encourage students to compare answers with one another, and, in the case of a disagreement, use the tools to figure out who is right.
Wherever this symbol appears, students should prove their answer is correct by setting up a demonstration with the math tools. Your job is to look at their demonstrations, ask questions to clarify or extend their understanding, and sign or initial on the line when you are satisfied. Encourage students to line up several demonstrations as they wait for you to circulate to their desks, rather than setting up one and waiting. Students can work individually or in pairs.