Students in pre-algebra and introductory algebra courses need to master many concepts and procedures in order to be successful in the courses that follow. There are various ways to help them build meaningful

understanding of these concepts, including investigations, open-ended problems, creative projects, writing, and group problem solving. An important adjunct to these methods is the use of carefully structured and sequenced sets of practice exercises. Students construct meaning as they work through them, and retention is enhanced. Certain features are designed into Punchline puzzles to make this practice more effective.

CAREFUL EXERCISE SELECTION. Exercises are sequenced to guide students in incremental, step-by-step fashion toward understanding of the concept or procedure involved. Students practice through an appropriate range of applications for the topic, and important variations and discriminations are highlighted. Exercise sets are designed to be challenging but doable, though the amount of instruction required will vary with the experience of the students.

KNOWLEDGE OF RESULTS. Students need feedback and confirmation when they work, especially when learning new skills. Built into Punchline puzzles are various devices for giving the student immediate feedback as exercises are completed. For example, if an answer is not in the scrambled answer list or code, (s)he knows it is incorrect. The student can try again or ask for help. Teachers are able to spend more time helping students who need help and less time confirming correct

answers. Students work with greater confidence.

MOTIVATING GOALS FOR STUDENTS. What Did Scientists Conclude After Discovering Bones on the Moon? Each puzzle title is an engaging riddle. Students construct the punchline in the process of checking their answers. The humor acts as an incentive, because students are not rewarded with the punchline until they complete the exercises. While students may wonder aloud who thinks of such dumb jokes, they secretly enjoy them and look forward to solving the puzzles. In addition, discovering the punchline gives the student a sense of closure and success. Incidentally: "The cow didn't make it."

OPPORTUNITIES TO WORK WITH A PARTNER. Several puzzles in this book are designed for partners. Each student does essentially the same exercises but with different numbers. Partners must work together to get the puzzle punchline. Students are encouraged to help each other, since both use the same solution processes, but not copy each other, since the numbers are different. There is interdependence combined with individual accountability, the twin hallmarks of effective cooperative learning. Together they produce an additional source of student motivation.

Punchline Bridge to Algebra includes puzzles for most topics in today's pre-algebra and beginning algebra programs--200 puzzles in all. They are organized into 14 sections that correspond to chapters in many textbooks. Each puzzle is designed for a specific topic listed in the Table of Contents and on the puzzle itself. Many puzzles provide space for student work. And, hopefully, their self-correcting feature will lighten the burden of correcting assignments.