Many second-graders remember the challenge of balancing on two wheels when they began to ride a bicycle. Some may have gained an appreciation of the importance of balance as they watched a younger brother or sister learn to walk. Children experience balance in many other ways: riding a skateboard, participating in gymnastics, practicing ballet, or even walking on the curb on the way to school. Many children also show an interest in stacking blocks and in seeing how high they can build a tower before it topples over. All of these experiences lay the foundation for an understanding of how weight affects balance.

Balancing and Weighing, a 16-lesson unit for second-graders, provides activities that help children explore the relationship between balance and weight. They begin their investigations by exploring different ways to balance objects. They then examine different strategies for comparing objects. Later, they compare one object with a standard unit to determine its weight.

In the first five lessons, students explore balance through a number of activities, such as building structures, observing a beam balance, and creating mobiles. Students begin by describing their ideas about balance and how weight affects it. They then construct and explore a beam balance. They discover the important role that weight plays in balance and how a fulcrum can be moved to compensate for unequal or unevenly distributed weight. By the end of Lesson 4, students have been introduced to three variables that affect balance: the position of weight, the amount of weight, and the position of the fulcrum. They apply these concepts to the task of building mobiles in Lesson 5.

In Lessons 6 through 9, students begin to compare objects. To do so, they use a tool called the equal-arm balance. Unlike the beam balance, the equal-arm balance has a fixed fulcrum, allowing students to manipulate only weight. As students compare four and then six objects, they develop strategies for placing them in serial order from lightest to heaviest.

During Lesson 10, students discover that weighing is closely related to balancing; in fact,

it is simply the process of balancing an object against a certain number of standard units. Students learn that they can weigh an object by placing the object in one pail of the equal-arm balance and adding Unifix Cubesª to the other pail until the beam becomes level. In Lesson 11, students use information they recorded on a data table in Lesson 10 to make bar graphs that show the weight of each object.

In Lessons 12 through 15, the emphasis of the investigations changes. In this sequence of lessons, students apply their comparing and weighing skills to solve problems that involve four foods of varying weights, shapes, and sizes.

They begin these investigations by observing and describing the properties of four foods. They then compare and weigh cupfuls of the four foods. The students observe that even though the four empty cups were identical, they weigh different amounts when filled with the foods. In Lesson 15, students discover that equal weights of the four foods occupy different amounts of space.

Lesson 16, the culminating activity, challenges students to use the equal-arm balance to find out which of five containers holds a certain number of

of marbles. Solving this problem requires students to apply the various comparing and weighing strategies they have used throughout the unit and provides an embedded assessment of their progress.

The activities in this unit build on students' previous experiences with balance and weight and their intuitive understanding of this relationship. Through hands-on investigations and class discussions, students will not only find answers to many of their questions but also come up with new questions about balancing and weighing.

Following Lesson 16 is a post-unit assessment that is matched to the pre-unit assessment in Lesson 1. Additional assessments provide further questions and challenges for evaluating student progress.