Modeling Division

Have students work in groups of four for this part of the lesson. Ask students to combine their collections of centimeter connecting cubes and count out 138 cubes. Have groups check the accuracy of their counts by having two or three group members verify that there are 138 cubes. Take note of the strategies students use to count out the cubes. Do they count each cube individually? Do they count by 2s, 5s, or 10s?

Present a problem situation for dividing the cubes equally among the four students.

Ask students to use the cubes to solve the problem. If a group has less than four students, ask them to divide the cubes into four piles with an equal number of cubes in each pile. As groups finish, ask each group to record answers to the following questions on a sheet of paper.

Ask students to give a detailed description of how they solved the problem. Suggest to the recorders that they draw a picture to represent the group's solution. Figure 1 shows one possible strategy for solving the problem.

Ask two or three groups to explain to the class how they solved the problem. Choose groups that represent a range of approaches. Some groups may use simple counting strategies while others may invent mental math strategies or use paper-and-pencil methods. All are worth displaying.

Have students put the counters back together in a single pile of 138. This time ask students to divide the counters into five groups but to do so using a different method from the way they solved the first problem. Have each group assign a new recorder. Again, have two or three groups share their methods with the class.