Comparing and Writing Numbers

Bubble Sort. Ask students to write a number (up to four digits) on a piece of paper. For greater variety, ask one-fourth of your class to write a one-digit number, one-fourth to write a two-digit number, one-fourth to write a three-digit number, and one-fourth to write a four-digit number. Tell students to line up randomly with their numbers. If the class is large, conduct the Bubble Sort with half the class at a time.

Explain that they will bubble sort with the head of the line as the largest number and the tail of the line as the smallest number. (The term “bubble sort” refers to the way that the larger numbers “bubble up” to the head of the line.) Have the first and second persons compare numbers. If the first person's number is larger, nothing is done. If the second person's number is larger than the first person's, they switch places. Now the second person and third person compare numbers, and order themselves appropriately. Then the third person compares with the fourth, and so on.

Since it is likely that the numbers will not be in order, start at the head of the line and repeat the two-way comparisons a second time, switching whenever necessary. Have students check to see whether they are in order by asking them to count off again. Speed up the ordering process the third time. Instead of going down the line and making one comparison at a time, have adjacent pairs compare their numbers at the same time. Remind students that they can switch only with the person immediately to the right or left. Periodically ask students to stop and check the order by counting off. Repeat the procedure until the numbers are in order from largest to smallest. Then ask students to read their numbers aloud for a final check.