# Group Work

Lynne transitions to the next part of the lesson by telling her students that they will be doing three tasks in their teams in order to get ready to play the Winding Game. She smiles and adds, “This is a very good year for many of us in this classroom.” One student asks why, but Lynne does not answer and proceeds to write the three tasks on the board as a warm-up exercise:

• 1. Check the work that we completed yesterday
• 2. Draw pictures for the three Chinese zodiac signs that your team was assigned.
• 3. Complete the equivalence chart (see Figure 5.3).

About a minute later, Simone points to a graph depicting birthday data collected by the class. The graph shows that about half of the class was born in 1990, a previous year of the horse. Thus, 2002 is a special year for those students. While Lynne continues to write, Wanda asks, “So in China are they celebrating the New Year today?”

Lynne explains that the actual celebration was the day before and then goes on to tell the class that last night a friend of hers went to a Chinese restaurant where they gave everyone a small red envelope to celebrate. Each envelope had a brand new one-dollar bill in it. The students want to leave immediately to get their red envelopes! Lynne quickly adds that the celebration was last night. A mixture of sighs and chuckles can be heard through the classroom. Her story prompts the students to share their experiences eating Chinese foods, using chopsticks, and going to Chinese restaurants. Lynne lets the conversations go on for another minute, then calls Jose to come to the front of the room to lead the class in the 12-table chant. With a rhythmic clapping, the students recite, “One times 12 equals 12, 2 times 12 equals 24, . . .”

Energized to start the three assigned tasks, the students move to their prearranged groups to begin. Groups sit at tables in the room or push desks together to make a table. Each student has a set of worksheets and access to a calculator, if needed. Students are permitted to leave their group to work out a problem on the board. There is a lot of give-and-take among the students as they exchange ideas and procedures, correct each other’s mistakes, and give each other help. Lynne and her assistant circulate around the room to monitor activities as the students work. I observed Yve- lyne, the visitor to the class, drawn into being an active participant. The group sitting nearest to the camera had been eyeing Yvelyne’s note-taking throughout the lesson. When the group work began, they were eager for her to join them, as a peer, not as an authority

Typical of the group work is Group A, consisting of three girls and two boys. They quickly finish checking yesterday’s work. For the next task, Michelle emerges as the leader, assigning the drawings of a tiger, rabbit, and a goat, one to each of three group members. Marcus, the drawer of the goat, is perplexed about how to draw his animal. Lynne intervenes at this point and tells him that any way he wants to draw the goat—either a picture or a symbol—is fine. Tymesha

FIGURE 5.3 Chinese Zodiac Equivalence Chart Equivalence Classes and Michelle work on the equivalence chart, a grid that students will discover places each of the numbers from 12 through 144 in a class from 0 to 11 depending on the remainder that results when dividing the number by 12 (see Figure 5.3). Ivan holds up his picture of the tiger to ask his group’s approval.

After a few minutes, the group tackles the equivalence chart but seems uncertain about how to proceed. Lynne asks them to look across the top of the chart (labeled “Equivalence Classes”) and to notice where the number 12 is located. She suggests that they find the pattern going across the chart to fill in the rows and to keep filling in until they reach 144. Michelle recognizes that 24 should go into the box below 12, and Lynne presses her to figure out how to fill in the numbers between 12 and 24. Tymesha asks if she can use a calculator to divide and then fill in the chart. Lynne replies, “Yes, you could, but you’ll get a decimal remainder, and then you’ll have to figure out what the remainder is as a whole number.” Michelle sees the pattern, begins to fill in her chart, and then shows Tymesha and the other team members how to get started on their charts. Making sure that everyone in this group has caught on to task 3, Lynne makes one last check of the other groups, collects each group’s zodiac drawings, and prepares the classroom for the Winding Game to follow