DIVIDED WE STAND
Grades 3 - 8

From deciding how many pieces of candy to share with friends to splitting a slice of cake evenly, children often involve themselves with the process of division without knowing it. This lesson allows students to use the mathematical skills of estimating, dividing, and graphing; and the scientific skills of gathering and recording data, observing, developing models, and interpreting data to understand better how the process of dividing can allow us to arrive at mathematical solutions quickly and logically.

It Figures, #11: Using Division

Students will be able to:

• know when to use division to solve a problem
• use the correct terminology when discussing division, including the terms quotient, divisor, and dividend
• analyze and graph collected data
• write division problems in standard equation format

For each student:

• 2 copies of bird pattern sheet
• copy of Feeding the Birds recording sheet
• copy of concert assignment/recording sheet
• graph paper
• 24 colored tiles or similar manipulative
• 20 sunflower seeds or similar manipulative
• drawing paper

For each pair of students:

• 48 colored tiles or similar manipulative
• 24 quarters, play coins or similar manipulatives

Brainstorm a list of activities in which students might use multiplication or division to solve a problem.

Create a vocabulary chart with the words students have heard used when discussing division problems, making sure to include and provide a definition of the words quotient, divisor, and dividend.

Distribute the concert seating directions sheet and review the directions for the activity with the class, highlighting for class members that (1) they are the manager of a small concert hall which is sponsoring a charity music festival, (2) the concert hall will hold only 24 chairs, (3) they are responsible for determining all of the possible seating arrangements that will allow for an equal number of chairs in each row, and (4) they must record their findings and report back to their boss with a written explanation. After students have completed the task, explain how the total number of chairs divided by the number of rows can be written in a mathematical format known as an equation. Point out the parts of the equation which are the dividend, divisor, and the quotient.

Explain to students that they will be viewing a video which shows situations where division is necessary to solve the problem, and presents strategies for solving division problems. To give students a specific responsibility while viewing, ask them to watch carefully and keep track of the number of times a situation is presented in which they think division could be used to solve the problem.

Explain to the students that you will be starting the video at the yard sale in which Cliff and Roger are trying to raise money to purchase flowers to plant at a convalescent home. They have received a donation of drinking glasses from a neighbor and are trying to decide how much to charge for the items.

Before starting the video, divide students up into working pairs and distribute 48 manipulatives and 24 quarters to each group to be used throughout the video.

START the video after the scene in which the two boys and the older woman leave the attic and the scene switches to the picture of the yard sale.

PAUSE the video after Cliff says, "... enough for 28 glasses." Ask the students how they think the boys could go about solving the problem. (If students generate a number of ideas for discussion, you may want to stop the video rather than pause.)

RESUME the video and pause when Roger says, "... we'll need 112 boxes." Ask the students if they believe this is a reasonable answer. Why or why not? What did the boys do wrong? RESUME the video and STOP video when Cliff says, "We'll have to put them into groups of four." At this point, ask the students to count out 28 manipulatives to represent the 28 glasses. Ask them to divide the manipulatives into groups of four to see how many groups can be made. When they have finished, tell them you will restart the video so they can check their answers.

RESUME the video and STOP video after Roger says, "How much would 2 cost?" and the sign which says "4 for $6.00" comes into view. Ask the students to use the 24 quarters (or representative quarters) to solve the problem. Have students share their strategies and answers with their peers.

RESUME the video and PAUSE after the narrator says, "How many loaves should he deliver to each shoe?" Ask the students to use 24 manipulatives to determine how many loaves should be delivered to each shoe.

RESUME the video and STOP video after Cliff says, "All we have to do is figure out how many groups of 6 are in 48." Explain to the students that they are now going to draw a representation of how many geraniums and begonias there should be in each flowerbed. Distribute blank drawing paper to each group and suggest that they use their manipulatives to first figure out how many of each type of flower there should be in each bed. Once they have solved the problem, they should arrange the appropriate number of flowers in each bed and color in their design. These representations can then be used to make a colorful display for the classroom.

RESUME the video and STOP video when the logo for It Figures appears on the screen. Challenge the members of the classroom to solve the new problem with the additional flowers that have been donated to the boys (18 petunias, 18 sage plants, 24 pansy plants and 42 impatiens.)

After viewing the video, explain to students they will be looking at how food supply can limit the size of a population in a habitat by using the strategies presented in the video. Distribute two copies of the bird pattern sheet to each class member and have them cut out each of the birds to use for data collection. Discuss the fact that a real bird in the wild would need many seeds and not just one to survive. Explain that for the purposes of determining how many birds the food supply could sustain, students need to complete the Feeding the Birds recording sheet. Distribute the sheets along with a bag of 20 sunflower seeds and allow time for any additional explanations or questions students might have or need. As students begin to complete the activity, move around the room to ensure they are organizing their materials and information correctly. (TIP: You may find it easier to pair up students to work on the project together, but ensure that every student completes a recording and graphing sheet.) After students have completed the activity, have them complete the graphing sheet using the data collected on the birdseed sheet.

After all students have completed the activities, discuss the results. Have students discuss what they have learned about how populations of birds might change when the population of sunflowers changes. (There would be more birds living in the habitat when there are more sunflowers. Fewer birds would live in the habitat when there are fewer sunflowers.) What events might result in the population of sunflowers changing? (drought, development of habitat land, storms) How does the graph you created help support what you learned from the activity? (It gives a visual image to show how, as the number of birds increases, the number of seeds available decreases.) Have students discuss how the strategies they learned from the video might make it easier to complete the activity a second time, using a different number of seeds and birds.

Contact a local cooperative extension agent or forest service agent and invite him/her into the classroom to discuss what he/she knows about how food supplies affect animal populations.

Invite parents of class members to come to school and explain the ways they use division in their workplaces and at home.

Art: Research the bird habitats in your area and make dioramas.

Science: Set up feeding stations near a classroom window and have students use field guides to help determine which types of birds use the stations.

If possible, set up two different feeding stations and use different types of feed in each. Students can observe and record which types of birds prefer which types of seeds, and then compare their conclusions with information found in most birding books.

Mathematics: Have students make pictures or bar graphs showing the percentages of birds observed in a set time period.

Provide students with larger numbers of chairs to continue the seat arrangement problem, and begin to focus on the use of factors and multiples to help solve the equations.

Continue to keep a chart of the times students use division throughout their school day posted in the room. Allow students to continue to add their findings throughout the unit.

Language Arts: Have students interview parents, grandparents, neighbors or others about how they have used mathematics in their lives and work places. Students can then write a report to share with their classmates and start a classroom bulletin board to display their work and show similarities and differences that they find.



RESOURCES
Chapman, Steve. How Much? How Many? A Funny Numbers Book. Chicago: Follett, 1972.

Froman, Robert. The Greatest Guessing Game. New York: Crowell, 1978.

Lauber, Patricia. The Story of Numbers. New York: Random House, 1961.

Paysan, Klaus. Birds of the World in Field and Garden. Minneapolis: Lerner Publication Co.,
1970.

Peppe, Rodney. Humphrey the Number Horse. New York: Viking Press, 1979.

Pierce, Georgia. Junior Science Book of Bird Life. Illinois: Gerard Publishing Co., 1967.

Sitormer, Mindel. How did Numbers Begin. New York: Crowell, 1976.

Scrivastava, Jane. Number Families. New York: Crowell, 1979.

Trivett, John. Building Tables on Tables. New York: Crowell, 1975.

Whitney, David. The Early Book of Multiplication. New York: F. Watts, 1969.

Master Teacher: Douglas Hoff
Mast Way Elementary School, Lee, NH

Click here to view the worksheet associated with this lesson.