Just Graph It!

Summary

Students will participate in a variety of graphing centers to learn how to collect and organize data.

Materials

Center #1 Bug Hunt Graphs

• Bowl full of sand.
• Plastic bugs
• Small garden shovels
• Bug Graph (pdf)
• Colored foam
• Peel off magnets
• Markers
• Wiggly eyes
• Bug wings
• Pipe cleaners
• Magnetic dry-erase board
• Colored pencils or crayons

Center # 2 "Zoorific" Graph 1

• Zoo Picture Graph Worksheet 1 (pdf)
• Zoo Picture Graph Worksheet 2 (pdf)
• Zoo Picture Graph Worksheet 3 (pdf)
• Zoo Picture Graph Worksheet 4 (pdf)
• Zoo Picture Graph Worksheet 5 (pdf)
• Zoo Picture Graph Worksheet 6 (pdf)
• Animal pictures for zoo picture graph (pdf)
• Scissors
• Glue sticks
• Blank Zoo Picture Graph Worksheet (pdf)

Center #3: Sticker Graph

• Sticker Graph (pdf)
• Sheets of six different kinds of stickers
• A wooden number cube with the six different stickers (each person in the center will need a number cube)
• Pencil

Center #4: Create Your Own Problem By Graphing The Room

• Create Your Own Picture (pdf)
• Pencils
• Model sentences (pdf)

Center #5: Manipulative Graphing

• Yogurt cups
• Collections of manipulatives to graph
• Large laminated four-column blank graph work mat/Manipulative graph
• 8 1/2 x 11 four-column blank graph identical to the large graph/ Manipulative Graph (pdf)
• Gallon zip lock bags
• Pencils

Center #6: Graphing With Bears

• Gummy Bear Sorting sheet (pdf)
• Colored pencils or crayons
• Sandwich bag with 15 gummy bears
• Gummy Bear Graph (pdf)
• Bear stamps
• Colored stamp pads
• Bear Patterns to trace (pdf)
• Colored construction paper
• Scissors
• Class bar graph

Additional Resources

Books

• Brain Boosters, by Sidney Martin and Dana McMillan; ISBN 0-912107-43-X
• Playing Math Game, by Anne Lewis and Francine Neugebauer; ISBN 1-56785-019-7
• Big Book of Absolutely Everything, Edited by Rosemary Alexander; Instructors best
• Science & Math Enrichment, by Elizabeth Stull and Carol Price; ISBN 0-87628-746-1
• Transition Magician, by Nola Larson, Mary Henthorne, and Barbara Plum; ISBN 0-934140-81-2
• Mathematics & Cooperative Learning Lessons for Little Ones, by Lorna Curran in consultation with Dr. Spencer Kagan; ISBN 1-879097-19-2
• The New Kindergarten, by Jean Marzollo; ISBN 0-06-091512-9
• Mathematics Their Way, by Mary Baratta-Lorton; ISBN 020186150X
• Hannah's Collections, by Marthe Jacelyn, ISBN 0-88776-690-0
• Charts and Graphs, by Wend Clemson and David Clemson, ISBN 1-58728-342-5

Background for Teachers

Graphing is a problem-solving tool used to help young children see relationships.

Graphs are not only valuable instruments for communicating data quickly and simply, but they can be tools for stimulating discussion, and aid in promoting mathematical thinking. Graphing activities for kindergarten students should include more than fixed displays of information. A hands-on, relevant lesson can be a successful way of teaching concepts which students are more likely to retain.

Learning should be supported with manipulatives. Manipulative materials help make abstract mathematical ideas concrete. They give children the chance to grab onto mathematical ideas, turn them around, and view them in different ways. Manipulative materials can serve in several ways to introduce concepts, to pose problems and to use as tools to figure out solutions. When children have the opportunity to work in centers with manipulatives they are making math connections by discovering learning on their own.

Students should have a basic knowledge of the following before they start working independently in graphing centers.

• Counting up to ten objects
• Identifying the numerals 0 through 10
• Identifying colors
• Identifying some bars as taller, longer, or shorter than others
• Comparing two sets of objects to determine which has more (or fewer) objects or if both sets have the same number of objects.

Real graphs are the most important of these graphing experiences. They form the foundation of all graphing activities. In this kind of graph children compare groups of real objects such as M&M's or skittles.

Picture graphs use pictures or models to stand for real things. These graphs are more abstract than real graphs because a picture, even if it is drawn by the child, only represents reality. An image of an M&M is not the M&M itself.

Symbolic graphs use symbols to stand for real things. This is the most abstract level of graphing, because the symbols must be translated back into reality to have meaning. A colored square or an "X" on a piece of graph paper can only stand, abstractly, for a real M&M which the child has.

Intended Learning Outcomes

1. Demonstrate a positive learning attitude
5. Understand and use basic concepts and skills
6. Communicate clearly in oral, artistic, written, and nonverbal form

Instructional Procedures

Invitation to Learn

Teacher will do a graphing activity called "Sit and Be Counted." The students will gather data about their birthdays for a bar graph, and then form the graph by sitting in rows. A clear, large floor space will be needed. Tape a line about 24 feet long onto the floor (In good weather, this activity could be done outside, making the line with chalk). On a piece of construction paper, label the line MONTHS OF THE YEAR, and place construction paper labels for the 12 months at equal intervals along the line.

The students will sit cross-legged on the floor behind the month in which they were born. The students will be asked to take places on the floor behind the card that indicates the month in which they were born. Make sure the children with the same birth month sit one behind the other in a row. Call children up month by month. Have the children look around at one another and describe what they see. Explain to them that together they are a people graph that shows data on class birthdays.

Questions that could be asked:

• Which month has the most birthdays?
• How does our people graph show this?
• How can you find two months with the same number of birthdays in them?
• What would you look for?
• How can you recognize a month where there are no birthdays?
• How many children were born in months that start with J? With M?

You could also try other people graphs, by gathering birthday data for questions like these:

• In which season does your birthday fall?
• How many birthdays fall on odd-numbered days?
• On even-numbered days?
• Were you born in this community?
• Were you born in another community?
• Were you born in another state?
• Were you born in another country?
• How can we shoe this information on paper?

A photograph could be taken of the people graph and it could be displayed on a bulletin board with other bar graphs.

Center #1 Bug Hunt Graphs

1. Have a large Tupperware bowl full of sand. There will be three kinds of bugs buried in the bowl. There will be striped bugs, spotted bugs, and bugs with wings.
2. Bright colored shovels with bug handles will be provided in the center.
3. The students will dig in the sand searching for 10 bugs each. They will put their bugs on the bug graph provided.
4. As they take the bug off their graph they will color in the graph square, making a symbolic graph.
5. The bugs will then be re-buried in the sand
6. They will ask each other questions concerning their graphs.
7. Foam art pieces will be provided for the students to design their own bug. They will each make a bug with stripes, or spots, or wings. Eyes, markers, material for wings, antennas, etc. will be available as they design their bug.
8. Magnets will be provided for the students to put on the back of their bug. They will then take their bug and graph it on the large metal class graph.

Center # 2 "Zoorific" Graph

1. Each student in the center will take a different colored picture with zoo animals. (Each colored zoo picture has a different number of animals so each students graph will be different.)
2. The students will count the animals and then graph the data learned on a graph that has the pictures of the animals. They will graph this information by coloring and cutting out the number of animals needed.
3. They will then take the cutout animals and glue them on the "Zoorific Graph" and record the correct number under the appropriate graph column.
4. The students will compare their graph with the other graphs in their center by discussing what animal has the most, the least or the same.
5. They will then draw their own zoo picture and graph their animals on the graph below their own picture.
6. When the class gathers back together, the students in this center will share their personal graphs with the class.

Center #3: Sticker Graph

1. The students will each take a sticker graph and sheets with six different stickers.
2. They will each take a wooden number cube that has one of the different kinds of stickers on each side of the number cube.
3. The students will then roll the number cube. They will peel off the sticker that is shown on the number cube and put it on the sticker graph.
4. When one roll of stickers is full they will stop.
5. At the bottom of each column they will write the number of stickers.
6. The students will then do it a second time with a different graph. They will then compare their two different graphs. They can ask themselves questions like: Which graph has the most stars? Which graph has the most circles? Which shapes have the same amount on each graph?

Center #4: Create Your Own Problem By Graphing The Room

1. The students will take a walk around the room and decide upon three different things they would like to graph. As they walk around the room they will think: What will I count? Where will I look? Examples are doors, windows, cupboards, tables, chairs, computers, etc.
2. Students will then come back to the table and draw their three items they have chosen at the bottom of their Create Your Own Problem graph.
3. Students will then walk around the room with their graph and record the data of their findings. They will record the data, making a symbolic graph, by coloring in a graph section for each item they found of their three things they chose to graph.
4. Students could do it a second time choosing three different items to graph.
5. The students then write some sentences about their graph. We practice making statements orally about our daily graphs each morning and afternoon. These are the model sentences that are on a chart in the classroom: There are more ____ than ____. There are ____fewer ____ than ____. There are an equal number of ____ and ____ etc.
6. You might want a student teacher, aid, or a parent to be available in this center to help them with their sentences for those that are not ready to do this kind of activity on their own. However, many can do a lot of sound spelling after the first of the year. Therefore, encourage them to write as much as they can.

Center #5: Manipulative Graphing

1. The center has six or seven yogurt cups holding small collections of manipulatives to graph -- plastic animals, pattern blocks, buttons, plastic fruit, colored pasta, etc. Each student will choose a yogurt cup.
2. The students will take one of the large four column blank graphs. (I made six of these so that six students can work at once). On the top is a line for the question or title. On the bottom of each column are lines to write the choices. Numbers go up the left side. I laminated these so students can use a dry-erase marker to label the graph.
3. The students take the manipulative in their yogurt cup and place the items on the real graph.
4. To be used with this center I made an identical graph on 8 1/2 x 11 paper and ran off lots of these, storing them in a ziploc bag. The students each take one of these graphs and make a simple bar graph by coloring in one section to represent each item on the real graph. They write their title and label the choices on this graph.

Center #6: Graphing With Bears

1. The students will take a Gummy Bear Sorting Worksheet. Each section will be labeled a different color. They will color each bear section the color indicated.
2. The students will then take a plastic bag with gummy bears. (Make sure to give your expectations of only touching and eating the gummy bears when given instructions to do so.
3. The students will sort the bears by placing them on the correct color of the sheet.
4. The students will then take a Gummy Bear Graph worksheet. They will color the bears in each column the colors they used on their "Gummy Bear Sorting" worksheet.
5. They will use the information they found out on their sorting worksheet and graph that data on the Gummy Bear Graph worksheet. They will use the bear stamps to stamp the correct number of each color of gummy bears. Then allow the students to eat the gummy bears.
6. The student will then take the same color of construction paper that they choose for their gummy bear. They will trace a bear pattern on their colored construction paper and cut it out.
7. They will then take their paper bear and tape it on the laminated class bar graph.

Extensions

• Teachers can add thematic manipulatives to the graphing centers to correlate with their current theme. For example, you could use colored candy hearts for the graph instead of gummy bears, dig up dinosaur bones for the dinosaur unit instead of bugs, have a winter nature picture instead of the zoo animal picture, or you could take a walk outside to choose things to graph instead of the walk in the room.
• For the more advanced learner, he/she could use journals to record all their data information.
• You could have a graphing magnet center. You could have yogurt cups of small object magnets and on a small metal sheet they could graph their three different kinds of magnets.
• For the more advanced students you might give them a graphing game called, "Graphing Logically." Two players chart their moves on a grid to determine the winner. A game board will be drawn on one side of a poster board, using markers and a ruler. Two students play this game at a time. To start the game, each player will need a bag of pennies (about 15 pennies in each bag). The players will determine who will use heads of the penny and who will use the tail of the penny. The students will need to know the rows and the columns on a graph. They will each take turns rolling two number cubes. When they roll the number cube they place a penny on the correct dot on the graph to show the outcome. For example: 6 and 3 could be row 3 and column 6 or row 6 and column 3. The first player to cover all dots in any vertical, horizontal, or diagonal row wins the game. The students must use logic to determine which of two possible moves will best increase their chances of completing a row.

Family Connections

Prepare a Take-Home Backpack, which has a graph template in it. The students will find three things to graph at home. They will then label the graph with a title and choices and color in their information. They will then bring it back and share with the class.

Assessment Plan

• Teacher observation is the best assessment for these graphing activities. Walk around with a clipboard and post-it notes to make quick notes of which students need special help, or use the class notes recording form attached in the Appendix. The following questions can be used to assess student learning.
  1. Which column has the least?
  2. Which column has the most?
  3. Are there more _____ or more_____?
  4. Are there less ______ or less ______?
  5. How many _______ are there?
  6. How many more ________are there than ________?
  7. How many less _________ are there than _______?
  8. How many ___________ are there altogether?
  9. Are any columns the same?
  10. Which row is the longest or tallest?
  11. Which row is the shortest?
  12. Are any rows the same?
• Circulate among the students to ensure they are graphing their own data showing their individual information. Observe their understanding of graphing as they work in each of the graphing centers.
• Observe the students and listen to the interaction and conversations as they make decisions, organize manipulative and solve problems during the graphing centers.
• The written graph and sentences are also good assessment tools, as you see the growth of their oral language.

Bibliography

Research Basis

Friel, S. N., Curfcio, F.R., & Bright, G. W. (2001). Understanding Graphs. Making sense of graphs: critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124-158. Retrieved November 26, 2006.

The Authors have done an extensive search of the research on understanding graphs. Graph comprehension involves "the abilities of graph readers to derive meaning from graphs created by others and themselves." Graph sense "develops gradually as the result of one's creating graphs and using already designed graphs in a variety of problem contests that require making sense of data."

"Number sense and symbol sense can be considered as representing certain ways of thinking rather than as bodies of knowledge that can be transmitted to others. A similar approach seems to be a profitable way to think about graph sense. Graph sense develops gradually as a result of one's creating graphs and using already designed graphs in a variety of problem contexts that require making sense of data."

Lilian, K. (1987), Another look at what young children should be learning? Eric Digest. Retrieved December 29, 2006.

The data on children's learning suggest that preschool and kindergarten experiences require an intellectually oriented approach in which children interact in small groups as they work together on projects that help them make increasing sense of their own experience.