Data Management and Analysis:
Elementary Level Ideas

Lillian Forsythe,
Grade One Teacher

   Data Management appears to me to be one of the easiest and most accessible strands of mathematics to link to all other subject areas. Children from the earliest years are able to draw pictures, use manipulatives and magazine cutouts, or just physically represent data they wish to present in visual form.
    Data Management activities need not always be in the form of a graph, although there are many ways to show information in that form [object graphs, pictographs, line graphs, bar graphs, circle graphs to name a few]. At different times, information might be shown through a time line, a grid, list, tally, a table where predictions, results or both may be recorded, or even through a diagram which represents information to be portrayed.
    Just think of the possibilities! This year with grade ones, we have represented information about self and families (Social Studies & Language Arts), about teeth (Health), about geometric shapes, bears, pumpkins, snow and weather (Science and Mathematics), about physical attributes or skills (Physical Education and Arts Education).
Here are just a few of the data management undertakings we have produced, analyzed and interpreted, and discussed as a class:

   Me: We made paper plate heads of ourselves, measured our heights and attached a strip of paper of the appropriate length. These we mounted on the wall in the hallway as we lined up our class from "Small to Tall."
    We also made pictographs to represent our hair and eye color. Children drew their heads only, on small squares of paper which were then easily glued to pre-made and laminated graphs, one for eye color and another for hair color. It was simple, visual and best of all reusable next year if glue sticks or rubber cement are used to attach the pictures.
Families: We produced a big book with each of our families lined up from small to tall and shown on a page in the book. Children drew pictures of their families on large sheets of paper (many included pets) which when bound into a book became a popular shared reading addition for the class.
Pumpkins: Prior to Halloween we predicted, measured, weighed and finally carved our jack- o-lanterns. We even counted all the seeds. We presented our information about the pumpkins in tables and graphs so that we were able to decide whether the largest pumpkin always produced the most seeds! The use of tallying can be introduced as a way of recording information prior to creating a graph.
Teeth: We gathered information as a homework project on the kind of toothpaste, number of visits to the dentist, lost teeth, cavities, brushings per day, flossing, etc. All information was placed on individual small 4 cm X 4 cm tooth outlines so that it could be displayed on the appropriate graphs as the information arrived back at school (again these are laminated sheets used again and again). We interpreted this information each day as the graphs changed. This brought in parent participation as they helped students gather the required information.
Grids: Using a large floor grid we named the rows and columns using coordinates (letters along the base and numbers up the side) such as A4, C5, G3, etc. The children then stood on appropriate named squares as we became familiar with this way of representing information. We later worked with map symbols on 1-inch squared paper as we practised putting our symbols at the correct coordinates. It was great fun! Children even completed a homework project with parents giving a coordinate for Christmas symbols to be put on a grid.
Timelines: As a way of helping children understand a sense of time, we each made our own time line on long strips of paper (mine was much longer than theirs). From birth to age six, children either used real pictures of themselves or pictures cut from magazines to represent important accomplishments along the line. These were often a new baby picture, age one birthday, playschool, new bike, kindergarten, and present time. Parents were most helpful in getting these done. We then compared and discussed differences. Interestingly some were done horizontally, while others were vertical timelines. Each timeline for the students was cut lengthwise from chart paper so it was about a metre long and 20 cm wide.
Favorites: These are fun whether we are choosing favorite colors and building a cube-a-link graph, drawing cones and building an ice-cream graph, or doing arm spans and handspans and making comparisons! We often ask about personal choices whether we're doing health, physical education, language arts, social studies, science or mathematics. It is quick and easy to tally, make a quick picture, or simply line up by choice and so represent the data.
Snow and Weather: Weather is presently being represented using a weather calendar, a line graph to record the high and low temperature, and a table where we recorded information about our collected samples of snow (we predicted and then measured temperatures, cleanliness, amount of water and melt time of four different snow samples). We had last year's temperature chart and so are able to compare this year's January weather with that of 1996 on the same line graph by using different colors. Even at grade one, children are able to read and compare information from charts and graphs.
Chance: With the number of lotteries, bingos, etc. evident in our society, children need exposure to what "chance" is about. Bagging different numbers of colored bears or cube-a- links (1 orange, 2 yellow, 3 blue, 4 red, etc.) for children to predict, draw and graphically represent their results gives them some understanding of why you may get more red than orange draws. Draws continue with each player drawing and then returning the object to the bag before the next player draws. Play continues until one of the colors on the graph has all spaces filled. The use of a coin to graphically represent heads and tails outcomes after 15 flips also works well for children to experience data representation and chance activities.
Other: We have made many graphs which illustrate class favorites-foods, colors, and activities just by using cube-a-links to represent the data. When linked together we can visually see and compare our favorites.
    Another way to represent data is by using string to show armspans, distances we can jump, etc. These can then be taped to a chart with the child's name beside the string. We are able to then compare our representations by their length with or without using standard measurement.

Graphing Smarties
Tonja (October 22, 1996)

Circle Graph
Which color was most? _____
Which color was least? _____

  Near Halloween or Valentine's Day the use of small candies lends itself not only to early division concepts but to graphing. The possibilities in a box of smarties are endless. How many were in each box? What colors were represented? How many of each? Circle graphs can be introduced by having students draw a circle, arrange their smarties evenly around the outside edge by color and then draw a line in from the circumference to the centre each time the color changes. Each part of the graph can then be colored the correct color. Simple as pie! Expressions on small hearts or colors of these candies can be graphed on grid paper where children construct their own bar graphs or work together as a class on a large wall graph.

   Children's work can be done individually, but often large class graphs are effective and encourage children to share and work cooperatively. Many of our most interesting graphs are class projects which require input from each student and help enhance participant self-esteem as we build and share information. Frequent chances to discuss interpretation and share what is shown on the graph helps student understanding of the importance of data management in our world and its usefulness in providing information.  

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