Math Background

Graphing Data: Overview

Your children have been sorting objects for a while. They are getting very good at recognizing the attributes of an object and sorting objects into different categories based on those attributes. They are also familiar with the gathering of information through class surveys, such as those in which they are asked to raise their hand if a dog is their favorite animal or if baseball is their favorite sport. Now children need to understand that, like objects, data from such surveys can be sorted and organized into categories. By relating sorting skills to the creation of charts and graphs, you will be helping children move from using concrete representations of data to more symbolic ones.

Introduce the idea of gathering and organizing data by relating the sorting skills that the children have developed to tally charts and then to picture graphs. When children sort objects, they are either given predetermined categories or they determine their own categories according to the attributes of the objects. When they create tally charts and picture graphs, children similarly organize data into categories. At this level, the categories are usually determined before data is collected.

Once children see the connection between sorting objects and sorting information, they are ready to learn ways in which to display this information. Until now, children have used various informal means to represent the data that they have collected, including check marks, slashes, and the raising of hands. Tally charts are a simple, more formal way to collect and organize data. The information in a tally chart is quickly understood, as it is displayed in easy-to-count groups of five. A simple classroom survey of children wearing shoes that tie, shoes that slip on, and sandals, for example, can be used to help children make the connection between a tally chart and the information collected. When the children can see that one tally mark is made for each piece of data, they will understand how to use tally marks to collect and organize data.

Shoe tally chart

Once children understand how to make a tally chart, they are ready to learn how to read and create picture graphs. Picture graphs use pictures to represent data. Although they are not as easy to count as tally charts, they make it easy to visually read and compare data. To read a picture graph, children count the number of pictures in each category to tell how many. At this level, children will be working with picture graphs in which each picture stands for one object or one vote. In Grade 2, children will be introduced to picture graphs in which each picture stands for more than one. Once they understand what each picture stands for, children will be able to compare and analyze data. They can determine which categories have more or less, compare two groups to find out how many more or less there are of one group, or find the total number of items in more than one group.

Shoe tally chart

After children have learned to read picture graphs, they are ready to learn how to make their own. To do so, children sort items and classify them into groups. Once the groups have been determined, they draw, color, or paste one picture on the graph for each object. Once the graph is completed, children can analyze and compare the data shown.

Bar graphs are the last type of data representation that children will learn about in this chapter. While picture graphs are a “semi-concrete” way of representing countable, or discrete, data, bar graphs are more abstract. Instead of using pictures, bar graphs use colored bars on a grid with corresponding numbers to represent how many are in each group. Children learn that they can find how many by looking at the number where each bar ends. Bar graphs allow children to more easily compare the number of items in each group, and allow them to read the numbers instead of counting the items each time data are used.

Shoe tally chart

Next, children become familiar with making bar graphs by collecting data, making tally charts with the data, and then creating a bar graph and analyzing its information. Starting with a tally chart helps children to both organize their data and to see that each tally mark can be represented by one colored box on the bar graph. As with picture graphs, each colored box of the bar graphs that the children will work with at this level represent one object or vote. Also, children will learn how to use bar graphs to compare data to find which group has the most or least, how many more or less there are of one group than another, or how many there are in two or more groups.

As you near the end of this chapter, your children will have expanded the means by which they are able to represent data. Once they have gained proficiency in using tally charts, picture graphs, and bar graphs, they will focus on using graphs to solve problems. Analyzing graphs to get information for problem solving demonstrates children's understanding of how a graph is organized and what it represents. Children can also write questions based on the information given in a graph. By writing questions, children reinforce their understanding of what a graph shows.


Houghton Mifflin Math Grade 1