D1.3 Display sets of data, using one-to-one correspondence, in concrete graphs and pictographs with proper sources, titles, and labels.
Skill: Representing Sets of Data
Once the data have been grouped into categories in a tally table, it is often very useful to represent them using a graph because of its visual effect. For example, a graph:
- presents information in an organized manner;
- is generally easier to read and interpret than a data representation using text or a table;
- allows you to see all the data at a glance and to get a first impression (for example whether the data is evenly or unevenly distributed between the categories);
- facilitates the next step in the inquiry process, which is the analysis of the data and interpretation of the results.
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 86.
For example, students can represent a set of statistical data much more succinctly and effectively with a table or graph than they can with a verbal description. However, they must learn to use the various conventional representations of data (for example, concrete graph, pictograph) correctly to ensure that the message being conveyed is accurate and that it is understood by others. Students can then use these representations to justify a conclusion or support an argument in a mathematical discussion with the class.
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 30.
Once the data has been collected and recorded, students must group it within a limited number of categories. There is no rule that dictates how to group the data. The choice of grouping depends largely on the type of data collected.
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 81
The source, title, and labels provide important information about data in a graph or table.
- The source indicates where the data was collected.
- The title introduces the data contained in the graph or the table.
- Labels provide additional information, such as the categories into which the data are sorted. On a pictograph, a key tells us how many each picture represents.
Source: The Ontario Curriculum. Mathematics, Grades 1-8 Ontario Ministry of Education, 2020.
The order of the categories is important in graphs with quantitative data. Numbers are placed in ascending order on the axis. In contrast, the order of the categories is not important in graphs with qualitative data (for example, the colours can be placed in any order).
Knowledge: One-to-One Correspondence
With one-to-one correspondence, there is one object for each piece of data in a concrete graph or one picture for each piece of data in a pictograph.
Source: The Ontario Curriculum. Mathematics, Grades 1-8 Ontario Ministry of Education, 2020.
Knowledge: Concrete Graph
In a concrete graph, data are represented, with one-to-one correspondence, in a concrete way by people or objects. The graph can be created on the floor, on a large tarp, or on a grid carpet. Using a grid, columns of same-sized rectangles or squares are formed in which a person or object can be placed. It is then easy to compare the data in every column since you only have to compare the length of the columns.
The concrete graph usually includes:
- a title;
- several columns or rows designated by categories;
- a representation of the data using people or objects arranged from the bottom of the column or from the left of the row and equally spaced.
Knowledge: Graph With Representative Material
In a graph with representative material, the data are represented, usually with one-to-one correspondence, in a concrete way by the same objects arranged in columns or rows. These objects may or may not be related to the data they represent. One may also choose to change objects from one category to another, but in this case it is important to use objects of the same dimensions or to place the objects in a grid.
The graph with representative material usually includes:
- a title;
- several columns or rows designated by categories;
- a representation of the data using the same objects arranged from the bottom of the column or from the left of the row and equally spaced.
Knowledge: Picture Graph
In a picture graph, the data are not represented by concrete objects, but rather they are represented iconically, usually with one-to-one correspondence, by pictures that are placed within a grid.
The picture graph usually includes:
- a title;
- several columns or rows designated by categories;
- a representation of the data using pictures arranged from the bottom of the column or from the left of the row and spaced equally.
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 91-94.
Knowledge: Pictograph
In a pictograph, data are represented by a single icon or picture. In Grade 1, pictures are placed in columns or rows with one-to-one correspondence.
The picture usually includes:
- a title;
- several columns or rows designated by categories;
- a representation of the data using pictures arranged from the bottom of the column or from the left of the row and spaced equally;
- a key indicating what each picture represents.
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 94-96.