D1. Data Literacy
Specific Expectations
Data Collection and Organization
D1.1
sort sets of data about people or things according to one attribute, and describe rules used for sorting
- sorting data about things:
- buttons by size, colour, or number of holes
- leaves by size, shape, colour, type of tree, or type of edges
- containers by size, shape, or purpose
- Data can be sorted in more than one way, depending on the attribute.
- Data can be sorted into categories using attributes, and the categories can be used to create tables and graphs.
Note
- A variable is any attribute, number, or quantity that can be measured or counted.
- Early experiences in sorting and classifying support students with understanding how data can be organized.
Have students sort a collection of things (e.g., buttons, leaves, containers) by one attribute at a time, such as colour, shape, number of holes, size, and so on. Repeat for other single attributes.
Have students describe the sorting rule for an already sorted collection of objects or data.
D1.2
collect data through observations, experiments, and interviews to answer questions of interest that focus on a single piece of information; record the data using methods of their choice; and organize the data in tally tables
- questions of interest and data collection methods:
Questions of Interest | Data Collection Methods |
What colours of shoes are my classmates wearing? | Observation:
|
How many times will a tennis ball bounce if I drop it from the height of my desk? | Experiment:
|
What do you like to do the most – play in the snow, toboggan, or skate? | Interview:
|
- collecting and recording data:
- Place a craft stick in a can to do a quick tally.
- data organized in a tally table:
- Data can be either qualitative (descriptive, e.g., colour, type of pet) or quantitative (numerical, e.g., number of pets, height).
- The type and amount of data to be collected is based on the question of interest.
- Data can be collected through observations, experiments, interviews, or written questionnaires over a period of time.
- Tally tables can be used to organize data as it is collected. The data is recorded in groups of five tallies to make it easier to count.
- The distribution of data among the categories can change as more data is added.
Note
- In the primary grades, students should collect data from a small population (e.g., objects in a bin, the days in a month, students in Grade 1).
Have students track one type of weather condition each day for a month and record their observations on a calendar. For example, they can record whether it snowed that day or not. When the collection period is over, guide students through the process of organizing their collected data in categories and then in a tally table.
Data Visualization
D1.3
display sets of data, using one-to-one correspondence, in concrete graphs and pictographs with proper sources, titles, and labels
- concrete graph:
- using paper clips to show the number of students in Group A that are wearing blue, red, or green shoes:
- pictograph:
- displaying the data from the concrete graph above:
- Different representations can be used to present data, depending on the type of data and the information to be highlighted.
- Both concrete graphs and pictographs allow for visual comparisons of quantities that are represented in the graphs.
- 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.
- 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.
Note
- The source can be included in the title of a graph.
- The structure of a concrete graph can be transformed into a pictograph.
Have students create a concrete graph, and then a pictograph, about a topic of interest, such as the favourite type of fruit among the students in Grade 1:
- concrete graph:
- pictograph:
Data Analysis
D1.4
order categories of data from greatest to least frequency for various data sets displayed in tally tables, concrete graphs, and pictographs
- pictograph:
- For the pictograph below, the frequency in order from greatest to least is kiwi, apple, plum, and banana. On the other hand, the frequency from least to greatest is banana, plum, apple, and kiwi.
- The frequency of a category represents its count.
- The frequencies in a tally table should match the frequencies in graphs of the same information.
- The category with the greatest frequency has the greatest number of tallies in a tally table, the greatest number of objects in a concrete graph, and the greatest number of pictures in a pictograph.
Note
- Ordering the categories by frequencies will support students when they identify the mode in Grade 2.
Ask students to rearrange the data in a concrete graph so that the categories are in order from greatest (highest) frequency to least (lowest) frequency.
Next, give students the same information in a pictograph. Ask them which category has the greatest (highest) frequency and to describe how they know – for example, “kiwi” on the pictograph has the greatest frequency because it has the longest line. Similarly, ask them which category has the lowest frequency and how they know.
Finally, give students the same information in a tally chart. Ask them which category has the greatest (highest) frequency and to describe how they know – for example, “kiwi” on the tally chart has the greatest frequency because it has a group of five like the apple category, and one more. Similarly, ask them which category has the lowest frequency and how they know.
D1.5
analyse different sets of data presented in various ways, including in tally tables, concrete graphs, and pictographs, by asking and answering questions about the data and drawing conclusions, then make convincing arguments and informed decisions
- question that requires reading and interpreting data from a graph or table:
- How many students chose plums as their favourite fruit?
- question that requires finding data from a graph or table and using it in a calculation:
- How many more students like apples than like bananas?
- question that requires using data from a graph to make an inference or prediction:
- What type of fruit do you think is the least liked fruit among students in Grade 2? Why do you think that?
- Different representations are used for different purposes to convey different types of information. Tally tables, concrete graphs, and pictographs are used to represent counts or frequencies of various categories.
- Information in tally tables, concrete graphs, and pictographs can prompt the asking and answering of questions like "Which category has the greatest frequency?".
- Sometimes, considering the frequency can support making informed decisions, such as what type of books should be ordered for the class library.
- Questions of interest are intended to be answered through the analysis of the representations. Sometimes the analysis raises more questions that require further collection, representation, and analysis of data.
Note
- There are three levels of graph comprehension that students should learn about and practise:
- Level 1: information is read directly from the graph and no interpretation is required.
- Level 2: information is read and used to compare (e.g., greatest, least) or perform operations (e.g., addition, subtraction).
- Level 3: information is read and used to make inferences about the data using background knowledge of the topic.
- Analysing data can be complex, so it is important to provide students with strategies that will support them to build these skills.
Provide students with familiar representations of new data, such as tally tables, concrete graphs, or pictographs, and ask them what questions they have about the data. Model the act of posing questions to support students in posing their own questions. Model asking questions using the three types outlined in the examples, and have students pose and answer their own questions, requiring them to think critically about the data.
Have students revisit previously collected and organized data. Ask them to pose questions that will require others to think critically about this data.