Grade 6 - Statistics and Probability (Data Analysis)

The sub-organizer contains the following sections:
Prescribed Learning Outcomes
Suggested Instructional Strategies
Suggested Assessment Strategies
Recommended Learning Resources

PRESCRIBED LEARNING OUTCOMES

It is expected that students will develop and implement a plan for the collection, display, and analysis of data gathered from appropriate samples.

It is expected that students will:

formulate a key question from a problem-solving context
identify appropriate data sources (first-hand, second-hand, a combination of first- and second-hand)
select and justify appropriate methods of collecting data (designing and using structured questionnaires, experiments, observations, and electronic networks)
select and justify the choice of an appropriate population sample to use to answer a particular question
discuss how the data collected are affected by the nature of the sample, the method of collection, the sample size, and biases
display data by hand or by computer in a variety of ways, including histograms, double bar graphs, and stem and leaf plots
read and interpret graphs that are provided
describe the general distribution of data:
- smallest and largest value
- frequency (which occurs most often/least often)
- value in the middle
- patterns
- analyse sets of data to make comparisons and test predictions

To view the prescribed learning outcomes for Statistics and Probabilities (Data Analysis) in other grades click on an icon below.

SUGGESTED INSTRUCTIONAL STRATEGIES

Students increase and practise skills for analysing information in graph form by doing projects of their own. They can review many mathematical ideas and relate mathematics to the real world as they consolidate and extend their understanding of statistical notions.

Provide students with a variety of graphs (from the National Council of Teachers of Mathematics Standards Document on Probability and Statistics, from newspapers, from textbooks) and have them work in groups to discuss potential biases. Brainstorm questions such as:
- Was first- or second-hand information used?
- Who do you think was surveyed?
- How might the information be different if another group was surveyed?
- How many people were surveyed?
- Was that number of people enough? Why or why not?
- Was the group of people surveyed a representative group?
- What predictions would you make here? Groups could make their predictions to the whole class.
Collect data from students on their food preferences. Have them redraw the information into double-bar-graph format using boys and girls as the variable and write a paragraph on comparisons and possible predictions.
Have students brainstorm problems that might require the use of data collection or surveys for solutions. Look for issues that can be viewed using two criteria (e.g., number of people and number of preferences).
Have students do a class survey that involves three different segments of the class. Have them create simple graphs to compare differences in results and then have them discuss sampling bias.

SUGGESTED ASSESSMENT STRATEGIES

Research projects provide students with real experiences in dealing with information and data first-hand. Students can develop and extend their skills and knowledge through activities that they plan and carry out independently or as part of a group. After they have had opportunities to practise the skills involved in formulating a question, planning a statistical investigation, and collecting and reporting data, have students make predictions about other populations. Students can then design and complete research projects as a final assessment activity.

Collect

Collect student graphs and look for their use of:
- correct naming of axes
- appropriate intervals for the data
- proximity of columns in bar graphs
Have students write about the data with regard to smallest, largest, most often, most common, middle, and potential patterns .

Question

Interview groups, pairs, or individual students regarding their project. Ask them whether the population sample that they have used for their project will answer the question accurately.

Self-Assessment

Have students complete a self-assessment of their projects. You might wish to help them develop a checklist with a set of criteria they can use. For example:
- Question: what is appropriate, inappropriate?
- sample
- data collection method
- recording of data
- computations
- choice of data display
- creation of display/graph