D1.2 Collect qualitative data and discrete and continuous quantitative data to answer questions of interest about a population, and organize the sets of data as appropriate, including using intervals.
Activity 1: Identify the Situation
This activity uses a contextualized situation to demonstrate how teachers have students clarify an issue and pose a question of interest. In addition, since the choice of the question of interest suggests the use of a survey, the step of formulating survey questions is also presented.
Note: This scenario can be adapted to a multitude of contexts, to the dynamics of each class, and to a problem situation that addresses current events.
Earth Day
As part of the planning for learning about data, Martin Tremblay, a Junior Division teacher, wants to conduct a survey with his students. Seeing that Earth Day is approaching, he decides to contextualize the situation by proposing the reading of a text on pollution. He gives each student a copy of the text, Respirer c'est mauvais pour la santé (this resource is only available in French).
Mr. Tremblay asks students, in an independent reading session, to read the text carefully, and then encourages them to clarify the problem by asking questions such as:
- Have you ever heard of smog before reading this text?
- What are some of the causes of air pollution?
- What do you think might be some possible solutions?
- Have you ever witnessed "impressive natural phenomena"?
- Do you know people who have respiratory problems like Luis'?
- Do you think that other types of pollution can have an impact on people's health?
All of the students' ideas are written on the board and then organized using a concept map.
Example
image The concept map contains expressions written in bubbles linked together by arrows. It begins with the bubble containing the expression "Smog". Encountering the out-of-bubble phrase "It causes", "Smog" is linked to "Air pollution". "Air pollution" is linked to "respiratory illnesses". Encountering the non-bubble expression "solutions", "Smog" is also linked to "concrete actions", which is linked to "public transportation" and "carpooling". Encountering the non-bubble expression "caused by", "Smog" is linked to "cars", "lifestyle", and "altitude and heat".
Note: From the analysis and discussion of this concept map, students will be presented with many important considerations related to the issue of air pollution. They see various facets of it, which are the result of the exchange of ideas. Students then realize that they have the opportunity, through their questions, to guide the direction of the survey. Mr. Tremblay then leads a discussion oriented towards the formulation of questions of interest, which is excerpted below.
Mr. Tremblay: Besides the ideas on the board, is there anything else you would like to know about pollution?
Students
Student 1 – I wonder if there are other diseases that are caused by pollution.
Student 2 – Is smog a recent phenomenon?
Student 3 – In our city, how many people use public transit to get to work? Do many families of students at the school use public transit?
Student 4 – Are there Canadian cities as polluted as Mexico City? What are the most polluted Canadian cities?
Student 5 – Do you think the families of the students at the school could leave their cars behind once a week like the residents of Mexico do in order to reduce the emission of harmful pollutants? What would be the consequences of such behaviour?
Student 6 – I think that we can take concrete action. I wonder what activities students at the school would be willing to participate in to highlight the importance of air quality.
By consensus, the class decides to look more closely at Student 6's question. The students choose to survey their peers to obtain data to answer it. The following excerpt demonstrates how Mr. Tremblay helps them formulate the survey questions.
Mr. Tremblay: If we were to survey the students in the school about activities to raise awareness about the importance of air quality, what questions could we ask them?
Student 1 – We could ask them if they want to improve the school's air quality.
Mr. Tremblay: What possible answers could they give to that question?
Students
Student 2 – It would be yes or no … We would know if the majority of students want to improve air quality.
Student 3 – But if we really want the students to participate, we should include suggestions for activities or actions in our question. For example, they could be asked a multiple-choice question such as:
To celebrate Earth Day, do you want to:
- improve the air quality in the classroom?
- buy a new plant for the class?
- organize a wind festival?
- plant trees in the schoolyard?
Mr. Tremblay: A series of possible actions or activities are proposed here. What is the person who chose the statement improve the air quality in the classroom telling you about the action they want to take?
Student 4 – It's true that this person might also want to buy a new green plant for the class.
Mr. Tremblay: OK then, how can you rephrase your question to make it more specific?
Students
Student 3 – If we really want to know the favourite activities of young people, we should perhaps ask them which they prefer.
Student 6 – The younger students don't have the same tastes as the older ones. We could also ask them if they are in the Primary or Junior Division.
After this exchange, students design a questionnaire comprising a few questions whose data will paint an interesting picture of the situation. Here is a sample of the questionnaire developed by the class.
Earth Day Activities
Circle the appropriate choice.
Are you in the Primary or Junior Division?
P
J
To celebrate Earth Day (April 22), Grade 6 students will organize an activity related to air quality. From the activities below, indicate with a check mark which activity you would prefer to participate in.
- Make a presentation during the Earth Day ceremony (for example, plant a tree, recite a poem, perform a skit).
- Make kites to promote wind energy.
- Take a walk outdoors.
- Participate in the creation of a mural that would illustrate elements related to air quality.
- Write short pieces (for example, poems, articles) about the importance of air quality. These articles will be posted on the school's website.
Students are now ready to begin the next steps in the inquiry process: collecting data, organizing the data, and interpreting the results.
Source: translated from Guide d’enseignement efficace des mathématiques, de la 4e à la 6e année, Traitement des données et probabilité, p. 38-42.
Activity 2: Collect Qualitative Data and Continuous and Discrete Quantitative Data
Ask students to formulate a question of interest that will allow them to collect qualitative or quantitative data (discrete or continuous). Then invite students to survey a population or find secondary data. Ask them to organize their data set in a frequency table. For students who have collected continuous data, encourage them to use appropriate intervals so that all of their data can fall within the defined interval values.
Activity 3: Set of Data in an Interval-Frequency Table
Here is a frequency table.
Amount Spent During the Last Visit to the Belize Shopping Center
| Amount Spent | Frequency |
|---|---|
| Less than $50 | 21 |
| $51 to $100 | 59 |
| $101 to $150 | 91 |
| $151 to $200 | 125 |
| $201 to $250 | 143 |
| Over $250 | 111 |
Source: Belize Mall Shoppers
Ask students the following questions:
- What do you know about this set of data?
- What type of data is collected?
- What is the mode for this set of data?
- Are the intervals for the data appropriate? Why?