D1.6 Analyse different sets of data presented in various ways, including in scatter plots and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions.
Activity 1: The Three Levels of Comprehension
Show students the graph below.
image The scatter diagram is titled "Time Spent Reading According to Age”. Scaled from four to twelve, the horizontal axis is named "Age of Child", while the vertical axis is named "Time in Minutes" and is scaled from zero to twelve. The dots show some negative relationship; time tends to decrease as age increases.
Source: translated from En avant les maths, 8e, Données, ML, p. 9.
Allow time for students to reflect on the data and form a general idea about what they think it means. Reflection can be done individually or in small groups. Teachers should then ask open-ended questions to help students communicate their observations and ideas in their own words and develop ideas from those of their peers. For example, they might ask:
- What do you notice about this graph?
- What is interesting about this graph? What can you say about this data?
Then ask questions related to each of the three levels of comprehension.
To get students to read the data, ask them the following questions:
- What is this graph about?
- What is the scale on the horizontal axis?
- What does the vertical axis represent in this graph?
To get students to read between the data, ask them the following questions:
- How many minutes did the 5-8 year olds read? Explain your thinking.
- At what age does a child spend the most time reading? the least time? Explain your thinking.
To get students to read beyond the data, ask them the following questions:
- Do you think the results would be the same if the survey had been conducted 5 years ago? If the survey was conducted 5 years from now? Why?
- If children aged 13 to 19 were included, do you think the results would be similar? Justify your answer.
- Do you think there is a relationship between age and time spent reading?
- What other questions can you ask yourself from this graph?
- What conclusion(s) can be drawn from this graph?
Source: adapted and translated from Guide d’enseignement efficace des mathématiques, de la 4e à la 6e année, Traitement des données et probabilité, p. 91-98.