One-to-One and Many-to-One Correspondence in Graphs
Grade 4 data work introduces many-to-one correspondence: on a bar graph, one square may represent 5 students rather than 1. This scale change allows large data sets to be displayed compactly. Reading scales is a critical literacy skill: misreading the scale changes every value in the graph. Students also begin to critically examine graphs: a scale that does not start at zero can exaggerate differences, misleading the reader.
Scale in graphs
Many-to-one correspondence: one symbol represents multiple data points. Bar graph: if each square = 5 students, a bar of 4 squares represents 20 students. Pictograph: if each smiley = 10 people, 3.5 smileys = 35 people (half symbols for intermediate values). The scale must be stated clearly and consistently; otherwise the graph is unreadable.
Choosing an appropriate scale
A class of 30 students chose a favourite sport: hockey 18, soccer 7, swimming 5. Using scale 1=1: the graph is 18 squares tall for the hockey bar, workable but large. Using scale 1=2: hockey bar is 9 squares. Using 1=5: hockey bar is about 3.6 squares, requiring a partial bar. Choose a scale that makes all bars manageable: 1=2 works here.
Critical graph reading
A graph showing company profits over 5 years can appear to show dramatic growth if the y-axis starts at 9.1 to $9.4 million. Starting at zero is the convention for honest comparison. Students who understand scale can detect this manipulation when they encounter it in media.