Before they draw the picture, they are to predict how they think the picture will be different and explain why. Students use ratios to describe the relationship between the pictures. Based on what they have learned from the grid drawing above, they are to predict what will happen when they change the window. Have the students change the y and the x min and max separately and record what happens to the graph. Students discuss how changing the values of the window makes the same graph look like different graphs.
Students draw conclusions as to how the graph varies in relation to how the window is changed.
Students discuss how advertisers and researchers use various types of graphs and make conclusions as to how the same data may appear to be different based on the scales used. The Earth is circular and yet some maps of the Earth are flat. Compare various types of maps and see if there is any type of pattern or ratio of changes. For example, the linear pattern is described by the repetition of a linear translation, T, of a basic design, whereas the linear pattern is described by the repetition of a 180 rotation, Ro, of a basic design. Students can identify the basic line and plane symmetry groups in famous art, such as Escher designs or Moorish tilings from the Alhambra in Spain.