 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Solutions for Session 4, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6| C7 | C8 | C9
C10 | C11 | C12   Problem C1 The "after" Quadperson has the same scale to its facial features; the nose is still four times as wide as it is tall, and so forth.   Problem C2 This "after" Quadperson does not have the same shape as the original. In particular, the nose becomes a flat line, but other features are scaled differently from "before."   Problem C3 Problem C1 is the relative comparison. Think about the angles and measurements in the body; we expect, for example, the head to be a certain fraction of the size of the torso, and so forth.   Problem C4 The change in Problem C1, a relative comparison, keeps these measurements in proportion, while the change in Problem C2, an absolute comparison, does not. In Problem C2, short lengths are made way too short (the nose, for example) by giving an absolute change in length, rather than a proportional change in length.   Problem C5 y1 = x/2.   Problem C6 y2 = x - 1/2.   Problem C7

Both graphs are straight lines. The graph of y1 goes through the origin (0, 0), while the graph of y2 does not. Additionally, the graph of y2 becomes negative if x < 1/2, not a good thing when measuring lengths.

 a. b.    Problem C8 Yes, the graph of y1 is proportional, since the input is always twice the output. Or, the output is half the input. (Compare that to the formula y1 = x / 2.) The graph of y2 is not proportional; try finding the outputs for two different values of x, then determine if they are proportional. This produces the different shape of Quadperson in Problem C2.   Problem C9 Note: Not drawn to the same scale as Quadperson activity   Problem C10

The equation for this table is y3 = 2x.

 X Y3 1 2 2 4 3 6 4 8 5 10 6 12   Problem C11 It is a proportional relationship because every output is twice the input, and if we multiply the input by any number, we multiply the output by the same number. This graph, like the last proportional graph, passes through the origin (0, 0).   Problem C12 All proportional relationships have the equation y = kx, where k is some constant number. A line graph represents a proportional relationship only when the line goes through the origin (0, 0).     Session 4: Index | Notes | Solutions | Video