Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 4, Part C:

 In This Part: Playing with Quadperson  | Graphs of Proportional Relationships

In Part B, you made relative comparisons involving mixtures. Scaling is another type of relative comparison problem. Scaling is used in graphic design, cartography, construction, and many other areas. In fact, if you have ever doubled a recipe or built a model airplane, you have dealt with problems of scale. Note 6

This Interactive Activity compares the effects of absolute and relative comparisons on a picture. Think about what would happen to a drawing if every line were made half as long. Would it look like the same picture at all? What would happen if you made every line a half-inch shorter? In this activity, you will see the effects of these changes on Quadperson, a drawing of a face made of quadrilaterals.

Problem C1

Compare the "before" and "after" Quadperson when you multiplied each length by one-half.

 Problem C2 Compare the "before" and "after" Quadperson when you subtracted half an inch from each length.

 Problem C3 Of Problems C1 and C2, which is a relative comparison? Which is an absolute comparison? Explain how you know. Which version looks more like the original Quadperson?

 Problem C4 Did the Quadperson look the same after a change made by an absolute comparison? Did the Quadperson look the same after a change made by a relative comparison? Why?

 Video Segment In this video segment, Andrea and Deanna compare the two versions of Quadperson and discuss why one Quadperson is more in proportion with the original than the other. Watch this segment after you've completed Problems C1-C4, and reflect on the onscreen participants' reasoning about the results of their drawings. Would every absolute comparison change the shape of Quadperson? Would every relative comparison maintain the shape of Quadperson? You can find this segment on the session video, approximately 5 minutes and 58 seconds after the Annenberg Media logo.

 Video Segment In this video segment, the onscreen participants discover the proportional change in area determined by the relative change in Quadperson. Can you explain why the two-dimensional area would change in the manner described in this segment? This topic will be further explored in the "Measurement" course. You can find this segment on the session video, approximately 8 minutes and 41 seconds after the Annenberg Media logo.

 Session 4: Index | Notes | Solutions | Video