Session 4 Notes: Proportional Reasoning

A B C D

Notes for Session 4, Part C

Note 6

Groups: Work in pairs on the Quadperson Interactive Activity. One person should do Problem C1 and one should try Problem C2.

After completing the Interactive Activity, consider which of the new Quadpersons looks more like the original Quadperson, and why. Discuss this in pairs and as a whole group. Explore which line segment drawn in Problem C2 was most dramatically affected by cutting half an inch of the length. In fact, it is the rectangle "nose" that becomes a line segment. Relative to the length of this segment, cutting off half an inch had a dramatic effect.

What would have happened if the original rectangle nose had been a mile long? What effect would cutting off half an inch have had then? Which line segment was most dramatically affected in Problem C1 by taking half its length?

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Note 7

Groups: Work on Problems C5-C8 in pairs or small groups. In these problems, create line segments that illustrate the effect of the two techniques. Notice that the graph for y₂ = (1/2)x represents a proportional relationship; that is, when x doubles, y doubles. This is also known as direct variation. The ratio of any two pairs of coordinates is always the same.

Notice that although this line passes through the origin (as does any graph of a proportional relationship), the graph for situation B -- y₁ = x + 1/2 -- does not.

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