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Learning Math Home
Patterns, Functions, and Algebra
 
Session 5 Part A Part B Part C Part D Part E Homework
 
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Notes for Session 5, Part B


Note 5

Groups: Discuss what everyone already knows about slope. Go over the definition of slope in the course materials, and then work on Problems B1-B4. Graph paper is needed for this exercise.

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Note 6

While working with the first Interactive Activity, choose different pairs of points. For each pair, it's important that the difference between the y coordinates and the difference between the x coordinates are computed by considering the pairs in the same order. That is, for points (x1, y1) and (x2, y2), the slope can be computed as either

(y1 - y2) / (x1 - x2) or (y2 - y1) / (x2 - x1).

Note that students sometimes confuse this by computing (y2 - y1) / (x1 - x2).

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Note 7

For Problem B3, consider measuring directly on the picture or tracing the picture onto graph paper to compute the ratios.

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Note 8

Think about the main points for this part of the session: The rise/run for a line is the same between any pair of points on the line; lines are the only kind of graph for which this is true.

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Note 9

Problem B7 focuses on the relationships between slope, scale, and the appearance of a line's graph. It's an important idea that slope only relates to "steepness" if you are comparing two lines with the same scale.

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Note 10

In Problem B8, participants should notice that the lines are all parallel and therefore do not intersect. You may want to talk briefly about what they know about parallel lines, as we will return to this idea in future sessions.

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