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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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Session 5 Materials:
Notes
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Session 5, Part B:
Slope (40 minutes)

In This Part: Thinking About Slope | Comparing Slopes | Slopes and Architecture

Slope is an important concept in mathematics, and in Part B we'll explore how it is used to solve problems. Note 5

Problem B1

write Reflect  

Take a minute to think about what you already know about slope. What does it mean? Where is it used?


 
 

You may be familiar with the idea of slope as a measure of steepness. The formula for slope is usually described as

slope = (change in y) / (change in x)

slope

The slope of a line is often described as a ratio of rise/run. Another way to think of slope is as the amount that the dependent variable changes for each increase by 1 in the independent variable. In other words, as x changes by 1, what happens to y?

The following Interactive Activity explores the concept of slope. Measuring slope requires two points. As you work with the examples in the Interactive Activity, ask yourself why the slope between pairs of points would change or why it would stay the same. Note 6


 
 

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. If you prefer, you can view the low-tech version of this acivity, which doesn't require the Flash plug-in.


 

Problem B2

Solution  

What happened when you tried to find the ratio of rise/run for the fourth example in the Interactive Activity, a curved object?


 

Problem B3

Solution  

The drawing below shows a cable attached to a wall.

curve and wall

Calculate the ratio rise/run for each pair of points:
Note 7

 

Points P and Q

 

Points P and R

 

Points Q and R


 

Problem B4

Solution  

Describe the difference between the rise/run ratios for the graph in Problem B3 and the ratios for the graph of a line.
Note 8


Problem B3 taken from IMPACT Mathematics Course 3, developed by Education Development Center, Inc. (New York: Glencoe/McGraw-Hill, 2000), p. 26. www.glencoe.com/sec/math

Next > Part B (Continued): Comparing Slopes

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