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Session 5, Part B:
Slope

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

Architects and carpenters use rise and run to describe and build staircases. The picture below shows the rise and run for each step and the total rise and run for the staircase.

staircase

Take it Further

Problem B10

 Solution    

An architect is designing a staircase for a house with a difference of 10 feet between floors. The staircase has 18 steps and a total run of 14 feet. What is the ratio (total rise/total run) of the staircase?


Problem B11

 Solution    

Find the rise and run for each step (what we'll call the step rise and run) in inches. What is the ratio (step rise/step run)? Explain your answer.


Problem B12

 Solution    

Find a nearby staircase and measure the rise and run of one step. How could you use this to estimate the total rise and run of the staircase?


Problem B13

 Solution    

Design a staircase with a total rise of 14 feet, a step rise between 6 and 8 inches, and a sum of step rise and step run between 17 and 18 inches. All steps should have the same rise and the same run. Your answer should include

a. 

the number of steps

b. 

the height of each step

c. 

the run of each step

d. 

the total run

e. 

the ratio (step rise/step run)

f. 

the ratio (total rise/total run) for the staircase.

There are many different solutions to this problem. Remember that the total of the step rise and the step run must be between 17 and 18 inches.   Close Tip
 
 


video thumbnail
 

Video Segment
In this video segment, taken from the "real world" example at the end of the Session 5 video, master carpenter Norm Abram describes the importance of slope in construction. Watch this segment after completing Part B.

In what other professions is slope used on a regular basis?

You can find this segment on the session video, approximately 21 minutes and 8 seconds after the Annenberg Media logo.

  

Problems B10-B13 taken from IMPACT Mathematics Course 3, developed by Education Development Center, Inc. (New York: Glencoe/McGraw-Hill, 2000), p. 41. www.glencoe.com/sec/math

Next > Part C: Rates

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