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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:

Session 5, Part B:

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.


Take it Further

Problem B10


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


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


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


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


the number of steps


the height of each step


the run of each step


the total run


the ratio (step rise/step run)


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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