LESSON:       Slope and Pythagorean Theorem.....Click Here to Download File

ACTIVITY: Designing a Wheelchair Ramp

PURPOSE OF THIS ACTIVITY:     To design a wheelchair ramp for a given location.  Scale drawings will be used to show the placement of the ramp.  The Pythagorean Theorem will be used to find the dimensions of the ramp.  The steepness of the ramp will not only be expressed as slope, but also as a ratio, a percent,  and an angle.

HYPOTHESIS:          Consider the following situation.  There are three steps that lead from the dining room down to the family room.  A wheelchair ramp needs to be constructed from the family room up to the dining room.  To the best of your ability estimate the following measurements.

Vertical Height of the Ramp ( cm )

30   40   50   60   70

Horizontal Length of the Ramp ( m )

3   4   5   6   7

Slant Height of the Ramp

3.5   4.5   5.5   6.5   7.5

Steepness of the Ramp;    height : length

1 : 4   1: 6   1 : 8   1 : 10   1 : 12   1 : 14

PART ONE:        How Steep is Steep:

To determine an appropriate incline for a wheelchair ramp

THE PROBLEM:

?Who can negotiate the steepest wheelchair ramp?

?Set up ramp

?Use the data chart to record the appropriate dimensions

?Use a wheelchair to negotiate the ramp and make note the difficulty

?Adjust the height of the ramp and repeat 

COMPLETE THE DATA CHART

?Record the name of the student riding the wheelchair

?Measure and record the slant height of the ramp

?Measure and record the rise - i.e.. the vertical height

?Use the Pythagorean Theorem to calculate the run - i.e.. the horizontal length

?NOTE:    i.     Pythagorean Theorem:  h2 = a2 + b2

              ii.   the TI-83+ may be used to complete column four

?Calculate the steepness of the ramp and express it in the appropriate format
 

slope:   m =                   percent:   % = slope  X 100

CONCLUSION:         What is a reasonable incline for a wheelchair ramp?

EXERCISE ONE:          Slope and the Pythagorean Theorem

Use the given information to complete the following data chart. 

Show some of your work at the bottom of the page.

SHOW SOME OF THE CALCULATIONS

PART  TWO:  Designing the Wheelchair Ramp I

PURPOSE:      To design a wheelchair ramp to fit a given location.          

THE PROBLEM:         To allow all students access to the tech wing at CSS, design a wheelchair ramp to fit the stairway leading to this area.

THE SOLUTION: 

?describe the location for the wheelchair ramp

?measure the area

?decide and calculate the appropriate measurements for the ramp

?make a scale drawing of the ramp and a scale drawing of the area with the ramp in place

?conclusion;  Will a wheelchair ramp in this location be appropriate?  Discuss the advantages and the disadvantages.

?extension;          i.          Investigate any other aspect of this ramp that may not have been taken into account.

                            ii.          Determine the amount of material required and the approximate cost of building this wheelchair ramp.        

EXERCISE TWO:  Designing the Wheelchair Ramp II

If a family member becomes confined to a wheelchair, the home must be outfitted with ramps to provide access for that person.  Here are a few criteria adapted from suggestions by rehabilitation specialists.

?The maximum incline recommended for wheelchair users is  1:12  ( i.e.,  for each cm in height, the ramp must extend  12  cm ).

?For exterior ramps in climates where ice and snow are common, the incline should be more gradual, at  1:20.                                                           

?For unusually strong wheelchair users, or for extra-powerful motorized chairs or if the person is lightweight but the pusher is strong, the ramp can have an incline of 1:7.  The steepest ramp should not have an incline exceeding  1:5.

?There should be at least 150cm of straight clearance at the bottom of the ramp. 

Refer to the given description as you design a wheelchair ramp for each of the following situations.  Make a scale drawing of a ramp that follows the criteria

listed above.  Construct a second scale drawing that displays the ramp in place.

Use appropriate measurements for the area described.

1.         Emily requires a ramp that leads from her back deck to a patio.  She is of average strength and operates a manual wheelchair.  The deck is  25cm above the patio.   

2.         Brendan lives in a split level house.  He owns a very powerful motorized chair.  He wishes to build a ramp that leads from his family room to hisliving room on the next level.  The height of the ramp must be 60 cm.

EXERCISE THREE     Pythagorean Theorem and Slope

1.         Use the Pythagorean Theorem to find the value of the unknown side.  Find the steepness of the hypotenuse relative to the other two sides. Express the steepness in three different ways.

            a)

            b)

            c)

                        slope =

2.         Use the information given in the diagram to find the values of x and y.  Find the slope of the ramp.

3.         Find the length of the diagonal of the box 40 cm by 30 cm by 20 cm.

4.         Find the length and the slope of the line segment AB, where A (-1, 3) and     B (4, 8).

5.         A 3.5 m ladder is leaning against a wall. The base of the ladder is 1 m from the wall.  How high up the wall does the top of the ladder reach? Determine the slope of the ladder.

QUIZ                                                   NAME: ____________________________

1.         The diagram represents the three steps to the             front door of a building.  The riser height             is 18 cm and the tread depth is 26 cm.             Design a ramp that will allow wheelchair             access to this building.             a)         Calculate the length and the slope of your ramp.             b)         The builder constructed a ramp 5.5 m long.  Will                         this ramp be acceptable? Discuss.

2.         Use a diagram to find the slope of the following line segments between the         following pairs of points.

            a)         A(3, 1),  B(6, 13)                   b)         P(-2, 4),  Q(5, -1)

3.         The line segment joining each pair of points has the given slope.  Determine        the value x or y.

            a)         (-1, 4), (5, y), slope = -                 b)         (x, -4), (-5, 8), slope = 4

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