5.1+Climbing+Stairs

7.06.09 MT Big idea: Many real world situations can be modeled and predicted using mathematics. Essential question: How steep is that line Notes from class: m=slope=rise/run= ∆y/∆x= y1-y2/ x1-x2 m=co-efficient slopesteepness ∆= "the change in" .45 rise/run .60 For the rate to match the guidlines it needs to equal to 17 and the rise/run needs to be between .45 and .60 7/10 7+ 10 = 17 (this goes with the guide lines) 7/10= .70 (doesn't work with the guidlines so overall rate doesn't work)

//Climbing stairs is good excercise. Some athletes run up and down stairs as part of their training. The steepness of stairs determines how difficult they are to climb. Stairs that are very steep are more difficult to climb than stairs that rîse gradually. Examining the steepness of stairs can help you understand the idea of steepness, or slope,of a line.
 * __5.1 Climbing stairs__

__Think about this!__ consider the following questions about the stairs you encounter at home, in your school and in other buildings . How can you describe the steepness of stairs? . Is the steepness the same between any two consecutive steps for a particular set of stairs?

The steepness of stairs is determined by the ratio of the rise to the run for each step. The rise and run are labeled in the diagram below. (look in your book the rise is basically the height and the run the width)

Carpenters have developed guidelines to ensure the stairs they build are relativley easy for a person to climb. In some states, carpenters work with these guidelines:

. The ratio of the rise to run for each step should be between 0.45 to 0.60 . The rise plus the run for each step should be between 17 and 17.5 inches.

__Problem 5.1__//**
 * Determine the steepness of a step of stairs.**

Measure at leas two steps in the sets of stais you choose Make a sketch of the stairs, and label it with measurments you found.**
 * To calculate the steepness you will need to measure the rise and run of a step.


 * How do the stairs you measured compare to the guidelines?**

__Breeze-way stairs__ __Calculation step 1 and 2:__ rate:7/12 7+12 = 19(doesn't match) 7/12= .58 (matches guidelines) __step 3:__ rate:11.5/7 11.5+7=18.5 (doesn't match) 11.5/7

Our stairs don't match the guidelines because first of all not all the steps are the same and the two first steps don't have a rise +run that matches the guidlines. And the third step completley doesn't match the guidelines. Overall these stairs are mainly to steep and don't match the guide lines.


 * __Problem 5.1 Follow-Up__

1. Make and label a scale drawing of stairs that don't meet the carpenters' guidelines. Explain why the stairs you drew are steeper (or less steep) than the stairs described in the guide lines. **

__Calculations__ rate= 16/20 16+20=36(doesn't match) 16/20

The steps are steeper becuase the rise over run is 0.8 when it is actually supposed to be between .45 and .60


 * 2.You can use the ideas about the steepness of stairs to find the steepness of a ramp.

In one state the construction code for an access ramp is a rise of 1 foot for a run of 12 feet. The access ramp at a football stadium in this state has the rise of 1 foot for a run of 8 feet. Many people in wheel chairs cannot get their chairs up the ramp without help. Make scale drawings of the stadium ramp and a ramp meeting the state code. **