ALGEBRA I
8th, 9th or 10th grade
Judith Roger
 
The student will investigate the meaning of slope as a rate of change.
 
 
TEACHER INFORMATION
 
Benchmarks
A.1, A.3, M.1, M.3, M.4, G.2, P.5 
Time Frame
1  class period
Curriculum Integration
slope, graphing, interpreting graphs, ratios
Materials
Rulers, yardsticks, wedged pieces of wood such as those used as doorstops, graph paper, calculators (optional)
 
Applications
construction, architecture, landscape design
Student Groupings
individual, pairs
 
 
Possible Obstacles to Student Learning
  • measuring accurately using a ruler
  • understanding the meaning of perpendicular in order to measure distance correctly
  • simplifying ratios
  • reading graphs
  • computing slope using a formula 
 
Opportunities for Assessment
Research:  Roofers are concerned with the slope of a roof which is called its pitch.  Investigate 
the meaning of the term "pitch" in relation to construction and explain how it is computed. 

Journal Entry:  Explain the meaning of slope using 3 methods:  1)  a description in words, 
2)  a mathematical formula, and    3)  a diagram 
Group Activity:  Have students find the slopes determined by  stairs around school, 
or the gym bleachers, or the stadium stairs or ramps. 

 
 
 
Lesson Procedure

Materials:  Rulers, yardsticks, graph paper, calculators(optional),  wedged pieces of wood that 
                    are used for doorstops  (These can be found in places where wood construction 
                    is done such as the shop class or a new home.) 

Procedure:  Engagement:  Graphs are often used to represent real life activities or 
                       situations.  Show some short video clips of action cartoons or movies . 
                       Then put on the overhead  four different examples of graphs that represent a 
                       distance vs. time as illustrated by the videos.  Have students match the videos 
                       to the graphs that represent the action taking place-- for example a very slow 
                       freight train, or a plane taking off. 
 
                       Relate slope of lines to rate of change. 
 
                       Review the mathematical formula for slope using two points: m = (y2-y1)/(x2-x1) 
 
                       Have students divide into groups of two (or three) .  Each group member should 
                       complete a worksheet.  Each group needs one sheet of graph paper, a calculator, 
                       two rulers, and two doorstops. 
 
                       The teacher may wish to set up stations for the yardstick question instead of giving 
                        a yardstick to each group. 

 
 
Worksheet
                                                                          Name ____________________ 
                                                                                             Date ___________    Per. ____ 

     WARMUP 
      1.  Find the slope of the line connecting the given points. 
            a)  A(2,5); B(6,9)                            b)  C(-1, -3);  D(-6, 3) 
 
  

         
      2.  Draw a line which has a negative slope.   
 
 
  

      3.  Draw a line which has an undefined slope. 
  

       4.  Suppose a piece of plywood is placed over the steps illustrated below.  Using 
            a ruler and your knowledge about ratios,  find the slope of the ramp 
            that would be formed by the sheet of plywood.   
 
 

      ACTIVITIES 

      5.  Find the slope of a yardstick if one end is placed on the edge of the chalkboard 
           tray (or your desk) and the other end is resting on the floor.  Explain how you 
           found your measurements, what units were used, and SHOW YOUR WORK. 
           Answer should be given as a ratio in simplest form  ________and in  
                                                                        decimal form __________.   
 
  

      6.  Each group should have 2 wooden doorstops.  Only one should have a 90 degree 
           angle.  Determine the slope of the inclined plane of the doorstop.  (This will be  
           the longest edge.)   Use two methods:  1)  Trace the doorstop on a piece of  
           graph  paper.  2)  Use a ruler and  find the appropriate measurements. 

 
Exploration and Extension
 
Discuss how the use of different units of measurement affected answers. 

Discuss  how different places can be chosen to take the measurements, yet the results should be 
the same.