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Michigan Department of Education Technology-Enhanced Lesson Plan Title: Exponential function, Seismograph, and the Richter Scale Created by: Dr. Pam Lowry, Lawrence Technological University Adapted by: Gail O. Sutton, Forest Hills Public and John Folsom, MDE Technology Enhanced Lesson Planning Project Lesson Abstract: Students will review exponents, build a simple Seismograph and demonstrate it, and understand the connection between the Seismograph and the Richter Scale. Subject Area: Mathematics Grade Level: 10-12 Unit of Study: Exponents and Logarithms MDE Technology-Enhanced Lesson Plan Code: Michigan Educational Technology Standards Connection: Michigan Grade Level Content Expectations Connection: o A2.5.2 Interpret the symbolic forms and recognize the graphs of exponential and logarithmic functions (e.g., f(x) = 10 x, f(x) = log x, f(x) = ex, f(x) = ln x); recognize the logarithmic function as the inverse of the exponential function. Michigan Curriculum Framework Connection: Estimated time required to complete lesson or unit: 4-5 class periods Instructional resources: o Graph paper o 4 bags containing 1 m&ms labeled 2 0 , 4 bags containing 2 m&ms labeled 2 1 , 4 bags containing 4 m&ms labeled 2 2 , 4 bags containing 8 m&ms labeled 2 3 , and 4 bags containing 16 m&ms labeled 2 4 (You can substitute another item for the m&ms.) o 4 bags containing 1 skittles labeled 3 0 , 4 bags containing 3 skittles labeled 31 , 4 bags containing 9 skittles labeled 3 2 , 4 bags containing 27 skittles labeled 3 3 , and 4 bags containing 27 skittles labeled 3 3 2f98bcee-c8ff-482f-9d62-8dc155bed225.doc - Page 1 (You can substitute another item for the skittles.) o Materials to build your seismograph which are listed at http://cse.ssl.berkeley.edu/lessons/indiv/davis/hs/Seismograph.html Sequence of Activities: Bags containing marbles Part 1: o Divide your class into groups and give each group a bag containing 1 m&ms, 2 m&ms, 4 m&ms, 8 m&ms, and 16 m&ms o Ask the groups to discuss the following: (see table below) if you increase the exponent from 0 to 1 as labeled on the bag, how does this affect the number of m&ms if you increase the exponent from 1 to 2 as labeled on the bag, how does this affect the number of m&ms if you increase the exponent from 2 to 3 as labeled on the bag, how does this affect the number of m&ms if you increase the exponent from 3 to 4 as labeled on the bag, how does this affect the number of m&ms # of m&ms Y= 2 x exponent 1 20 0 2 21 1 4 22 2 8 23 3 16 24 4 o Ask each group to discuss the relationship between increasing the exponent and the number of m&ms in each bag and lead them to see the ratio of the number of m&ms in one bag to the number of m&ms in the next bag is always 1:2 o Ask each group to graph the ordered pairs (0,1), (1,2), (2,4), (3,8), (4,16) on their graph paper and use their graphing calculator to plot the points in order to visualize their exponential function 2f98bcee-c8ff-482f-9d62-8dc155bed225.doc - Page 2 Part 2: o Now give each group a bag containing 1 skittle, 3 skittles, 9 skittles, 27 skittles, and 81 skittles o Ask the groups to discuss the following: (see table below) if you increase the exponent from 0 to 1 as labeled on the bag, how does this affect the number of skittles if you increase the exponent from 1 to 2 as labeled on the bag, how does this affect the number of skittles if you increase the exponent from 2 to 3 as labeled on the bag, how does this affect the number of skittles if you increase the exponent from 3 to 4 as labeled on the bag, how does this affect the number of skittles # of skittles Y= 3 x exponent 1 30 0 2 31 1 4 32 2 8 33 3 16 34 4 o Ask each group to discuss the relationship between increasing the exponent and the number of skittles in each bag and lead them to see the ratio of the number of skittles in one bag to the number of skittles in the next bag is always 1:3 o Ask each group to graph the ordered pairs (0,1), (1,3), (2,9), (3,27), (4,81) and use their graphing calculator to plot the points in order to visualize their exponential function o Ask each group to discuss the relationship if each bag contained 1 bingo chip, 10 bingo chips, 100 bingo chips, 1,000 bingo chips, 10,000 bingo chips o Ask each group to use their graphing calculator to graph this relationship and discuss how this graph compares to the m&ms or skittles. 2f98bcee-c8ff-482f-9d62-8dc155bed225.doc - Page 3 Building your own seismograph o Each group will build their own Seismograph following the directions located at http://cse.ssl.berkeley.edu/lessons/indiv/davis/hs/Seismograph.html. o Ask each group to discuss why Seismographs are used and then demonstrate the Seismograph they built The Richter Scale o Have the students find information about Charles Richter and discuss this with the class. o Have the students complete the following table. Explain to the class that on a Richter scale, a magnitude of 0 is given to an earthquake that registers amplitude of .001 mm on a seismograph that is 100 km away. Amplitude in Exponential Exponent Exponent + 3 Richter Scale mm of form Magnitude Seismogram 100 km away .001 10 3 -3 -3+3=0 0 .01 .1 1 10 100 1,000 10,000 100,000 1,000,000 Assessments: Pre-Assessment o In a journal or a paper to turn in, write down everything you currently know about a Seismograph and the Richter scale, making any connections to exponents and logarithms. o Have the students describe an exponential function and discuss what happens when the base changes. o Have the students describe a common logarithmic function. Post-Assessment o How does the graph of y= 10 x exponential function compare to the function y=log(x)? o Why do the graphs for y= 10 x and y=log(x) looks so similar? Technology (hardware/software): o Graphing calculator o Internet 2f98bcee-c8ff-482f-9d62-8dc155bed225.doc - Page 4 Key Vocabulary: Exponential functions, Logarithms, Seismograph, Richter scale Application Beyond School: Teacher Reflection and Notes: 2f98bcee-c8ff-482f-9d62-8dc155bed225.doc - Page 5

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posted: | 8/2/2011 |

language: | English |

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