Total Duration: |
61 to 90 Minutes |
Materials and Resources: |
Poster Paper or Poster with grid lines, sticky notes of different types, straight edge, markers, loose leaf graph paper, student may use their own devices or teacher issued graphing calculators. |
Technology Resources Needed: |
Computer with Internet access, LCD Projector and Document camera to share student paper or calculator work (helpful but not necessary). Smartview with calculator can be used too. |
Background/Preparation: |
Teacher:
Students:
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ENGAGE As students enter the classroom, they should be given a group indicator that tells where to sit. Inform the students that their mission will be to determine the inverse of linear functions. EXPLORE 1. Student groups should develop a table of values for each linear function assigned, reverse the coordinates, find the slope of this set of coordinates, develop equations for the coordinate sets, and graph both equations on the same axes. They should record these findings on their own paper (this information can be keyed into their graphing calculators). 2. The students should come back to the classroom and key their information into their graphing calculators (using the list key on the graphing calculator) to determine the slopes and equations. They should look for patterns of symmetry from graphs. The groups must agree on findings and be able to justify. 3. For students who are unable to find slopes and understand function inverses, provide necessary feedback to move them forward with their thinking. Refer to Slope (Rise over Run): https://www.youtube.com/watch?v=zTa0xTu9Yv4. (If your school system does not allow youtube access, you may download the video using http://www.keepvid.com/.) Refer to: http://www.coolmath.com/algebra/16-inverse-functions/05-how-to-find-the-inverse-of-a-function-01.htm EXPLAIN 1. The teacher should be sure that students are using graphing tables and slope correctly to develop equations. 2. Groups will discuss properties discovered and begin justifying their ideas as well as creating equations and graphs to match their tables in the calculator. 3. Allow students the time to prepare attractive posters to share with the class to begin discussions about Inverse functions and tables, along with having the groups share their findings using the Smartview function of the calculator. EVALUATE Use the provided rubric to assess student work individually and as a group. Students should justify all reasoning stated on the poster. The Assessment Process is on-going. The teacher should visit each group and ask questions to make sure students apply the properties of functions and their inverses. Display the posters in the classroom and have students present conclusions. As students present posters and graphing calculator findings, they should compare posters for other information not listed on their group's poster. |
Assessment Strategies |
Use the rubric provided to continuously assess student work individually and as a group. The teacher should visit each group and ask questions to make sure students apply the properties of functions and their inverses. |
Acceleration: |
Extensions can be to include understanding the process for algebraically finding inverses of functions and why the process works. Also, Does the process work for quadratic and higher functions? Justify the reasoning! |
Intervention: |
For extra practice or for students who were absent have them visit: http://www.mathsisfun.com/sets/function-inverse.html http://www.regentsprep.org/regents/math/algtrig/ATP8/inverselesson.htm |
View the Special Education resources for
instructional guidance in providing modifications and adaptations
for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.
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