Summary
Students will define function, domain, and range and apply these concepts to a variety of relations.
Essential Question(s)
How can we represent relations between quantities?
Snapshot
Engage
Students will consider three everyday objects that can be considered functions.
Explore
Students will consult multiple texts to create their own definitions of function, domain, and range.
Explain
Students will share their definitions and critique the definitions of others.
Extend
Students will apply their definitions to several examples of relations.
Evaluate
Students will watch a video and write an argument about why the Google search engine is or is not a function.
Materials
Function Junction PowerPoint (attached)
Function Junction Explore Handout (attached; 1 per student)
Internet access for video
Small whiteboards or dry-erase pockets (1 per every 4 students)
Dry erase markers
Engage
Go to slide 2 to introduce the essential questions and then to slide 3 to introduce the lesson objectives to students.
Go to slide 4, have students complete a Think-Pair-Share strategy to answer this question. Give students several minutes to think on their own and several more minutes to share with a partner. Then call on several pairs to share their thoughts.
Go to slide 5, review the answers to the "riddle." All of the objects can be considered functions. Ask students to share what they recall about functions.
Explore
Pass out the Explore Handout. Have students work in pairs to review the descriptions given on the handout and create definitions for function, domain, and range.
Explain
Have between three and five groups share their definitions of function. Record the definitions on the PowerPoint, chart paper, or whiteboard. Have other pairs compare and contrast the definitions created. Have the class work together to create one class definition of a function.
Repeat the above procedure with the terms domain and range.
Review slides 8-10 on the PowerPoint to reinforce the meaning of these three terms.
Extend
Group two pairs of students together to form groups of four. Each group of four is a "team." Review the rules of the game "What's My Rule?" on slide 11 with students. Play each round of "What's My Rule?" on the following slides. For each round, pick one or two groups to share how they decided what the rule was, if it was a function, and if so, what the domain and range were. Continue playing rounds until you are convinced most students understand what a function is.
Evaluate
Advance to the last slide of the PowerPoint (slide 21). Tell students they will need to be able to answer this question based on what they are about to hear in the video.
Click the link to show the video.
After the video is complete, have students write a Two-Minute Paper in response to the prompt on the screen.
Resources
Collins, W. (2001). Mathematics applications and connections: Course 2. New York: Glencoe McGraw Hill.
Davidson, D. M. et al. (2001). Pre-algebra: Tools for a changing world. Needham: Prentice Hall.
YouTube Video "How Search Works": Google. (2010, March 4). How search works [Video file]. Retrieved from https://www.youtube.com/watch?v=BNHR6IQJGZs
Two-Minute Paper Instructional Strategy: K20 Center. (n.d.). Two-minute paper. Instructional Strategies. Copyright 2015 Board of Regents of the University of Oklahoma. Retrieved from https://learn.k20center.ou.edu/strategy/d9908066f654727934df7bf4f506cf73
Think-Pair-Share Instructional Strategy: K20 Center. (n.d.). Think-pair-share. Instructional Strategies. Copyright 2015 Board of Regents of the University of Oklahoma. Retrieved from https://learn.k20center.ou.edu/strategy/d9908066f654727934df7bf4f5064b49
Sullivan, M. (2002). College algebra (6th ed.). Upper Saddle River: Prentice Hall.
Sullivan, M. & Sullivan, M., III. (2000). Precalculus: Enhanced with graphing utilities (2nd ed.). Upper Saddle River: Prentice Hall.