Title: Family Ties - Familes of Functions (Linear, Exponential, Quadratic)

Author(s): Renee Yake, Tara Hartman, Michelle Herman

Subject Area: Algebra

Topic: Linear, Exponential, and Quadratic Functions

HSCEs or GLCEs: A2. 3. 1, A2. 3. 2, A2. 3. 3, and A2. 4. 1

Tags: Algebra, Exponential, Functions, Linear, Quadratic, applications, description, families, function, graph, More…table, verbal

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This is just what I needed! Thanks!
Hello Authors of Family Ties-Family of Functions,
I like this lesson plan you have created which allows students to compare and contrast the differences between the function families and their various representations ( graphic, verbal, table, and symbolic). I would like to use this lesson with my students with a few amendments. I will change the name of Iron Mountain to a more common name that my students will be able to identify. I will also change the problem involving playing soccer to basketball which my students will be able to relate to because they do not play soccer, but they do play basketball. I will use this lesson to create centers which will include each of the problems for students to explore and discuss amongst themselves in small groups of 3 - 4 students.
Each small group will be assigned one of the nine problems to present to the class on large chart paper.
This is a great written assessment to see how much students actually understand, in addition to a great way to review the function families.

Dear colleagues,

Thanks for posting your lesson plan on the AFA site.  I am in the course currently and like what you've done.  I appreciate that you've given very concrete examples of how we represent information, i.e., verbally, graphically, algebraically and numerically.  I am using your lesson plan with some changes for my 9th grade Algebra I class; I teach at a high school in Lansing with students with disabilities.  To adjust your lesson plan for my classroom, I have:

a.  added pieces of gum as a "hook" as they enter with their daily warm-up serving as an intro to the lesson.  (On the wall in our room are the various terms used in this exercise);

b.  shortened the problem sets to accommodate my learners' attention and time on task;

c.  adjusted the names and tasks to ones more familiar; and,

d.  allowed for whole group instruction rather than pairs/triads depending on the class.

Additionally, there will be an exit ticket where I can assess each student's daily learning.


Thanks for sharing this with me.  By the way, I'm originally from Iron River; loved the reference to Iron Mt. and Kingsford!


Mary Haas

Thank you Britt for sharing this lesson.  This lesson is a great way to have students work on higher level thinking skills.  It allows them to work on evaluation, analytical and synthesis skills.  It really reaches all types of learners and addresses a lot of the new Common Core Standards.  I really like that we all don't have to reinvent the wheel and this is a great forum to go for lessons.  I like the flexibility for students to work in groups and/or individually. 

Thanks for sharing!  I think I will start my Algebra II course this fall with the Family Ties lesson as a review.  It will provide me and with a great opportunity to formatively assess my students - and them with a chance to self-assess!  This lesson has both context and multiple representations, both characteristics of the functions-based approach to Algebra. 

I think I will use one of the problems as homework the day before the lesson and then begin the next day will a whole class discussion of the problem.  I will be sure to highlight function families, multiple representations, and context during the discussion.  Students will then work in cooperative groups on one of the other 8 problems, creating a poster to share with the class.  To wrap up the lesson, groups will present their results, comparing and contrasting with the results of other groups.  I think I'd like to assign some kind of graphic organizer as homework so that students are able to summarize their thoughts and reflect on their learning.

Thanks again for sharing your work.

Brit, I am working with the "Family Ties" lesson posted 3-15-10 for my summer section of Algebra for All (summer 2011).  I liked the variety of applications that were given in your 9 problem lesson.  I will be using this in an Algebra 2 class this fall or winter.  (It has been a while since I have taught Algebra 2, so I can't exactly predict when I will use the lesson.)  My preference on problem 7 was to give the verbal problem along with the equation that you had specified,  I was guessing that you wanted to give your class the challenge of writing their own word problem there.  Not knowing in advance how long it had been since we had covered exponentials I decided to have a problem to use if it is necessary. 


I also felt, since I will be teaching Algebra 2, that I could expand the number of families studied in this lesson to four, the logarithm family.  Being a science teacher, logarithms have several applications in science, I have only included the Richter Scale application with the equation and data.  My preference is to let the class work on the graph as a way to learn more about logs.  I also give a comparison of two Richter Scale measurements (for 20th century San Francisco earthquakes) that students should be able to answer using their graphs, or the equation given.  Thanks for the lesson that you posted and the nine problems for the student handout.

I really like this lesson and I plan to use it with my students this fall. I will use it at the beginning of the school year when we discuss what is a function, domain and range, and families of functions as introduction to the topics we will cover for the year. I think it will work well at the beginning with my Algebra 1 students because they have already been exposed to linear equations and adding quadratics and exponentials will allow my students explore future topics in the context of what a function is and trends in the shapes of functions based on their type.


Some changes I am going to make include allowing the students to work in groups. The group members will be assigned specific tasks. The use of technology will allow the entire class to participate. I have access to the N-Spires with the Navigator system so students can provide instant feedback to their fellow classmates. The technology also gives me an opportunity to include an informal formative assessment addition to the summative assessment that will be included at the end. 


I like to use the examples that students provide from the activities as posters in the classroom, so I like them to present their group activity to the class and get approval as to its accuracy before students transfer the information to the chart paper (eliminates waste during a time when budgets are already tight and chart paper can become a luxury item).

I really like this lesson.  Thanks for sharing.  I especially like the fact of how easily one could modify the actually problem.  Thus, the treasure is in the worksheet you created.  Thanks again.

This lesson has 9 application problems in a nice format.  Each problem has section for a verbal description, equation, table and graph.  The problems all have different starting points. Some start with the description, some with the table, some with the equation.  Thanks for sharing!

Thank you so much for sharing your work with this lesson. I love how neat and clean it feels. I have special ed and ELL students that can get very overwhelmed. This will be a great lesson for everyone in my class. I have included it on my website as a test review. Thanks again! http://algebra1teachers.com/Unit1week4.html


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