Lesson Title: ______8.F.3 Function Families____
Date: _____________ Teacher(s): ______________
Course: ___CCM8_____________
Start/end times: __2 -50 minute class periods__
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
8.F.3 Interpret the equation y  mx  b as defining a linear function, whose graph is a straight line; give examples
of functions that are not linear. For example, the function A  s 2 giving the area of a square as a function of its side
length is not linear because its graph contains points (1,1), (2,4), and (3,9), which are not on a straight line.

Lesson Launch Notes:
Exactly how will you use the

first five minutes of the lesson?
Think-Pair-Share Activity:
Have students think about all the different ways that we
can represent functions and the key defining
characteristics for each representation. Have students
partner with each other to discuss their ideas and then
have partners share out one idea to the whole group.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.
Have students create a set of graphs for a function family.
Have them also create an answer key for the graphs for the
function family they choose.
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson?
1. Place students in groups of 3-4. Students are going to be participating in an activity called Examining Function
Families – Which Does Not Belong?
2. Give two groups the set of linear functions, give two groups the set of quadratic functions, and give two groups a
set of exponential functions.
3. Each group is going to have the same task, but with a different function family. Each group of students is going
to come up with a table of values using the range of the following x-values 3,2,1,0,1,2,3. Once the
students have created a table of values have them graph each of the functions in the set on the graphs provided
on the Function Family Student Resource Sheet. Students can have the option here to look at the functions
graphed by using a graphing calculator, or using the website: http://www.mathsisfun.com/data/functiongrapher.php

Students are then going to describe the graphs by answering the following questions:
a. What do the graphs have in common?
b. Which graph is different?
c. Which graph doesn’t belong in this function family?
d. What looks different about the graph, and the equation?
e. Is your function family linear, quadratic, or exponential?
Consider having these questions on the tables for each of the groups or on the board for students to refer to during
the activity. Question e might be difficult for the quadratic group if they have never worked with quadratic
functions in name. Consider using questioning to help the students understand the meaning of quadratic functions.
4. Allow about 20 -25 minutes for each group to complete the activity by graphing the set of functions and
answering the provided questions.
5. Once all groups have finished, combine the two groups with linear function families together, the two groups
with quadratic function families together, and the two groups with exponential function families together. Now
you should have your class into three larger groups, one for each function family.
6. Distribute a sheet of chart paper to each group. Have the students sketch the graphs of their function family on
the chart paper along with the “one that doesn’t belong” and their rationale as to why this graph does not belong
in this function family. Explain to students that they are going to be presenting their function family to the class.
The group should select students to be the recorders and some students to be the presenters. Another option for
students would be to allow them to use Glogster http://www.glogster.com/ to create an online poster on their
function family.
7. Select the group representing the Linear Function Family to present first. Have students present the graphs and
the “one that doesn’t belong” and why to the class. Have students place their chart paper on the board for
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: ______8.F.3 Function Families____
Course: ___CCM8_____________
Date: _____________ Teacher(s): ______________ Start/end times: __2 -50 minute class periods__
display.
8. Next, select the group representing the Quadratic Function Family to present to the class. Once this group has
presented their information, draw a Venn diagram on the board or document camera. Have the students compare
the two function families posted on the board. Ask students to define which function family is linear? And
which function family is quadratic? Label these as each one of the circles in the Venn diagram. (See below)
Have students complete the Venn diagram as a class comparing the key features of Linear Function Families to
Quadratic Function Families. Enccourage students to think about the many ways they are similar and different
in terms of the equations and graphical representations. The differences should be filled in the outer parts of the
circle and their similarities should be placed in the inner and adjoining parts of the circles.
9. Select the Exponential Function Family group as the final group to present to the class. Once this group has
presented their information, draw a second Venn diagram with three adjoining circles on the board or document
camera. Have the students compare the three function families posted on the board. Have students complete the
Venn diagram as a class comparing the key features of Linear Function Families to Quadratic Function Families
to Exponential Function Families. Encourage students to think about the many ways these function families are
similar and different in terms of the equations and graphical representations. The differences should be filled in
the outer parts of the circle and their similarities should be placed in the inner and adjoining parts of the circles.
10. Leave the chart paper for each function family and the Venn Diagrams comparing the function families as
visuals around the room for the remainder of this lesson.
11. Bring students together as a whole class and make sure each student has a graphing calculator. Write the
2
quadratic function: y  4 x  6 on the board. Ask students, “Which function family would this equation belong
to and why?” Have students graph this function in the y= function of the graphing calculator and then press
graph. Have all students look at the graph on the graphing calculator, this might be a good time to talk about the
vertex of the graph and it’s location for quadratic functions with students.
 explain to students how they can find the table of values for any function by selecting 2nd Graph
12. From here,
function on the graphing calculator allowing you to go to view the table of values. Also, take the time to show
students how to find an exact value for x, by using the 2nd Window, which is the Table Set function on the
graphing calculator allowing you to select the exact value for x where you would want Table view to begin.
Ask students why this might be an important or useful feature for graphing functions.
13. Distribute the Function Families Summary Resource Sheet to students. Allow students to work in pairs to
complete the summary sheet for their notes. Have pairs partner with other pairs when they have finished to share
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: ______8.F.3 Function Families____
Course: ___CCM8_____________
Date: _____________ Teacher(s): ______________ Start/end times: __2 -50 minute class periods__
their work and make sure their graphs, and key features are correct. Consider going over the summary sheet as
a whole class share out as well.
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student mastery? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened (and conceptual) understanding.
Students will be able to use their knowledge of multiple representations of functions to graph several equations and
describe the key similarities and differences of the equations and graphs. Also, students will be using graphing
calculators to graph functions and to find the table of values. Students will be able to articulate the differences
between three function families: linear, quadratic, and exponential.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Key Vocabulary: linear functions, quadratic functions, exponential functions, function families
Connections: Students will have to make connections to 8.F.1 and the multiple representations of functions. They
will also need to recall strategies for creating a table of values and graphing them to make a function. Students will
need to be proficient in graphing for this lesson.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Examining Function Families – Which Does Not
Belong Resource Sheet
Linear Function Families Resource Sheet
Quadratic Function Families Resource Sheet
Exponential Function Families Resource Sheet
Function Families Venn Diagram Resource Sheet
Function Families Summary Resource Sheet
Graphing Calculators
Computer with Internet access
Glogster
Document Camera
Chart Paper
Markers
Graph Paper (optional)
One option would be to have the students trade their set of
function family graphs from the closure and then complete
the activity we did in class using their peer created
function family sets.
A second option would be to have students use Glogster
http://www.glogster.com/ to create an online
advertisement poster for the function family of their
choice but not the function family they completed the
poster for in class.
Lesson Reflections: What questions, connected to the lesson objectives and evidence of success, will you use to
reflect on the effectiveness of this lesson?
How well do my students understand the differences in the three function families presented?
Are my students able to identify functions based on their equations?
Are my students able to identify functions based on their graphs?
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.