Lesson Title: Comparing Offers 8.F.A.2
Date: _________
Teacher(s): ____________________
Course: Common Core Mathematics 8
Start/end times: 2 50-minute classes
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions.) For example, given a linear function represented by a table of
values and a linear function represented by an algebraic expression, determine which function has the greater rate
of change.
MP1:
MP2:
MP3:
MP5:
MP6:
MP7:
MP8:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Have students complete a think-pair-share review of
their understanding of the following terms:
 function
 table of values
 rate of change
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.
Take class data on the number of students who would
accept Mr. Jones’s job offer vs. the number of students
who would not accept the offer. Have a conversation
with students as to why they think their classmates would
or would not have taken the job offer.
(Look for evidence of MP3.)
(Look for evidence of MP3.)
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. Have students think back to the previous lesson and the part-time job yard work scenario. Consider having a few
of the group posters from the Gallery Walk from lesson 8.F.A.1 (Lesson 2 Show me the money) still displayed in
the classroom for the Lesson Launch and the opening activity.
2. Introduce the new scenario: One of your neighbors, Mr. Jones, is interested in hiring you on a part-time basis to
help with yard work such as raking, weeding, and shoveling in the winter. However, he wants to pay you $10 to
come to his house to work and then $8 for each hour you are working instead of $12 an hour. Your parents are
encouraging you to take Mr. Jones’s offer. You are not so sure…
3. As a class have students discuss their initial reaction to Mr. Jones’s offer. Have students brainstorm the equation
for this situation. Display the possible equations on the board for students to reference. Then have students
break into pairs for the Stations Activity. (Look for evidence of MP2.)
4. Each pair will start at one of the two stations. There will be two choices at each of the stations. The Technology
Station will have a Graphing Functions Applet Activity on the computer and a Graphing Calculator Activity.
Pairs will have to choose between one of these two choices at the Technology Station. The Graphing Station
will have Peg Boards or Geo Boards as one option and graph paper as another option to graph both functions.
Pairs will have to choose between one of these two choices at the Graphing Station. Partners can use the multiple
representations graphic organizer to record their investigations as they move through the stations. Another
option is to have students record key information, table, graph, etc. in their math notebooks. Students will need
to use this information at the end of the lesson to help them make a decision and present the information to the
class. (Look for evidence of MP5.)
5. Before you send the students to the station activities, be sure to explain each station and state the goal of each
activity.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Comparing Offers 8.F.A.2
Course: Common Core Mathematics 8
Date: _________
Teacher(s): ____________________
Start/end times: 2 50-minute classes
Station Activities: (Look for evidence of MP1, MP2, MP6, and MP7).
Technology Station:
a.
Graphing Function Applet Activity – Using the given scenario, pairs will complete the graphing
investigation on the computer applet (http://cs.jsu.edu/~leathrum/Mathlets/grapher.html). Consider having
the following questions on a sheet for students to answer as a pair: What do the graphs look like? Have
them draw a sketch of the graphs. Have students write a conjecture based on what they have seen with the
graphs of the two functions. Have students consider the realistic values for x and y. Have students find the
y-intercept for both functions.
b. Graphing Calculator Activity – Pairs will use the graphing calculators to graph the functions. Pairs will
enter the equations into the calculator. What do the graphs look like? Have them draw a sketch of the
graphs. Have students write a conjecture based on what they have seen with the graphs of the two functions.
Teachers should help students adjust the window so the x-min and y-min are zero, since you cannot have
negative values. Have students consider the reasoning behind values being less than zero. Since x-max is
the number of hours worked, have students think about realistic values.
Graphing Station:
a. Peg Boards or Geo Boards – Pairs will create a table of values for the two scenarios on a separate sheet of
paper. (Students can use the table of values for y  12x from the previous lesson.) Students should plot the
values for each equation using pegs or rubber bands of different colors. Have students identify the yintercepts for both functions. Ask students to compare the table of values for each function. What do they
notice about both graphs?
of values for the two scenarios. (Students can use the table of values
b. Graph Paper – Pairs will create a table
for y  12x from the previous lesson.) Students should plot the values for each equation using graph paper.
Students can use colored pencils to show the two different graphs. Have students identify the y-intercepts
for both functions. Ask students to compare the table of values for each function. What do they notice
about both graphs? Students should realize that Mr. Jones’ offer has an initial feel of $10 for just coming to

do the yard work and then an hourly rate of $8 per hour, where your initial offer just has an hourly rate of
$12 per hour with not initial fee for just coming to do the work.
6. If students need more time, you can have them go back to a station for clarification.
7. Once students have completed the Station Activities, have students get into groups of four to five. Have students
create a visual representation and summary to present to their parents to explain why you are going to accept or
not accept Mr. Jones’s offer. The representation must include and address the differences in tables, graphs,
equations, and scenarios. Students may draw by hand using a poster, or create on a computer by making a Glog
(http://edu.gloster.com/), or a word file. (Look for evidence of MP3.)
8. Have each group present their summary of information and decision regarding the job offer to the class.
9. Take class data on the number of students who would accept Mr. Jones’ job offer vs. the number of students who
would not accept the offer. Have a conversation with students as to why they think their classmates would have
choose to work for Mr. Jones or not. (Look for evidence of MP2, MP3, and MP8.)
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 decide if it is a better business decision to take Mr. Jones’ job offer. Is it the best choice for
them? Why or Why not?
Students will be able to explain and compare both equations and what the mean in the context of the problem.
Students should be able to explain what the initial fee means for Mr. Jones’ offer and how that is different from your
original charge to the neighbors.
Students should notice that for the first two hours of work, Mr. Jones’ offer is the better option, meaning that you
will make more money than your original wages of $12 per hour. However, for any hours you work after two hours,
you are making less money with Mr. Jones’ offer. Students will need to consider this in their conclusion summary
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Comparing Offers 8.F.A.2
Course: Common Core Mathematics 8
Date: _________
Teacher(s): ____________________
Start/end times: 2 50-minute classes
for their presentation. One thing for students to consider is the potential number of hours of work on Mr. Jones’
yard.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Key Vocabulary: rate of change, initial value, slope
Connections: Students will need to connect to their prior understanding of slope and y-intercept from standards
8.EE.B.5 and 8.EE.B.6. Students will also need to connect to their prior understanding of input, output, and function
tables from standard 8.F.A.1.
Misconceptions: Students may confuse the y-intercept with the x-intercept. You may need to help students
understand that when x  0 , the point is on the, the point is on the y-axis that is why that point is called a yintercept. When dealing with a real world scenario, students may have difficulty understanding what the y-intercept
means in the context of the problem. In this case, Mr. Jones, will be paying you an initial fee of $10 for just showing
up to work on his yard.

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?
Initial scenario and Mr. Jones’s scenario
Multiple representations graphic organizer
Colored pencils
Graph paper
Chart paper
Markers
Computer
Glogster accounts
If you choose to accept Mr. Jones’s offer, write an
acceptance proposal to Mr. Jones. If you did not choose
to accept his offer, explain why and offer a counter
proposal in your favor. What might be a reasonable offer
to bring back to Mr. Jones? (Students may use their
journal or computer.)
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 the students understand how to create a table of values and graph functions?
Are students able to understand the rate of change (slope) and y-intercept in different real world scenarios?
How will I differentiate upcoming lessons to meet the needs of the various learners in my class?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.