Instructor: Elizabeth Proll
9th grade Algebra 1 Common Core
Lesson Title: Linear vs. Exponential Function Word Problems
Date: Wednesday, November 19th
1. LESSON CONTEXT AND RATIONALE
Culture and Context
The target class population consists of nine students, with 44% Hispanic, 33% Black,
and 22% Caucasian and 66.6% of which receive free or reduced lunch.
I have designed this lesson to reinforce problem solving when approached with a
word problem. We have currently covered a unit on both linear and exponential
functions, which both included solving word problems. Our current “mini” unit is
comparing linear functions to exponential functions, and thus is the focus of the word
problems presented to the class. Throughout the school year, I have encouraged and
helped my students begin forming positive attitudes towards mathematics in order
to enhance lesson meaning through dialogue based on prior knowledge and
experiences of the students’ (Wlodkowski & Ginsberg, 1995). During this lesson
along with my assistance, students will review their knowledge of how to set up both
linear and exponential equations, as well as determine which equation is the most
appropriate to use from the verbal description given. Word problems are very
relevant to the real world, as they are examples that the students themselves may
someday encounter, in variation to be given an equation, table, or graph. This lesson
relates such real world examples to the lives of students and asks them to use
mathematics in order to arrive at a solution.
Identity and
Intellectual
Development
This lesson offers students an opportunity to compare and contrast linear and
exponential function word problems. Key words to represent each kind of function
will be presented, as a problem solving technique, as well as assistance setting up the
equation based off the given information in the word problem. Furthermore, this
lesson promotes conceptual understanding which pertains to the everyday life of all
students.
Lesson Rationale
This lesson is the concluding lesson to our current “mini” unit of comparing linear
and exponential functions to one another. We have previously focused two units on
linear and exponential functions separately, and this unit is a combination of the two
former. We have focused the past week on comparing equations, graphs, and tables
of both linear and exponential functions and thus will conclude with word problem
comparisons. The following day of class will consist of a test review day leading up to
this unit test the day after.
My intent for teaching this topic in this manner is that I have recently experimented
with small group, whole class, and individual classroom assignments. While students
work in groups, I have observed that they are often off task unless I am assisting
their group directly and get confused often and easily. Additionally, when assigned
individual work, the students do not demonstrate appropriate autonomy, and
instead feel as though they are able to chat with their friends and complete any
assigned class work for homework instead. Therefore, these notes and classroom
discussion will be delivered whole group, but still not teacher-centered. I plan to ask
many questions of my students and encourage discussion of the differences between
linear and exponential functions.
Management
During this lesson, the students will transition from an individual warm up activity,
to whole group notes/discussion. In order to transition students between each
lesson component, I will make sure to warn students of the upcoming transitions
with time limit warnings and ensure that directions are clearly explained. Specifically
for the warm up, a timer will be presented on the board with a countdown from two
minutes to ensure students are aware of their remaining time to complete the
problem.
Instructor: Elizabeth Proll
9th grade Algebra 1 Common Core
Lesson Title: Linear vs. Exponential Function Word Problems
Date: Wednesday, November 19th
2.
STANDARDS & REQUIREMENTS
CCGSP or GPS
Standard(s)
MCC9-12.F.IF.1 Compare properties of two functions, each represented in a different
way (algebraically, graphically, numerically, in tables, or by verbal descriptions).
MCC9-12.F.BF.1 Write a function that describes a relationship between two
quantities.
MCC9-12.F.LE.1 Distinguish between situations that can be modeled with linear
functions and with exponential functions.
Individual Education As this is a mathematics resource class, each student in this class has individual
education plan goals. The majority of the target class population have not met a
Plan Goal(s) and
standard score on middle grades CRCT testing and have also scored below average on
Benchmarks
the Wechsler Individual Achievement Test in mathematics. Additionally, a majority of
the students within this class have curriculum mastery goals outlined in their
individual education plans, such as evaluating and performing operations with real
numbers and algebraic expressions/equations as measured by 80% accuracy.
Modification(s)
/Accommodation(s)
All students are offered access to the use of a calculator, as defined in their IEP
accommodations. Additionally, the majority of students within this class are
provided with breaking material into manageable parts, additional time to respond,
extra time if effort is shown, and checking work frequently to ensure understanding.
Several students also require giving short and concise directions, providing a copy of
all notes/study guides, graphic organizers, reading aloud, as well as presenting
information visually.
Differentiation
Each student will participate in the whole group discussion/note taking. I will
observe student work for understanding and learning, give multiple means of
representation, and promote autonomy of each student in order for all to be
successful. “One approach to meeting each student’s needs is to provide tasks within
each student’s zone of proximal development and to ensure that each student in the
class has the opportunity to make a meaningful contribution to the class community
of learners… instruction within the zone of proximal development allows students,
whether with guidance from the teacher or by working with other students, to access
new ideas that are beyond what the students know but within their reach” (Small,
2010, p. 2). I often call on students to answer questions aloud, beginning with a
question that I know they are capable of answering. Then, I continue to ask them
questions to arrive at a more difficult answer, that requires deeper conceptual
thinking, thus enhancing their zone of proximal development.
3. RESOURCES
Academic Language
The key language demand of this lesson is writing and speaking. Each student will
discuss with the teacher and their peers to solve the given example word problems.
Language Functions
The primary language functions of this lesson are to predict, evaluate, and explain.
Each student pair will predict whether they feel the given problem represents a
linear or exponential function, write the appropriate equation in response, and
finally check their work to ensure they have the correct equation.
Language
Vocabulary
Key Vocabulary to be used throughout this lesson:
Exponent
Variable
Y-Intercept
Interest
Slope
Equation
Decay
Power
Coefficient
Rate
Growth
Instructor: Elizabeth Proll
Lesson Title: Linear vs. Exponential Function Word Problems
 Class Notes and Homework assignment
Materials
9th grade Algebra 1 Common Core
Date: Wednesday, November 19th
 Calculator
 Projector
Technology
Promethean Board- Unfortunately, the use of the classroom Promethean Board is
unavailable for this lesson as the smart board pen is unresponsive when attempted
to use.
Calculator- All students will have access to the use of a calculator if needed. A
majority of the students have an accommodation of a calculator, which are kept at
the front of the classroom for easy access.
4. LESSON PROCEDURE
Enduring
Understanding
Understand how to interpret linear and exponential functions that arise in
applications in terms of the context.
Understand how to construct and compare linear and exponential models and solve
problems.
Understand how to interpret expressions for functions in terms of the situation they
model.
Essential
Question(s)
How do I interpret functions that arise in applications in terms of context?
How do I build a linear or exponential function that models a relationship between
two quantities?
How can we use real-world situations to construct and compare linear and
exponential models and solve problems?
Lesson Objective(s)
Students will construct and compare linear and exponential models and preserve in
solving them using real-world contexts.
Assessment Link
Students will demonstrate their learning by completing their homework to compare
linear and exponential models as they write functions to describe linear or
exponential relationships between two quantities.
Introduction to
Lesson
A warm up will be presented at the opening of the class period which asks students
to examine a table of values and determine if the relationship is linear or exponential
as well as write an equation to express the relationship. This warm activity is
relevant due to the need to interpret and compare linear vs. exponential functions
using multiple representations: graphs, equations, tables, and verbal descriptions.
Following the warm up activity which reinforces prior student knowledge, I will
distribute the class notes for the day and begin the discussion to compare linear and
exponential verbal descriptions.
The introduction/warm up activity should take no more than 5 minutes to complete.
Body of Lesson
Students will participate in the whole group discussion of linear and exponential
word problems. I will use Socratic questioning in order for the work and problem
solving to be student-centered, as I guide them towards the end goal. I will also
circulate the room and oversee dialogue and student work individually. The group
discussion and student participation will also be used to assess student
comprehension.
The body of the lesson will take approximately 30 minutes to complete, depending on
student needs and level of comprehension.
9th grade Algebra 1 Common Core
Instructor: Elizabeth Proll
Lesson Title: Linear vs. Exponential Function Word Problems
Date: Wednesday, November 19th
Students will summarize what they have learned through filling in a comparison
Closure
chart of things to look for in word problems regarding linear and exponential
functions. The closing discussion should take approximately 5 to 10 minutes to
complete.
If any additional class time remains at the conclusion of the days notes, I will
distribute the homework assignment to each student and use it as a ticket out the
door instead.
Students will also be assigned an additional homework assignment of a test review
guide in order to begin preparing for their test on Friday. The review should be
started this evening so that questions may be asked the day before the test for
clarification.
5. ASSESSMENT
Evaluation
(Assessment Plan
for IEP Goals and/or
504 Plans)
I will assess student learning through evaluating student participation, conceptual
understanding, and appropriate language use as they discuss and answer questions
with myself and the whole class. Feedback will be provided when questions are
answered, as well as when I circulate the classroom and observe student work. The
student homework assigned for the evening is an additional form of assessment,
which will include additional feedback during its return, while a summative
assessment will be given in two days at the conclusion of the current unit.
6. REFLECTION
Analyzing Teaching
Effectiveness
References
Small, M. & Lin, A. (2010). More Good questions: Great Ways to differentiate secondary
mathematics instruction, Ch.1: Why and how to differentiate math instruction, 1-16.
Teacher College Press: USA.
Wlodkowski, R. & Ginsberg, M.B.J. (1995). A framework for culturally responsive teaching.
Strengthening Student Engagement, 53(1), pp. 17-21.