Lesson Title: Building Polynomial Functions: Addition, Subtraction, Composition Course: CC Algebra II, Unit 4
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
Build a function that models a relationship between two quantities.
F.BF.A.1 Write a function that describes a relationship between two quantities.
b. Combine standard function types using arithmetic operations.
Perform arithmetic operations on polynomials.
A.APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the
operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
MP1:
MP2:
MP3:
MP5:
MP6:
MP7:
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.
Common Core Algebra II, Unit 4
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Perform the following operations on the given
functions:
f (x)  2x 2  4 x  3
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.
To be determined by teacher
g(x)  5x  9
h(x)  4 x 2
1.
2.
3.
4.
f (x)  g(x)
f (x)  g(x)
h(x)  g(x)
g h(x)
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
Building Polynomial Functions: Addition, Subtraction, and Composition
1. Assign students to groups of 3-4. Have students work collaboratively on Scenario 1 from the Building
Polynomials activity. (See Building Polynomials PowerPoint. Each scenario should be completed and discussed
before moving on to the next one.)
2. Facilitate student-led small-group discussions. (Use some of the suggestions on the teacher resource sheet to
help facilitate the discussion. Be sure to touch on what happens when two functions are added, subtracted, or
composed.) (Teacher Resource: Building Polynomials) (Look for evidence of MP1, MP2, MP3, MP5, MP6, and
MP7.)
3. Select one student from each group to share the approach that his/her group used to write the function. After the
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Building Polynomial Functions: Addition, Subtraction, Composition Course: CC Algebra II, Unit 4
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
students share, debrief the class to pull together big ideas. (Look for evidence of MP2, MP3, and MP6.)
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 success? 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 should be able to apply addition, subtraction, and composition of functions when given a scenario.
Students should be able to write a new function using the given scenarios. Students should be able to simplify
polynomial expressions within each of the functions created in the scenarios.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
This is a follow-up lesson for students to practice applying addition, subtraction, and composition of functions.
Composition of functions:
1. Students may need reminders about function notation.
2. Students may have some difficulty with information presented as an application.
3. Students may have some difficulty recognizing how to apply the functions provided within the application
scenarios.
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?
Teacher Resource: Building Polynomials PPT
Building Polynomials Student Resource
LCD Projector
Calculators
To be determined by teacher
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Were the students able to identify the appropriate operations from the given scenarios? Were the students able to
successfully create a function given the information in the scenarios? Were the students able to explain how they
created the functions from the given scenarios?
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 (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.