SUBJECT: Mathematics
GRADE LEVEL: 8/Rm. 205
NUMBER OF STUDENTS: 19
LESSON DURATION: 82 minutes
TITLE: 7.7 Normal Form
STANDARDS:
CCSS – Mathematical Practices
 MP1 – Make sense of problems and persevere in solving them.
 MP2 – Reason abstractly and quantitatively.
 MP4 – Model with mathematics.
OBJECTIVES:
 All students will be able to:
o expand polynomials and express them in normal form.
o determine whether polynomials in different forms are equivalent.
VOCABULARY
 normal form
MATERIALS/RESOURCES:
 CME Project Algebra 1
 Document Camera (ELMO)
 Math notebook
 Pencil
 Calculator
 Polynomials – Standard Form worksheet
 Polynomials Challenge Sheet
 Lesson 7.7 Quiz (problem 1)
LESSON INSTRUCTIONAL PROCEDURES
- Go over the homework from the night before (Polynomials Worksheet).
- Discuss any problems students struggled with.
A. Introduction (motivation/warm-up/lead-in)
 Have students explain how these are similar: x 1x 1  x 2 1 & 3 5  4 2 1
 What is this called? x 1x 1  x 2 1 (Identity: a statement where two
expressions are equivalent)


B. Development: Instruction and Activities

 Have the students
read through Minds in Action: episode 29. Two students will take
roles as Sasha and Tony.
 Sasha and Tony say that they proved the identity to be true. Sasha came up with the
following: x 3  2x 2  3x 1 and Tony came up with this: 3x  3x 2  x 3 1. Are their
equations equivalent?
?


x 3  2x 2  3x 1 3x  3x 2  x 3 1
Can
to make them easier to compare?
 you think of a method for organizing polynomials


- Arrange the terms by degree from highest to lowest
Have the students work on #7 in For You to Do:
-Are the following polynomial expressions equivalent?
3x  7x 4  2x 2  6  3x 2  x 4  210  23x 4  2x 2  x  3x 2  x 6
Discuss how to arrange the monomials in order. Discuss normal form (standard form).
- Polynomials are often written with the largest degree at the beginning.
- To write a polynomial in one variable in normal form, expand it completely and
arrange the monomials by degree from largest to smallest.
Discuss which of the following examples are in normal form (standard form). If the
polynomial is not in normal form, rewrite it in normal form.
1
- 7x 3  3x 2  x  5
- y 2 1y 1
2
1
- 5  3x 2  x  7x 3
- x 2  3x  9
2
If time permits, have students complete
 the following:
Here is a polynomial.

7x 10 16x 3  5x 2  6x 4 10x
a. Write the polynomial in normal form.
b. What is the degree of the polynomial?
c. What is the coefficient of x?

d. What is the coefficient of x 4 ?
e. Find a polynomial that when added to this one gives a sum of degree 3.
?






C. Differentiated Instruction

 ELL Students
- Allow students to work in pairs or in their small groups (table groups).
 Special Education – mild-moderate memory and processing learning disability
- Provide students with tiered questioning to help them build upon the main concept
of the lesson.
- Allow students to work in pairs or in their small groups (table groups).
 Talented and Gifted
- Challenge students by having them complete Polynomials Challenge Sheet.
D. Closure
 What was important about today’s lesson? OR If I asked you to write one thing about the
lesson, what would you say was important?
- Have students turn and talk about the lesson for 30 seconds and then come back to
the class. Discuss their answers.
- Why is it important to understand “normal form”?
 Provide students at least 10 minutes to begin the homework.
- HW Polynomials – Standard Form worksheet (18 problems-Due Monday along with
the Ch. 7 Mid-Chapter Test)
DIFFERENTIATED ASSESSMENT for ELL, LD, Gifted, and General Education


Informal: While the students work, walk around the room making sure students are on
task and are actively engaged in learning. Look for correct answers and anything that may
need further explanation or if it is something that should be shared with the class.
Formal: Students will complete Polynomials – Standard Form worksheet (18 problemsDue Monday along with the Ch. 7 Mid-Chapter Test) for homework.
REFERENCES AND RESOURCES
 CME Project Algebra 1, Teacher’s Edition