Title of Unit
Curriculum Area
Developed By
Exponents & Polynomials
Algebra I
Lauren McCloskey
Grade Level
Time Frame
7/8
2-3 weeks
Identify Desired Results (Stage 1)
Content Standards
A-APR.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. N-RN. 1.Explain how the definition of the meaning of rational exponents follows from extending the properties of integer
exponents to those values, allowing for a notation for radicals in terms of rational exponents. 2.Rewrite expressions involving radicals and rational exponents using the
properties of exponents.
Understandings
Essential Questions
Overarching Understanding
Overarching
Students will understand the rules of exponents (zero and negative exponents and
operations using exponents) and why they work the way they do.
Students will understand how exponents can be valuable in representing situations
mathematically.
Students will be able to perform operations between polynomials (addition,
subtraction, and multiplication) and understand that they must be common
denominators.
Students will recognize special products of binomials through patterns.
Related Misconceptions
Students often confuse the different rules of exponents when simplifying
expressions.
Students often combine “unlike terms” when dealing with polynomials.
Students will struggle to FOIL two binomials together, forgetting all of the pieces.
Students will struggle to fully simplify when dealing with exponents and
polynomials.
Students may struggle to recognize when a situation is exponential.
Knowledge
How can we use exponents to
represent real world situations?
How can we use patterns to
determine rules in math?
How can you communicate your
mathematical thinking about
patterns clearly?
Topical
How do the rules of exponents
help us to combine exponential
expressions with addition,
subtraction, multiplication, and
division?
How do we use our
mathematical knowledge of
multiplication when dealing with
polynomials?
How do you deal with combining
polynomials with addition or
subtraction?
Objectives
Skills
Students will know…
Students will be able to…
Students
Students
Students
Students
Students
product.
Students will be able to simplify expressions with negative and zero
exponents.
Students will be able to perform operations between expressions
with exponents.
Students will be able to perform operations between polynomials
(adding, subtracting, multiplying)
will
will
will
will
will
know
know
know
know
know
what a negative and zero exponent means.
what a polynomial is.
the rules of simplifying polynomials.
what a polynomial looks like.
when multiplying two binomials together results in a special
Assessment Evidence (Stage 2)
Performance Task Description
Goal
Role
Audience
Situation
Product/Performance
Standards
Assess students knowledge of exponent operations and polynomial operations.
Chapter 7 Quiz & Test
Koponen (mentor) and McCloskey (intern)
One class period. In the usual classroom.
Completed test.
Listed above under Content Standards.
Other Evidence
Homework quizzes, exit slips, clicker responses, discussions, and group work
Learning Plan (Stage 3)
Day in Unit
Lesson
Topic
1
(7-3)
Exponent
Rules
2-3
Exponential
Units
4
(7-1)
Integer
Lesson Learning Objective
Description of how lesson
contributes to unit-level
objectives
Assessment activities
Students use patterns to
determine the rules of
exponents.
Students work on their own to write
out the repeated multiplication that
creates an exponential expression to
determine the rules of combining
exponential expressions in
multiplication, power to a power,
and a group to a power.
Students practice their volume,
surface area, area, and
perimeter skills and apply them
with monomials expressions as
the lengths, widths, and heights
of shapes
Measuring the room and finding p,
a, sa, v. using monomial dimensions
finding p, a. day 2 finding sa, v
using monomial dimensions
Students create an exponential
function by looking at patterns
Students will first see exponential
expressions and start towards being
able to simplify exponent expressions
Students will share ideas about rules
with their tables, check their answers
to see if they understand and are
able to apply (self-assessment)
Students will use exponential units in
measuring the classroom in a variety
of ways and will see the repeated
multiplication of exponents at work in
the real world
Students will demonstrate their
knowledge on practice problems that
teacher will see while monitoring
Students will complete the water spill
lab and will understand what an
Students will demonstrate
understanding during group work,
Exponents
Students use patterns to
understand simplifying zero
exponents and negative
exponents
5
(7-4)
Division of
Exponents
6-8
Summing
up
Exponent
Rules,
Review &
Quiz
(7-5)
Polynomials
Students understand the
division rules of exponent
expressions and are able to
apply these to simplify
Students will write out exponents as
repeated multiplication in order to
see what exponential expression
division looks like
Students put all the rules
together and simplify
exponential expressions that
include use of a variety of rules
9
10
(7-6)
Adding and
Subtracting
Functions
Students define polynomials
and are able to identify them
based on the number of terms
and degree
Students see adding and
subtracting functions, review
combining like terms
exponential situation looks like in real
life. Students will understand why
zero and negative exponents simplify
as they do and be able to apply this
knowledge to simplify exponential
expressions with zero and negative
exponents
Students will continue to work on
understanding all the rules of
exponential expressions and work on
applying them when simplifying
completion of lab, class discussion,
and performance on the homework
quiz the following day
Students will be able to simplify any
exponential expression with integer
exponents and use the operations of
exponents appropriately.
Students will be able to complete
problems on their mixed review
worksheet and respond as
appropriate to the models done in
class
Students will be able to recognize
different types of polynomials so that
they can understand them and work
towards being able to perform
operations on them.
Students practice operations with
polynomials, review combining like
terms with addition and subtraction,
look at adding together functions as
well as expressions
Students will correctly identify
polynomials and define them on their
homework assignment
Students will demonstrate
understanding on their lab, as well as
in checking their homework in class
the next day.
Students will contribute to class
discussion about adding together
functions. Students will be able to
combine like terms on their
homework assignment.
11& 12
(7-7)
Multiplying
Students use Algebra Tiles to
understand multiplying
binomials together
13
(7-8)
Special
Products
Students work through a lab to
create rules for the special
products of multiplying
binomials
14&15
Review and
Test
Students are able to perform
multiplication on polynomials
(monomials and binomials) and
combine this with the other
operations they have looked at
Students are able to recognize
situations of special products and use
their knowledge to multiply these
special cases without FOILing
Students will demonstrate
understanding of why they are FOILing on the lab and be able to apply
their knowledge on the homework
Students will demonstrate
understanding on the lab and in class
discussion, as well as on their
homework assignment