CCMR 8 - Module 1 – Topic A – Exponent Notation and Properties of Integer Exponents
Stage 1 – Desired Results
ESTABLISHED GOALS
Student Background (According to NY Engage)
(Standards)
Module 1 builds on students’ understanding from previous grades with regard to
transforming expressions.
 Students were introduced to exponential notation in Grade 5 as they used
8.EE.A.1
whole number exponents to denote powers of ten (5.NBT.A.2).
Know and apply the properties
 In Grade 6, students expanded the use of exponents to include bases other
of integer exponents to generate
than ten as they wrote and evaluated exponential expressions limited to
equivalent numerical
whole-number exponents (6.EE.A.1).
expressions. For example, 32 ×
 Students made use of exponents again in Grade 7 as they learned formulas
3−5 = 3−3 = 1/33 = 1/27
for the area of a circle (7.G.B.4) and volume (7.G.B.6)
Transfer
Students will be able to independently use their learning to… make sense out of very
large and very small numbers, using the number line model to guide their
understanding of the relationship of those numbers to each other (8.EE.A.3) in
terms of value in a variety of contexts.
UNDERSTANDINGS
Students will understand that…the
value of an exponential expression
changes dependent on the
characteristics of the exponent.
Meaning
ESSENTIAL QUESTIONS
How does the value of my number change
when the exponent changes as to “sign” or
size?
Acquisition
Students will be skilled at applying the
Properties of Exponents to include:
 Power of a Product
 Power of a Quotient
 Power Raised to another Power
 Numbers Raised to the Zero Power
 Numbers Raised to a Negative Power
Standards of Mathematical Practice (for this Topic)
Students (will know)…
 How to manipulate operations
on numbers in integer
exponents and understand the
effect upon the value of said
number.
MP.2
Reason abstractly and quantitatively.

Students use concrete numbers to explore the properties of numbers in exponential form and then prove
that the properties are true for all positive bases and all integer exponents using symbolic
representations for bases and exponents

Students use symbols to represent integer exponents and make sense of those quantities in problem
situations.
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Students refer to symbolic notation in order to contextualize the requirements and limitations of given
statements (e.g., letting 𝑚, 𝑛 represent positive integers, letting 𝑎, 𝑏 represent all integers, both with
respect to the properties of exponents).
MP.3
Construct viable arguments and critique the reasoning of others.

Students reason through the acceptability of definitions and proofs (e.g., the definitions of 𝑥 0 and 𝑥 −𝑏
for all integers 𝑏 and positive integers 𝑥).

Students keep the goal of a logical argument in mind while attending to details that develop during the
By AnnMarie Daniele (August/September 2018)
reasoning process.
MP.6
Attend to precision. Beginning with the first lesson on exponential notation, students are required
to attend to the definitions provided throughout the lessons and the limitations of symbolic
statements, making sure to express what they mean clearly. Students are provided a hypothesis,
such as 𝑥 < 𝑦, for positive integers 𝑥, 𝑦, and then are asked to evaluate whether a statement, like
−2 < 5, contradicts this hypothesis.
MP.7
Look for and make use of structure. Students understand and make analogies to the distributive
law as they develop properties of exponents. Students will know
𝑥 𝑚 ∙ 𝑥 𝑛 = 𝑥 𝑚+𝑛 as an analog of 𝑚𝑥 + 𝑛𝑥 = (𝑚 + 𝑛)𝑥 and (𝑥 𝑚 )𝑛 = 𝑥 𝑚 ∙ 𝑛 as an analog of 𝑛 ∙ (𝑚 ∙
𝑥) = (𝑛 ∙ 𝑚) ∙ 𝑥.
MP.8
Look for and express regularity in repeated reasoning. While evaluating the cases developed for
the proofs of laws of exponents, students identify when a statement must be proved or if it has
already been proven. Students see the use of the laws of exponents in application problems and
notice the patterns that are developed in problems.
Evaluative Criteria
Students will be able to apply the
properties of integer exponents
to generate equivalent
expressions and explain their
understanding of those
“concepts”.
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Stage 2 – Evidence and Assessment
Assessment Evidence
PERFORMANCE TASK(S):

Students will create a web “study guide page” for Exponents that will
summarize and provide examples of their understanding of each of the
Properties of Exponents to include examples from other sources (outside of
NY Engage).
OTHER EVIDENCE:
 Exit Tickets (Quizzes) after each Lesson 1-5
 Topic – Integer Exponent Quiz (PARCC Questions via Edulastic)
Stage 3 – Learning Plan
Summary of Key Learning Events and Instruction
Pre-Diagnostic of Foundational Integer Skills (7th Grade) – printed for each student and shared with parents via
notification email (September 2019).
Generalized Note-taking using Fold-able Graphic Organizer that summarizes and gives both concrete
(numerical) and abstract (variable) examples of each of the Properties of Exponents.
Direct Instruction of Key Concepts from Module 1 – Topic A – Lessons 1 – 5
Integrated use of the Simple Calculator to aid students in complex multiplication/division when appropriate to
allow students to focus on problem-solving.
Guided Practice to include Class Work (Exercises) and some Homework (Problem Sets)
Independent Practice – using Integer Operation sprints when appropriate
Independent Practice – using Sprints from NY Engage M1 Lesson 4 and Lesson 8 and other sources as
appropriate.
Integration of C/L Mathia Module 1 as classwork (guided practice) and homework (independent practice).
Flexible dynamic (changing) grouping to allow students to benefit from various interactions.
PLAN for ongoing, continuous Sprint practice (all occasional quizzes) throughout upcoming quarters to allow
students to continue developing both confidence and mastery!
By AnnMarie Daniele (August/September 2018)