Grade/Course: Grade 8
Instructional Unit 6: Exponents
Instructional Schedule: Third Nine Weeks (suggested for 15 days)
( Bold text is new content )
Adapted from Timothy Kanold Scope-and-Sequence documents
Standards:
Evidence Of Standard:
(student should be able to…)
Work with radicals and integer
exponents.
(BA/PASS 2.2a) Know and apply the
properties of integer exponents to
generate equivalent numerical
expressions. For example, 32 ∙ 3−5 =
1
1
3−3 = 3 = .
3
27
-Identify the properties of integer
exponents (laws of exponents).
-Apply properties of integer
exponents when multiplying and
dividing with like bases.
-Simplify numerical expressions by
applying the properties of integer
exponents:
1. zero rule (𝑎0 = 1).
2. product rule (𝑎 𝑥 ∙ 𝑎 𝑦 = 𝑎 𝑥+𝑦 ).
𝑥
3. quotient rule (𝑎 ⁄𝑎 𝑦 = 𝑎 𝑥−𝑦 ).
1
(PASS 2.2c) Recognize positive and
negative rational numbers and use
the order of operations to simplify
numerical expressions that include
rational numbers and exponents.
4. negative rule (𝑎−1 = 𝑎 ).
5. power rule (𝑎 𝑥 )𝑦 = 𝑎 𝑥∙𝑦 ).
-Classify expressions according to
whether or not they are equivalent
with one, two, or three properties.
-Recognize positive and negative
rational numbers and use the order of
operations to simplify numerical
expressions that include rational
numbers and exponents.
Prerequisite Knowledge:
(standards linked to content taught in
previous grades)
Assessment Tools:
(formative assessments, quizzes,
mastery tasks/activities)
(BA/PASS 2.1, 2.2b) Use numbers
expressed in the form of a single digit
times an integer power of 10
(scientific notation) to estimate very
large or very small quantities, and to
express how many times as much
one is than the other. For example,
estimate the population of the United
States as 3 × 10^8 and the population
of the world as 7 × 10^9, and
determine that the world population
is more than 20 times larger.
(BA/PASS 2.2b) Perform operations
with numbers expressed in scientific
notation and choose units of
appropriate size for measurements
of very large or very small quantities
(e.g., use millimeters per year for
seafloor spreading). Interpret
scientific notation that has been
generated by technology.
-Write numbers in scientific notation.
-Apply the laws of exponents to the
power of 10.
-Use scientific notation to estimate
very large and/or quantities.
-Use scientific notation to determine
how many times as large one number
is in relation to another.
-Convert numbers from scientific
notation to standard form and
vice/versa.
-Perform operations with numbers
expressed in scientific notation
without technology.
-Use scientific notation and choose
measurements of appropriate size of
very large and/or small quantities.
-Interpret scientific notation that has
been generated by technology
(ex: Recognize 3.7E-2 from technology
as 3.7 𝑥 10−2).
-Perform operations with numbers
expressed in scientific notation with
technology.
Solve real-world and
mathematical problems involving
volume of cylinders, cones, and
spheres.
(BA/PASS 4.1) Know the formulas for
the volumes of cones, cylinders, and
spheres and use them to solve realworld and mathematical problems.
(PASS 1.1d) Rewrite and solve
problems using appropriate formulas
(literal equations).
-Identify the shapes of cones,
cylinders, and spheres.
-Use appropriate formulas for volume
of cones, cylinders, and spheres in
mathematical and real-world
situations.
-Manipulate multi-variable equations.
-Solve a multi-variable for a
designated variable using appropriate
formulas (literal equations).
Resources/Exemplar Tasks:
( list possible task/activities students could engage in within this unit)
Standards for Mathematical Practice:
(highlight practice standards to be emphasized in the instructional unit)
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of instruction.
8. Look for and express regularity in repeated reasoning.
( BA: Broken Arrow rigor standard; PASS: Priority Academic Student Skills standard; BA/PASS: Combination standard )