Common Core Mathematics 8 (CCM-8) Starting Points
Unit 1: The Number System and Exponents
Essential Questions:
o What is the definition, description, and difference of rational and irrational
numbers?
o Can students identify and provide examples of rational versus irrational numbers?
o Can students use a number line that extends indefinitely, such as π?
o Are students able to recognize the properties of integer exponents to compare
large and small numbers?
o How do radicals and exponents influence one’s understanding of other content,
such as geometry and science?
Curriculum Standards:
8.NS.A. Know that there are numbers that are not rational, and approximate them
by rational numbers.
1. Know that numbers that are not rational are called irrational. Understand
informally that every number has a decimal expansion; for rational numbers show
that the decimal expansion repeats eventually, and convert a decimal expansion,
which repeats eventually into a rational number.
2. Use rational approximations of irrational numbers to compare the size of
irrational numbers, locate them approximately on a number line diagram, and
estimate the value of expressions (e.g.,  2 ).
Note: Students may need review of fraction operations. Check student
understanding and review as needed.
8.EE.A. Work with radicals and integer exponents.
1. Know and apply the properties of integer exponents to generate equivalent
numerical expressions.
2. Use square root and cube root symbols to represent solutions to equations of the
form x 2  p and x 3  p , where p is a positive rational number. Evaluate square
roots of small perfect squares and cube roots of small perfect cubes. Know that
2 is irrational.
3. Use numbers expressed in the form of a single digit times an integer power of 10
to estimate very large or very small quantities, and to express how many times as
much one is than the other.
4. Perform operations with numbers expressed in scientific notation, including
problems where both decimal and scientific notation are used. Use 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.
This document represents one sample starting points for the unit. It is not all-inclusive and is only
one planning tool. Please refer to the wiki for more information and resources.
Approximate Length of Unit: 28-40 days
Standard(s)
7.NS.A
Days
2-14
Notes
Big ideas:
Assess prior understanding of integers and rational
numbers
Address misconceptions
Resources:
 Common Core 6 Wiki
 Common Core 7 Wiki
8.NS.A.1
8.NS.A.2
5
Big ideas:
Expand number system to include irrational numbers
Understand irrational numbers and their decimal
approximations
Use rational numbers to approximate irrational numbers
Resources:
 Lesson: Rational and Irrational Numbers
 Task: Discovering Pi
 Task: Patio Predicament
 Task: The Name Game
Assessment Items:
 Illustrative Mathematics: Comparing Rational and
Irrational Numbers
 Illustrative Mathematics: Converting Decimal
Representations of Rational Numbers to Fraction
Representations
 Illustrative Mathematics: Irrational Numbers on a
Number Line
8.EE.A.2
8.NS.A.2
5
Big ideas:
Evaluate square roots and cube roots of perfect
squares/cubes
Approximate square roots of non-perfect squares
Resources:
 Lesson: Cube Hotel
This document represents one sample starting points for the unit. It is not all-inclusive and is only
one planning tool. Please refer to the wiki for more information and resources.
Assessment Items:
 Illustrative Mathematics: Estimating Square Roots
 Illustrative Mathematics: Calculating the Square
Root of 2
 Illustrative Mathematics: Placing a Square Root on
the Number Line
8.EE.A.1
8
Big ideas:
Develop understanding of exponent properties conceptually
(integer exponents)
Extend understanding to variable base
Resources:
 Lessons: Laws of Exponents Part I & II
Assessment Items:
 Illustrative Mathematics: Extending the Definitions
of Exponents, Variation 1
8.EE.A.3
8.EE.A.4
8
Big ideas:
Explore real-world contexts
Build understanding of scientific notation through powers
of 10
Express how many times more quantities are
Perform operations with numbers in scientific notation
Resources:
 Lesson: Scientific Notation
 Task: Land Purchases in U.S. History
 Google Earth Lesson: Finding Distances to Earth
Assessment Items:
 Illustrative Mathematics: Ants vs. Humans
 Illustrative Mathematics: Ant and Elephant
 Illustrative Mathematics: Giantburgers
 Illustrative Mathematics: Pennies to Heaven
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.
This document represents one sample starting points for the unit. It is not all-inclusive and is only
one planning tool. Please refer to the wiki for more information and resources.