8th grade Mathematics Curriculum Guide – Unit 1
2016 – 2017
Unit 1: Real Number System, Radical and Integer Exponents, and Scientific Notation
Time Frame: Quarter 1 (Estimated Days on Unit: 24 – 30)
Connections to Previous Learning:
Students in Grade 7 learn to differentiate between terminating and repeating decimals. In Grade 8, students realize that terminating decimals are
repeating decimals that repeat the digit zero. They use this concept to identify irrational numbers as decimals that do not repeat a pattern. They learn to
use rational approximations of irrational numbers to represent the value of irrational numbers on a number line. Students in Grades 6 and 7 have
learned to use expressions, equations and inequalities to represent problem solving situations. Students in Grade 8 will expand upon those skills to
include work with very large and very small numbers involving the use of integer exponents.
Focus within the Grade Level:
Beginning with familiar number sense topics helps students transition into the Grade 8 content. Turning decimal expansions into fractions and
deepening understanding of the meaning of decimal expansions sets a firm foundation for understanding irrational numbers. Students will learn that the
square roots of perfect squares are rational numbers, and that the square roots of non-perfect squares, such as √2 or √7, are examples of irrational
numbers. Students will understand the value of square roots and cube roots and use this understanding to solve equations involving perfect squares and
cubes. Further work with exponents, including scientific notation, naturally flow from the understanding of squares and cubes.
Connections to Subsequent Learning:
Solving equations of the form 𝑥 2 = 𝑝 reminds students about inverse operations which they will need to explore the topics of solving linear and
proportional equations later in the year. Exponents and roots also connect closely to work with the Pythagorean Theorem and volume of rounded
objects later in Unit 3.
Unit 1
Clover Park School District 5/11/16
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8th grade Mathematics Curriculum Guide – Unit 1
2016 – 2017
Common Core Standards in this unit:
 Indicates was presented to students in the 7th grade curriculum in the Clover Park School District.
Know that there are numbers that are not rational, and approximate them by rational numbers. (Supporting Cluster)
 8.NS.A.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 that repeats eventually into a rational number.
 8.NS.A.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.𝜋 2 ).
Work with radical and integer exponents. (Major Cluster)
 8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
 8.EE.A.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 (Will cover later unit before Pythagorean Theorem). Evaluate square roots of small perfect squares and cube roots of small perfect cubes.
Know that √2 is irrational.
8.EE.A.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.
8.EE.A.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. Interpret scientific notation that
has been generated by technology.
Mathematical Practices
1.
2.
3.
4.
5.
6.
7.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make sure of structure.
8. Look for and express regularity in repeated reasoning.
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8th grade Mathematics Curriculum Guide – Unit 1
Unit 1
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2016 – 2017
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8th grade Mathematics Curriculum Guide – Unit 1
2016 – 2017
Stage 1 Desired Results
Transfer Goals
Students will be able to independently use their learning to…
 Know that there are numbers that are not rational, and approximate them by rational numbers.
 Work with and evaluate expression with radicals and integer exponents.
Meaning Goals
UNDERSTANDINGS
Students will understand that…
 Every number has a decimal expansion.
 The value of any real number can be represented in
relation to other real numbers such as with decimals
converted to fractions, scientific notation and
numbers written with exponents (8 = 23 ).
 Properties of operations with whole and rational
numbers also apply to all real numbers.
 Square roots can be rational or irrational.
 Properties of integer exponents can be used to
generate equivalent numerical expressions.
 All real numbers can be plotted on a number line.
 Exponents are useful for representing very large or
very small numbers.
 Scientific Notation can be used to estimate very large
or very small numbers.
ESSENTIAL QUESTIONS
 Why are quantities represented in multiple ways?
 How is the universal nature of properties applied to real numbers?
 When are exponents used and why are they important?
 How can I represent very small and large numbers using integer exponents and
scientific notation?
 What are applications using scientific notation?
 What is the difference between rational and irrational numbers?
 Why do we approximate numbers?
Acquisition Goals
Students will know…
 Decimals that “terminate” actually repeat the digit

Unit 1
zero. (2.5 = 2.500000….)
Numbers that repeat in their decimal form are called
rational.
Students will be skilled at…
 Distinguishing between rational and irrational numbers. (8.NS.1)
 Converting a decimal expansion which repeats eventually into a rational
number. (8.NS.1)
 Finding rational approximations of irrational numbers. (8.NS.2)
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8th grade Mathematics Curriculum Guide – Unit 1





Numbers that do not repeat in their decimal form are
called irrational.
The number √2 is irrational.
The square root of the area of a square represents
the side length of the square.
Exponent operation properties.
The cube root of the volume of a cube represents the
side length of the cube.










Unit 1
2016 – 2017
Using rational approximations of irrational numbers to compare the size of
irrational numbers, locate them approximately on a number line, and estimate
the value of expressions. (8.NS.2)
Evaluating square roots of small perfect squares and cube roots of small perfect
cubes. (8.EE.2)
Using square root and cube root symbols to solve and represent solutions of
equations. (8.EE.2)
Applying the properties of integer exponents to generate equivalent numerical
expressions. (8.EE.1)
Estimating very large or very small quantities using a single digit times a power
of ten. (8.EE.3)
Expressing how much larger one number expressed as a single digit times a
power of ten is than another in the context of the situation. (8.EE.3)
Expressing numbers in scientific notation. (8.EE.4)
Performing operations with numbers expressed in scientific notation and a mix
of scientific notation and decimal notation. (8.EE.4)
Choosing appropriate units of measurements for a given number in scientific
notation. (8.EE.4)
Interpreting scientific notation that has been generated by technology. (8.EE.4)
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8th grade Mathematics Curriculum Guide – Unit 1
2016 – 2017
Stage 1 Established Goals: Common Core State Standards for Mathematics
Students will be able to independently use their learning to…
Know that there are numbers that are not rational, and approximate them by rational numbers.
8.NS.A.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.
8.NS.A.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.𝜋 2 ).
Explanations, Examples, and Comments
Vocabulary: Cards
ALD
Target A: Know that there are numbers that are not rational and approximate them by
rational numbers.
Level 1 students should be able to identify square roots of numbers less than 100; identify pi
as not rational; and understand that every rational number has a decimal expansion.
Level 2 students should be able to identify approximate locations of familiar irrational
numbers on a number line; identify numbers as rational and irrational; and convert between
fractions and terminating decimals.
Level 3 students should be able to use rational approximations of irrational numbers to
locate them on a number line and to make numerical comparisons; convert between
fractions and repeating decimals; and compare rational numbers.
Level 4 students should be able to approximate irrational numbers to a specified level of
precision and should be able to use the approximations to solve problems or estimate the
value of an expression.
Unit 1
Clover Park School District 5/11/16
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Decimal expansion
Decimal notation
Decimals: terminating and repeating (7th)
Estimate
Evaluate (5th)
Expand (7th)
Integers (7th)
Irrational numbers
Natural numbers
Perfect Square
Radical
Rational numbers (7th)
Square root
Whole numbers (4th)
Item Specs Version 2.0
- Target A
Item Specs Version 3.0
- Target A
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8th grade Mathematics Curriculum Guide – Unit 1
Unit 1
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2016 – 2017
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8th grade Mathematics Curriculum Guide – Unit 1
2016 – 2017
Stage 1 Established Goals: Common Core State Standards for Mathematics
Students will be able to independently use their learning to…
Work with radical and integer exponents.
8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
Explanations, Examples, and Comments
Vocabulary
-
Pre-requisite skills:
-
-
Evaluating variables
Combining like terms
Distributive property
Base
Exponent
Evaluate (5th)
Power
Variable (6th)
Term
Order of Operations problems involving exponents should be reviewed at this time.
ALD
Target B: Work with radicals and integer exponents
Level 1 students should be able to identify and calculate square roots of familiar perfect squares and
calculate the square of integers. They should be able to translate between standard form and scientific
notation.
Level 2 students should be able to identify and calculate the cube root of familiar perfect cubes and
calculate the cube of integers. They should be able to use appropriate tools (e.g., calculator, pencil and
paper) to translate larger or small numbers from scientific to standard notation. They should be able to
work with and apply the properties of integer exponents of degree 2 or less in order to produce or
identify equivalent numerical expressions.
Level 3 students should be able to identify that the square root of 2 is irrational, calculate or
approximate to an appropriate degree of precision the square or cube of a rational number, solve
quadratic and cubic monomial equations, and represent the solution as a square or cube root,
respectively. They should be able to work with and perform operations with scientific notation and
work with and apply the properties of integer exponents in order to produce or identify equivalent
numerical expressions.
Level 4 students should be able to use scientific notation and choose units of appropriate size for
realistic measurements, solve binomial quadratic and cubic equations, and represent the solution as a
square or cube root, respectively.
Unit 1
Clover Park School District 5/11/16
Item Specs Version 2.0
- Target B
Item Specs Version 3.0
- Target B
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8th grade Mathematics Curriculum Guide – Unit 1
2016 – 2017
Stage 1 Established Goals: Common Core State Standards for Mathematics
Students will be able to independently use their learning to…
Work with radical and integer exponents.
8.EE.A.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.
(standard will be covered again in unit 3 with Pythagorean Theorem and Volume)
Explanations, Examples, and Comments
Pre-requisite
-
Vocabulary
Powers of 2 and 3’s
The solving for 𝑥 2 = 𝑝 and 𝑥 3 = 𝑝 will come in Unit 3: Geometry
Order of Operations problems involving exponents and radical for a grouping symbol should be
reviewed at this time.
ALD
Target A: Know that there are numbers that are not rational and approximate them by
rational numbers.
Level 1 students should be able to identify square roots of numbers less than 100; identify pi
as not rational; and understand that every rational number has a decimal expansion.
Level 2 students should be able to identify approximate locations of familiar irrational
numbers on a number line; identify numbers as rational and irrational; and convert between
fractions and terminating decimals.
Level 3 students should be able to use rational approximations of irrational numbers to
locate them on a number line and to make numerical comparisons; convert between
fractions and repeating decimals; and compare rational numbers.
Level 4 students should be able to approximate irrational numbers to a specified level of
precision and should be able to use the approximations to solve problems or estimate the
value of an expression.
Unit 1
Clover Park School District 5/11/16
-
Square root
Cube root
Exponent
Perfect cube
Perfect square
Power
Radical
Evaluate (5th)
Item Specs Version 2.0
- Target A
Item Specs Version 3.0
- Target A
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8th grade Mathematics Curriculum Guide – Unit 1
2016 – 2017
Stage 1 Established Goals: Common Core State Standards for Mathematics
Students will be able to independently use their learning to…
Work with radical and integer exponents.
8.EE.A.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.
8.EE.A.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. Interpret scientific
notation that has been generated by technology.
Explanations, Examples, and Comments
Pre-requisite
-
Item Specs Version 2.0
- Target B
Item Specs Version 3.0
- Target B
Base
Exponent
Power
Scientific notation
ALD 8th
Target B: Work with radicals and integer exponents
Level 1 students should be able to identify and calculate square roots of familiar perfect squares and calculate
the square of integers. They should be able to translate between standard form and scientific notation.
Level 2 students should be able to identify and calculate the cube root of familiar perfect cubes and calculate
the cube of integers. They should be able to use appropriate tools (e.g., calculator, pencil and paper) to
translate larger or small numbers from scientific to standard notation. They should be able to work with and
apply the properties of integer exponents of degree 2 or less in order to produce or identify equivalent
numerical expressions.
Level 3 students should be able to identify that the square root of 2 is irrational, calculate or approximate to an
appropriate degree of precision the square or cube of a rational number, solve quadratic and cubic monomial
equations, and represent the solution as a square or cube root, respectively. They should be able to work with
and perform operations with scientific notation and work with and apply the properties of integer exponents in
order to produce or identify equivalent numerical expressions.
Unit 1
Clover Park School District 5/11/16
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8th grade Mathematics Curriculum Guide – Unit 1
2016 – 2017
Level 4 students should be able to use scientific notation and choose units of appropriate size for realistic
measurements, solve binomial quadratic and cubic equations, and represent the solution as a square or cube
root, respectively.
Stage 2 - Evidence
SAMPLE Assessment Evidence
PERFORMANCE TASK(S):
Evaluative Criteria:
Common Assessment
See Sample Assessments for Unit 1.
See Day 22 and Day 23.
Washington State: Materials to help districts and others understand the
OTHER ASSESSMENT EVIDENCE:
organization and content of the standards and the content and evidence
base used to support the standards:
http://mathpractices.edc.org/pdf/Rational_Exponents.pdf
Washington State: Instructional materials, Resources and Course
Support: http://www.k12.wa.us/Mathematics/Resources.aspx
Washington State: Professional Learning Support:
http://www.k12.wa.us/Mathematics/profdev.aspx
Washington State: General Assessment Resources:
http://www.k12.wa.us/Mathematics/Assessment.aspx
SBA Sample Items
8.EE.1 (B.203)
8.EE.3 (B.494)
8.EE.2 (B.144)
8.EE.2 (B.323)
8.EE.3 and 8.NS.2 (A.133)
8.EE.4 (A.145)
8.NS.1 (A.136)
8.EE.2 (E.138)
SBA Review by Target
Target A
Target A MT
Target B1
Target B2
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8th grade Mathematics Curriculum Guide – Unit 1
2016 – 2017
Stage 3 – Learning Plan Sample
Summary of Key Learning Events and Instruction that serves as a guide to a detailed lesson planning
LEARNING ACTIVITIES:
Additional Resources by Standard
A suggested guide to layout of unit by days
8.NS.A.1 and 8.NS.A.2
Basic number
8.NS.A.1 and 8.NS.A.2
http://www.youtube.com/watch?v=Rn_OhPKBjB0
Day 1: Rational Numbers
- Holt Course 3: 2-1 Rational Numbers and 2-2 Comparing and Ordering
Square root
- Graphic Organizer of the Real Number System (only rational)
http://www.youtube.com/watch?v=BbX44YSsQ2I
- Graphing Organizers (three options to consider)
Real Number System 1
Power Point of Real Number System
Real Number system 2
The Laundry Problem: Activity
Real Number System 3
Real Number Race: Review Activity more of a
- Ordering of Real Numbers: Class Review Activity (only rational numbers today)
Game
Writing Perfect Squares: Worksheets
Day 2: Square Roots (perfect squares only) and Rational Numbers
Finding the Square Root: Worksheets
- Holt Course 3: 4-5 Squares and Square Roots
Square and Square Roots: Worksheets
- Ordering Real Number Activity (only rational adding some perfect squares to the mix)
Estimating Square Roots Application word
problems: worksheet
Day 3: Irrational Numbers
Estimating Square Roots word problems:
- Lab on Irrational Lab on Irrational: Is it Rational?
worksheet
- Holt Course 3: 4-5 Squares and Square Roots
- Holt Course 3: 4-6 Estimating Square Roots
Day 4: More review of Rational and Irrational numbers
- Rational or Irrational Reasoning (Georgia Task)
- Translating Between Repeating Decimals and Fractions (MP: 7 and 8)
Lesson
Resources
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8th grade Mathematics Curriculum Guide – Unit 1
2016 – 2017
Stage 3 – Learning Plan Sample
Day 5: Real Number System
- Holt Course 3: 4-7 Real Numbers
- Graphic Organizer of the Real Number System
- Rational or Irrational Card Game
Directions
Cards
Power Point
- Radicals and irrational Numbers : Station Activity
Day 6: Real Number System Ordering
- Holt Course 3 Curriculum Companion: 4-7A Identify and Graphing Irrational Numbers
- Using Rational Approximations of Irrational Numbers: Station Activity 8.NS.2
Day 7: Review of 8.NS.A.1 and 8.NS.A.2
- Squareville Sign: Activity
8.EE.A.1
Day 8: Exponents
- Holt Algebra 1: 1-4 Powers and Exponents
- Chess-Wager Activity (Start)
Day 9: Exponents
- Chess-Wager Activity
- Video for Chess-Wager show first:
http://www.pbslearningmedia.org/asset/vtl07_vid_chesswager/
- Holt Algebra 1: 7-1 Integer Exponents
Day 10: Exponents
- Exploring Exponents TI Activity
Student papers
Teacher papers
- Ants versus Humans: Activity https://www.illustrativemathematics.org/contentstandards/8/EE/A/1/tasks/823
Unit 1
Clover Park School District 5/11/16
8.EE.A.1
Holt Resources to check out
Explorations in text
- Holt Algebra 7-1
- Holt Algebra 7-3
- Holt Algebra 7-4
Challenge in text
- Holt Algebra 7-1
- Holt Algebra 7-4
Power Points
- Exponents introduction
- Zero and Negative Exponents
- Fractions with Negative Exponents
- Multiplying Exponents
- Factoring, Fraction Exponents
- Divide Powers, Multiply & Divide
Monomials
- Review Game
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8th grade Mathematics Curriculum Guide – Unit 1
2016 – 2017
Stage 3 – Learning Plan Sample
-
Or
Extending the Definitions of Exponents: Activity
https://www.illustrativemathematics.org/content-standards/8/EE/A/1/tasks/395
Day 11: Multiplication Properties of Exponents
- Holt Algebra 1: 7-3 Explore Properties of Exponents
Day 12: Division Properties of Exponents
- Holt Algebra 1: 7-4 Division Properties of Exponents
Day 13: Exponents review
- Exponents Break It Down lesson and practice: worksheet or
- I Am You Are Activity or
- Exponent Practice: worksheet
- Review of All
Exponent Game
Laws of Powers
Matching or Around the Room Activity
Crossword Puzzle
Simplify the Expression and Color
More Worksheets
Exponent Bing review
Exponent Rules TI Activity
- Student papers
- Teacher papers
Day 14: review or add combining like terms
- Combining Like Terms: worksheet
8.EE.A.2
Day 15: Square Roots
- Holt Algebra 1: 1-5
- Holt Algebra 1: 1-6 Order of Operations (Order of Operation with square root)
8.EE.A.2
Square Root Game
Estimating Square Roots Scavenger Hunt
Cube and Cube Roots Worksheet
Day 16: Cube Roots
- The Roots of a Cube: lab
- Perfect Patterns: worksheet
Day 17: Cube Roots
- Rational and Irrational Numbers: Stations Activity
Day 18: Square Roots and Cube Roots
- Loop Activity
Unit 1
8.EE.A.3 and 8.EE.A.4
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8th grade Mathematics Curriculum Guide – Unit 1
2016 – 2017
Stage 3 – Learning Plan Sample
8.EE.A.3 and 8.EE.A.4
Day 19: Scientific Notation
- Holt Course 3: 4-4 Scientific Notation
- Micro world
Day 20: Scientific Notation
- Holt Algebra 1: 7-2 Power of 10 and Scientific Notation
- Pennies to Heaven: Activity or
https://www.illustrativemathematics.org/content-standards/8/EE/A/3/tasks/1291
- Orders of Magnitude: Activity or
https://www.illustrativemathematics.org/content-standards/8/EE/A/3/tasks/1593
Day 21: Scientific Notation
- Holt Course 3: 4-4 Problem Solving
- Holt Algebra: 7-2 Problem Solving
- Scientific Notation: worksheet
Day 22: Scientific Notation
- Adding and Subtracting with Scientific Notation steps and practice: worksheet
- E. Coli (Georgia Task) or
- Giant Burgers (Georgia Task)
Holt Course 3 Curriculum Companion: 4-4A
Operating with Scientific Notation
Exploration from Text
- Holt Course 3 4-4
- Holt Algebra 7-2
Challenge from Text
- Holt Course 3 4-4
- Holt Algebra 7-2
Additional Packet of Practice Worksheets
Additional Packet of Practice Worksheets
Problem Solving with Exponents and Scientific
Notation: Stations Activity
100 people and key: Activity
A million dollars and key: Activity
Choosing Appropriate Units: Activity
https://www.illustrativemathematics.org/contentstandards/8/EE/A/4/tasks/1981
Estimating Length Using Scientific Notation
Projector Resources Lesson
Day 23: Scientific Notation
- Multiplying and Dividing with Scientific Notation steps and practice: worksheet
- What on Earth?: I.12 Making Sense of Problem Solving: I.12
Day 24: Scientific Notation
Review
Common Assessment
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