Unit 1: Number Systems, Irrational Numbers and
Scientific Notation
Content Area:
Course(s):
Time Period:
Length:
Status:
Mathematics
Generic Course
1st Marking Period
6 weeks
Published
Unit Overview
Work with exponents, rational numbers, irrational numbers, perform operations with numbers in scientifc notation
Benchmark assessment 1 will be given after chapter 2 in Glencoe Course 3 book.
Transfer
Students will be able to independently use their learning to appropriately apply skills in real-life situations ...
Know there are irrational numbers.
Be able to find decimal expansion of all rational numbers
Approximate irrational numbers on a number line
Apply properties of exponents
Write and understand scientific notation
Perform operations with numbers in scientifc notation
Meaning
Understandings
Students will understand that numbers are rational and irrational and can be written in different ways.
Essential Questions
At the end of this unit, students should be able to answer

How can mathematical ideas be represented?

Why is it helpful to write numbers in different ways?
Application of Knowledge and Skill
Students will know...
Students will know...

Decimals that “terminate” actually repeat the digit zero. (2.5 = 2.5000000000 ) (8.NS.1)

Numbers that repeat in their decimal form are called rational. (8.NS.1)

Numbers that do not repeat in their decimal form are called irrational. (8.NS.1)

The number is irrational. (8.EE.2)

The square root of the area of a square represents the side length of the square. (8.EE.2)

Exponent operation properties. (8.EE.1)

Apply exponent rules to perform operations with numbers in scientific notation.
Students will be skilled at...
Students will be skilled at...

Distinguish between rational and irrational numbers. (8.NS.1)

Convert a decimal expansion which repeats eventually into a rational number. (8.NS.1)

Find rational approximations of irrational numbers. (8.NS.2)

Use 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)

Evaluate square roots of small perfect squares and cube roots of small perfect cubes. (8.EE.2)

Use square root and cube root symbols to solve and represent solutions of equations. (8.EE.2)

Apply the properties of integer exponents to generate equivalent numerical expressions. (8.EE.1)

Estimate very large or very small quantities using a single digit times a power of ten. (8.EE.3)

Express 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)

Express numbers in scientific notation. (8.EE.4)

Perform operations with numbers expressed in scientific notation and a mix of scientific notation and decimal
notation. (8.EE.4)

Choose appropriate units of measurements for a given number in scientific notation. (8.EE.4)

Interpret scientific notation that has been generated by technology. (8.EE.4)
Academic Vocabulary
From Marzano Proficent Scale:
Approximation, compare, convert, decimal, estimate, expansion, expression, irrational number, nonrepeating,
nonterminating, number line, rational, rational number, size, value
Compare, cube root, decimal, digit, equation, equivalent, evaluate, exponent, expression, integer, large, measurement,
number, numerical, operation, perfect cube, perfect square, power of 10, quantity, reasoning, scientific notation, small,
solution, square root, symbol
Additional words:
Radical, Square root, Cube root, Equation, Variable, Property, Unknown, Solution, Integer, Inverse operations
Learning Goal 1
Know that there are numbers that are not rational, and approximate them by rational numbers. Use rational
approximations to estimate roots and to compare real numbers
TECH.8.1.8.F.CS2
Plan and manage activities to develop a solution or complete a project.
CRP.K-12.CRP11
Use technology to enhance productivity.
CAEP.9.2.8.B.7
Evaluate the impact of online activities and social media on employer decisions.
TECH.8.1.8.A.3
Use and/or develop a simulation that provides an environment to solve a real
world problem or theory.
CAEP.9.2.8.B.3
Evaluate communication, collaboration, and leadership skills that can be
developed through school, home, work, and extracurricular activities for use in a
career.
CAEP.9.2.8.B.4
Evaluate how traditional and nontraditional careers have evolved regionally,
nationally, and globally.
CAEP.9.2.8.B.1
Research careers within the 16 Career Clusters ® and determine attributes of
career success.
Target 1--(Level 1 Recall)
SWBAT:
Write fractions as decimals and decimals as fractions.
Note Clarifications from PARCC EOY:
i) Tasks do not have a context.
ii) 50% of tasks require students to write a fraction a/b as a repeating decimal by showing, filling in, or otherwise
producing the steps of a long division a ÷ b.
iii) 50% of tasks require students to write a given repeating decimal as a fraction.
iv) Tasks should involve no more than two repeating decimals i.e. 2.16666..., 0.23232323.
CCSS.Math.Content.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.
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4
Model with mathematics.
CCSS.Math.Practice.MP6
Attend to precision.
CCSS.Math.Practice.MP7
Look for and make use of structure.
CCSS.Math.Practice.MP8
Look for and express regularity in repeated reasoning.
Target 2--(Level 3 Strategic Thinking)
SWBAT:
Write and evaluate expressions involving powers and exponents
Clarification from PARCC EOY:
i)Tasks do not have a context.
CCSS.Math.Content.8.EE.A.1
Know and apply the properties of integer exponents to generate equivalent
numerical expressions.
CCSS.Math.Content.8.EE.A.2
Use square root and cube root symbols to represent solutions to equations of the
form �² = � and �³ = �, where � is a positive rational number. Evaluate square
roots of small perfect squares and cube roots of small perfect cubes. Know that √2
is irrational.
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4
Model with mathematics.
CCSS.Math.Practice.MP8
Look for and express regularity in repeated reasoning.
Learning Goal 2
Work with radicals and integer exponents
Use and/or develop a simulation that provides an environment to solve a real
world problem or theory.
CAEP.9.2.8.B.6
Demonstrate understanding of the necessary preparation and legal requirements
to enter the workforce.
TECH.8.1.8.B.CS1
Apply existing knowledge to generate new ideas, products, or processes.
CRP.K-12.CRP11
Use technology to enhance productivity.
CAEP.9.2.8.B.1
Research careers within the 16 Career Clusters ® and determine attributes of
career success.
Target 3--(Level 3 Strategic Thinking)
SWBAT:
Apply the properties of integer exponents to simplify and write equivalent numerical expressions. Simplify a real
number expressions by mutiplying and dividing monomials
Clarifications for PARCC EOY:
i) Tasks do not have a context.
ii) Tasks center on the properties and equivalence, not on simplification. For example, a task might ask a student to
classify expressions according to whether or not they are equivalent to a given expression.
iii) 50% of expressions should involve one property
iv) 30% of expressions should involve two properties
v) 20% of expressions should involve three properties
vi) Tasks should involve a single common base
CCSS.Math.Content.8.EE.A.1
Know and apply the properties of integer exponents to generate equivalent
numerical expressions.
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4
Model with mathematics.
CCSS.Math.Practice.MP7
Look for and make use of structure.
Target 4--(Level 1 Recall)
SWBAT:
Use the Laws of Exponents to find powers of monomials
Clarifications from PARCC EOY:
None provided
CCSS.Math.Content.8.EE.A.1
Know and apply the properties of integer exponents to generate equivalent
numerical expressions.
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4
Model with mathematics.
CCSS.Math.Practice.MP7
Look for and make use of structure.
Target 5--(Level 2 Skill/Concept)
SWBAT:
Simplify expressions involving negative exponents.
CCSS.Math.Content.8.EE.A.1
Know and apply the properties of integer exponents to generate equivalent
numerical expressions.
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4
Model with mathematics.
CCSS.Math.Practice.MP7
Look for and make use of structure.
Target 6 -- (Level 3 Strategic Thinking)
In real-world problem solving situations choose units of appropriate size for measurement of very small and very large
quantities.
Performance Clarifications for EOY:
i) Task have “thin context”.
ii) The testing interface can provide students with a calculation aid of the specified kind for these tasks. iii) Tasks may
require students to recognize 3.7E-2 (or 3.7e-2) from technology as 3.7 x 10-2
CCSS.Math.Content.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.
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4
Model with mathematics.
Target 7 -- (Level 1 -Recall)
Use scientific notation to write large and small numbers.
CCSS.Math.Content.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 (e.g., use millimeters per year for seafloor spreading).
Interpret scientific notation that has been generated by technology.
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4
Model with mathematics.
CCSS.Math.Practice.MP7
Look for and make use of structure.
Target 8 -- (Level 2- Skill/Concept)
Compute with numbers written in scientific notation.
Interpret scientific notation when using technology
CCSS.Math.Content.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 (e.g., use millimeters per year for seafloor spreading).
Interpret scientific notation that has been generated by technology.
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4
Model with mathematics.
Target 9 -- (Level 2 - Skill/Concepts)
Find square roots and cube roots.
CCSS.Math.Content.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., π²).
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4
Model with mathematics.
Target 10 A -- (Level 2 --Skill/Concept)
Estimate square roots of non-perfect squares.
CCSS.Math.Content.8.EE.A.2
Use square root and cube root symbols to represent solutions to equations of the
form �² = � and �³ = �, where � is a positive rational number. Evaluate square
roots of small perfect squares and cube roots of small perfect cubes. Know that √2
is irrational.
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4
Model with mathematics.
CCSS.Math.Practice.MP5
Use appropriate tools strategically.
Target 10 B -- (Level 2 - Skill/Concept)
Estimate square and cube roots.
CCSS.Math.Content.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., π²).
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4
Model with mathematics.
Target 11 -- (Level 2 - Skill/Concept)
Compare mathematical expressions
CCSS.Math.Content.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., π²).
CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP4
Model with mathematics.
CCSS.Math.Practice.MP5
Use appropriate tools strategically.
Summative Assessment
Chapter Test/Unit Test
Unit Project
Performance based assessment
Formative Assessment and Performance Opportunities
Mid Chapter check assessments
Inquiry Labs
Tests
Quizzes
Informal Assessments
Graded Classwork
Surveys
WhiteBoard Activities
Exit tickets
Group activities
Projects
Teacher Observations
Student Interviews
Differentiation / Enrichment
See Unit resources below for specific targeted resources
• Factoring
.
• interactive math journals
.
• interactive math notebooks
.
• Lesson Extentions
.
• Manipulatives
.
• Modifications as per IEP/504
.
• Perfect squares and cubes
.
• Review and Practice
.
• Rules of operations with integers
.
• Simplifying radicals
.
• Small Group Instruction
.
• Understanding of Distributive Property
.
Unit Resources
Additional files located in folder
•
http://www.youtube.com/watch?v=0fKBhvDjuy0
.
• 21st Century Career in Engineering in Glencoe
.
• Added program resources in Glencoe Chapter
.
• Aleks online supplement
.
• Graphic Novels in Connect ed
.
• http://achievethecore.org/coherence-map/#8/35/396/196/1
.
• http://connected.mcgraw-hill.com/
.
• http://illuminations.nctm.org/LessonsList.aspx?grade=3&standard=all
.
• http://insidemathematics.org/index.php/8th-grade
.
• http://learnzillion.com/
.
• http://www.illustrativemathematics.org/
.
• https://www.khanacademy.org/
.
• Inquiry Labs
.
• multilingual glossary in Connect ed
.
• Power up for PARCC in connect ed
.
• RTI lessons in the strategic intervention guide in Glencoe
.
• Support for English Language Learners in Glencoe
.
• Unit 1 Chapter 1 10 lessons in Glencoe
.
• Unit 1 Project
.