Grade Level: 8 Subject: Math
Standard(s): (bold the priority standards)
Unit Topic: Rational and Irrational Numbers
Explanations and Examples:
8.NS.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.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). For example,
by truncating the decimal expansion
of √2, show that √2 is between 1 and
2, then between 1.4 and 1.5, and
explain how to continue on to get
better approximations.

Concepts:(What students need to know)
1Retrieved

Length of Unit: 1 week
Students distinguish between rational and irrational numbers. Any number that can be
expressed as a fraction is a rational number. Students recognize that the decimal
equivalent of a fraction will either terminate or repeat. Fractions that terminate will
have denominators containing only prime factors of 2 and/or 5. This understanding
builds on work in 7th grade when students used long division to distinguish between
repeating and terminating decimals. Students convert repeating decimals into their
fraction equivalent using patterns or algebraic reasoning.
Example: Change 0.4 to a fraction.
Students locate rational and irrational numbers on the number line. Students
compare and order rational and irrational numbers. Additionally, students understand
that the value of a square root can be approximated between integers and that nonperfect square roots are irrational.
 Students also recognize that square roots may be negative and written as -28. To
find an approximation of 28, first determine the perfect squares 28 is between, which
would be 25 and 36. The square roots of 25 and 36 are 5 and 6 respectively, so we
know that 28 is between 5 and 6. Since 28 is closer to 25, an estimate of the square
root would be closer to 5. One method to get an estimate is to divide 3 (the distance
between 25 and 28) by 11 (the distance between the perfect squares of 25 and 36) to
get 0.27. The estimate of 28 would be 5.27 (the actual is 5.29).Students can
approximate square roots by iterative processes.
 Examples: Approximate the value of 5 to the nearest hundredth.
Skills:(What students need to be able to do)
Blooms / DOK Levels:
from www.corestandards.org, p.3, Introduction: Common Core State Standards for Mathematics.
Revised 6/2013
 Rational
 Evaluate
 Irrational
 Convert
 Decimal
 Approximate
 Approximation
 Locate
 Conversion
 Estimate
 Repeating
 Compare
 Terminating
 Square roots
Essential Questions: (Open-ended questions that the students
should be able to answer by the end of the unit)
 How can we represent this decimal as a fraction?
 How can a repeating decimal become a fraction?
 How can you determine whether a number is rational or
irrational?
 Why is it helpful to write numbers in different ways?






1/1
2/1
2/2
1/1
1/2
1/2
Corresponding Big Ideas: (Foundational understandings that
students need to discovered by the end of the unit)
 Rational numbers can be compared and ordered on a
number line.
 Rations numbers are added, subtracted, multiplied, and
divided in much the same way as integers.
 A rational number is a number that can be written in the
a
form , where a and b are both integers and b is not equal
b
to 0.
Vocabulary:
Mathematical Practices:
Resources:
(Practices in bold are to be emphasized in the unit.)
 Rational
 Glencoe Math Common Core
1. Make sense of problems and persevere in solving
Course 3 Volume 1
 Irrational
them.
 Carnegie Learning Math Series
 Decimal
2. Reason abstractly and quantitatively.
Course 3 Volume 1
 Approximation
3.
Construct
viable
arguments
and
critique
the
reasoning
 Kansas Flipbook with unwrapping
 Conversion
of
others.
 New Jersey School District
 Repeating
4.
Model
with
mathematics.
Curriculum Organizer
 Terminating
5. Use appropriate tools strategically.
 Square roots
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Assessment for Learning: (How do you know the student has mastered the standards? Include both Pre and Post
Assessments)
Pre-Assessment:
Page 2 of 4
Revised 6/2013
Rational and
Irrational Numbers Pre-Assessment.docx
Scoring Guide:
Rational and
Irrational Pre-Test Scoring Guide.docx
Post-Assessment:
Rational and
Irrational Numbers Post-Assessment.docx
Scoring Guide:
Rational and
Irrational Post-Test Scoring Guide.docx
Task
square root
organizer.docx
Engaging Learning Experiences
Description: (Standards addressed, Blooms / DOK Levels, links to rubric,
resources, instructional strategies, etc.)
Pre-Assessment/Warm-Up for students to complete on index card-“My Favorite No”
(quick assessment to know where to start)
Suggested
Length of Time
10 minutes
5/1
square root
organizer rubric.docx
Always, Sometimes, Never
Page 3 of 4
http://fawnnguyen.com/2012/03/19/always-sometimes-never.aspx?ref=rss
8.NS.1,2
60 minutes
Revised 6/2013
2/1
Always Sometimes
Never Rubric.docx
Square Roots go Rational
http://illuminations.nctm.org/LessonDetail.aspx?id=L854
60 minutes
Square roots go
rational.pdf
square roots go
rational rubric.pdf
8.NS.2
1/2
Rational and Irrational
Numbers Station Task
120 minutes
8.NS.1
2/2
Using Rational
Approximations of
Irrational Numbers
120 minutes
8.NS.2
2/2
Page 4 of 4
Revised 6/2013