Unit Concept Map
Grade Level: 8th Grade Pre-Algebra
Course Essential Question:
Subject: Mathematics
Unit Topic:
Unit 1: Real Number System
Unit Essential Question:
In what ways can we represent and apply rational and irrational numbers to math situations?
PA Standards/Anchors(Assessment Anchor/Eligible Content)
Assessment Anchor: M08.A-N.1 Demonstrate an understanding of rational and irrational
M08.A-N.1
Demonstrate an understanding of rational and irrational numbers
M08.A-N.1.1.1
Determine whether a number is rational or irrational. For rational numbers, show
that the decimal expansion terminates or repeats (limit repeating decimals to
thousandths).
M08.A-N.1.1.2
Convert a terminating or repeating decimal into a rational number (limit repeating
decimals to thousandths).
M08.A-N.1.1.3
Estimate the value of irrational numbers without a calculator (limit whole number
radicand to less than 144).
M08.A-N.1.1.4
Use rational approximations of irrational numbers to compare and order irrational
numbers.
M08.A-N.1.1.5
Locate/identify rational and irrational numbers at their approximate locations on a
number line.
Concepts: By the end of the unit, students will:
 Distinguish between a rational and an irrational number
 Estimate irrational number values (without a calculator)
 Compare, contrast, and order irrational numbers
 Locate rational and irrational numbers on a number line
 Identify rational and irrational numbers on a number line
Skills: By the end of the unit, students will:
 Convert fractions to decimals accurately
 Convert decimals to fractions accurately (terminating and repeating
decimals)
 Convert between decimals, fractions, and percents accurately
 Add, multiply, subtract, and divide rational numbers in various
forms (i.e., -4 + ¾)
 Apply order of operations to simply numeric expressions
 Estimate square root using a variety of representations (i.e., the
number line, greater than, less than)
 Locate and identify rational and irrational numbers
Vocabulary
Rational number
Irrational number
Repeating decimal
Square root
Square (of a number)
Exponent (for order of
operations)
Expression
**Some of the vocabulary
terms may already be known
to students but are still
prudent to review**
Formative Assessments
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Daily exit tickets
(focused after each
lesson and can also
be spiraled to
include the previous
day’s content)
Usage of white
boards to assess
student’s ability to
accurately convert
between F* to D**,
D to F***, F to P, P
to F, P to D, and D to
P
Life-size number line
to “order” students
from greatest to
least (and vice
versa) rational
and/or irrational
number value
Mad math minutes
of converting
common fractions to
decimals and/or
fractions (i.e.,
fourths, fifths,
halves, thirds)
End of class quizzes
Summative Assessment
(if necessary, two summative assessments can
be given)
 Summative assessment #1:
o Identification of rational numbers
on the number line
o Compare and contrast of rational
and irrational numbers
o Rational number conversions
o Square root estimations
 Summative assessment #2:
o Operations with rational numbers
o Simplifying numeric expressions via
order of operations
 Summative assessment #3 (optional): longterm project of student application of
content in a situational setting (i.e., creating
a sales catalog for a discount department
store, designing a model home and applying
the conversions necessary to build the home
to size, etc.)
*F = fraction
**D = decimal
***P = percent
Suggest Unit Lessons:
 Defining a rational number
 F to D to P
 Order of Operations
 Defining an irrational numbers
 Representing irrational numbers
 Differentiating between a rational and irrational number
 Square roots
Resources
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Prentice Hall
Mathematics PreAlgebra
Study Island
Number lines
Fraction tiles/circles
Yellow/red counters
Calculators
Key Lesson Questions (1-2 questions per unit lesson):
1. What is a rational number? In what ways can I represent them and use them in math?
2. What is the correct order of operations in math? How can the order of operations affect the solutions
to math problems?
3. What is an irrational number? In what ways can I represent them and use them in math?
4. How can we tell the difference between a rational number and an irrational number?
5. What does it mean to be the “square root” of a number? How do square roots relate to the squares of a
number?