Unit 1
Value and Magnitude of Rational Numbers
Grade 8
5E Lesson Plan Math
Grade Level: 8th
Lesson Title: Unit 1: Value and
Magnitude of Rational Numbers
THE TEACHING PROCESS
Subject Area: Math
Lesson Length: 6 Days
Lesson Overview
This unit bundles student expectations that address sets and subsets of rational
numbers, ordering rational numbers, and converting between standard decimal
notation and scientific notation. According to the Texas Education Agency,
mathematical process standards including application, tools and techniques,
communication, representations, relationships, and justifications should be
integrated (when applicable) with content knowledge and skills so that students
are prepared to use mathematics in everyday life, society, and the workplace.
During this unit, students continue to examine the sets and subsets of rational
numbers and use a visual representation, such as a Venn diagram, to describe
the relationships between the sets and subsets. Rational numbers are the focus of
this unit as students order a set of rational numbers that arise from mathematical
and real-world situations. Students extend previous understandings of the
relationships within the base-10 place value system as they convert between
standard decimal notation and scientific notation. Both positive and negative
numbers are represented with standard decimal notation and scientific notation,
including values greater than and less than one.
Unit Objectives:
Students will…
- examine the sets and subsets of rational numbers and use a visual
representation, such as a Venn diagram, to describe the relationships between the
sets and subsets.
- order a set of rational numbers that arise from mathematical and real-world
situations including the use quantifying descriptors such as fastest/slowest,
coldest/warmest, etc
- extend previous understandings of the relationships within the base-10 place
value system as they convert between standard decimal notation and scientific
notation.
-use technology as appropriate to justify responses
Standards addressed:
TEKS:
8.1A Apply mathematics to problems arising in everyday life, society, and the
workplace.
8.1C Select tools, including real objects, manipulatives, paper and pencil, and
technology as appropriate, and techniques, including mental math, estimation, and
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Unit 1
Value and Magnitude of Rational Numbers
Grade 8
number sense as appropriate, to solve problems.
8.1D Communicate mathematical ideas, reasoning, and their implications using
multiple representations, including symbols, diagrams, graphs, and language as
appropriate.
8.1E Create and use representations to organize, record, and communicate
mathematical ideas.
8.1F Analyze mathematical relationships to connect and communicate
mathematical ideas.
8.1G Display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication.
8.2A Extend previous knowledge of sets and subsets using a visual
representation to describe relationships between sets of real numbers.
Supporting Standard
8.2C Convert between standard decimal notation and scientific notation.
Supporting Standard
8.2D Order a set of real numbers arising from mathematical and real-world
contexts. Readiness Standard
ELPS:
ELPS.c.1C use strategic learning techniques such as concept mapping, drawing,
memorizing, comparing, contrasting, and reviewing to acquire basic and gradelevel vocabulary
ELPS.c.2D monitor understanding of spoken language during classroom
instruction and interactions and seek clarification as needed
ELPS.c.3D speak using grade-level content area vocabulary in context to
internalize new English words and build academic language proficiency
ELPS.c.3H narrate, describe, and explain with increasing specificity and detail
as more English is acquired
ELPS.c.4H read silently with increasing ease and comprehension for longer
periods
ELPS.c.4J demonstrate English comprehension and expand reading skills by
employing inferential skills such as predicting, making connections between ideas,
drawing inferences and conclusions from text and graphic sources, and finding
supporting text evidence commensurate with content area need
ELPS.c.1H develop and expand repertoire of learning strategies such as
reasoning inductively or deductively, looking for patterns in language, and
analyzing sayings and expressions commensurate with grade-level learning
expectations
ELPS.c.2E use visual, contextual, and linguistic support to enhance and confirm
understanding of increasingly complex and elaborated spoken language
ELPS.c.2F listen to and derive meaning from a variety of media such as audio
tape, video, DVD, and CD ROM to build and reinforce concept and language
attainment
ELPS.c.5B write using newly acquired basic vocabulary and content-based
grade-level vocabulary
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Unit 1
Value and Magnitude of Rational Numbers
Grade 8
ELPS.c.5G narrate, describe, and explain with increasing specificity and detail to
fulfill content area writing needs as more English is acquired.
Misconceptions:
-Some students may think that a negative power of ten may imply a negative
number, rather than realizing the relationships within the base-10 place value
system and powers of 10.
-Some students may think that multiplying by a power of ten means to add zeros
to the end of the number.
-Some students may think that the number of zeros in a number in standard
decimal form translates to the digit exponent when converting to scientific notation.
(e.g., the number 1,254,000,000,000 has nine zeros, however the exponent of the
power of 10 when the number is written is scientific notation is 12, not 9.)
Vocabulary:
Base – the number in an expression or equation which is raised to a power or
exponent
Counting (natural) numbers – the set of positive numbers that begins at one and
increases by increments of one each time {1, 2, 3, ..., n}
Decimal notation – a representation of a real number, not including counting
(natural) numbers, which uses a decimal point to show place values that are less
than one, such as tenths and hundredths (e.g., 0.023, etc.)
E – a symbol used in a calculator to indicate that the preceding number should be
multiplied by ten raised to the number that follows
Integers – the set of counting (natural numbers), their opposites, and zero {-n, -3,
-2, -1, 0, 1, 2, 3, ..., n}. The set of integers is denoted by the symbol Z.
Order numbers – to arrange a set of numbers based on their numerical value
Place value – the value of a digit as determined by its location in a number such
as ones, tens, hundreds, one thousands, ten thousands, etc.
Powers– denoted by a number or variable in the superscript place of the base
which designates how many times the base will be multiplied by itself if it is
positive, or by its inverse if it is negative. If the power is 1, the base will be
multiplied by 1 and simplified will not change. If the power is 0, the simplified form
will equal 1.
Rational numbers – the set of numbers that can be expressed as a fraction ,
where a and b are integers and b ≠ 0, which includes the subsets of integers,
whole numbers, and counting (natural) numbers (e.g., -3, 0, 2, , etc.). The set of
rational numbers is denoted by the symbol Q.
Scientific notation – a representation of a number by using a method to write
very large or very small numbers using powers of ten that is written as a decimal
with exactly one nonzero digit to the left of the decimal point, multiplied by a power
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Unit 1
Value and Magnitude of Rational Numbers
Grade 8
of ten (e.g., 2.3 x 10−2, etc.)
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Related Vocabulary:
Ascending
Multiplicative identity
Set of numbers
Base-10 place value system
Number line
Subset of numbers
Descending
Repeating decimal
Terminating decimal
Exponent
List of Materials:
-Student cards
-Notebook or foldable materials
-You tube Video (if you are going to use it)
-Diagram on white board
-Stations (teacher will need to create their own)
-Ordering and Comparing Rational Numbers Handout
-Powers of 10 video
(http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/)
-Scientific Notation Matching cards
-Least to greatest scientific Notation Tiles
INSTRUCTIONAL SEQUENCE
Phase Engage (1/2 Day 1)
Students will use experience and reasoning skills to review the rational number
system.
Materials:
-Day 1 Rational Number Cards
-Rational Number System Diagram
Activity:
1. As students enter the room you will pass out Day 1 Rational Number
Card.
2. Prior to students entering the room you will need to have the blank Rational
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Unit 1
Value and Magnitude of Rational Numbers
Grade 8
Number System diagram on the board.
3. Students will then work together to place the cards on the diagram where
they see fit. Have them use prior knowledge and ask other classmates for
help.
4. Once all the cards are placed where they see fit then lead a class
discussion about the number system.
5. The following picture is the diagram to use for the engage piece just leave
off the irrational section.
What’s the teacher doing?
-
Engaging with the students.
*Where do you think that
number should go?
Answers may vary ( under the
rational section because…..
or in the whole number
section because…., etc
*Do you think it could be
placed in more than one
place? Answers will vary
here also depending on their
prior knowledge of these
number sets
* Can you compare it to any
numbers that you already
know? Yes, because……. Or
No, because….. answers are
going to vary since this is a
prior knowledge skill base
What are the students doing?
-
Actively working with classmates
to place their cards on the
diagram.
-
Asking questions to classmates
and teacher to help decide where
the card should be placed.
*What would this look like
on a number line? If you
organize this Venn diagram
on a number line the whole
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Unit 1
Value and Magnitude of Rational Numbers
Grade 8
numbers would be your
benchmark spots. The
integers would be your
benchmark spots on the left
of zero. The rational numbers
would be somewhere in
between the integers and
whole numbers.
*Could the number line help
you here?
-
Reassuring students it is ok if the
cards are not in the correct
places we are using prior
knowledge and recall.
Phase _Explore_(1/2 Day 1)
Procedures and strategies for rational number conversions
Materials:
-Interactive notebook or colored paper for foldable
-Rational Number System Diagram
-you tube video linked below
Activity:
1. Have students look at the numbers on the diagram built as a class. Ask
questions to determine if any of the numbers are equivalent.
2. In your interactive notebook or on a foldable review/discuss the ways you
can convert between numbers.
Ex. Fraction to Decimal, Decimal to fraction,
3. Use the cards on the diagram as your examples that way you can correct
the diagram if cards were misplaced. Have them record the final diagram in
their journal
4. Teacher will need to include definitions in the notebook as well.
Ex. Rational, whole numbers, integers, etc.
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Unit 1
Value and Magnitude of Rational Numbers
Grade 8

There is also a Youtube video you could show at this time if you would like.
( http://www.youtube.com/watch?v=cLP7INqs3JM)
*part of the video shows irrationals. Just show the rational number system
part to your class

Examples of rational numbers that could be used with your students:
1
8
3 11
, √49, − 4 ,
7
5
9
2
, 16 , −√25, 100 , .675, 3
What’s the teacher doing?
What are the student’s doing?
- The teacher will be facilitating the
discussion
- Students will be engaged in class
*Is this number like any other
discussion over how to convert
numbers you’ve worked with?
rational numbers
Yes it is I know that 1/8 can be
- Students will be recording the
written as a decimal. Yes I know
procedures in their notebooks or
foldables
that √49 𝑐𝑎𝑛 𝑎𝑙𝑠𝑜 𝑏𝑒 7.
Students should be asking
*Is it greater than 1? answers
questions as well
will vary depending on which
Students should be able to give
number you are asking about
examples to the teacher also
*Is it less than 1? Answers will
vary depending on which number
you are asking about.
*What does this number look
like in comparison to zero? It
will be on the left hand side of
zero between -1 and -2
because…. Or they could answer
it is between 0 and 1 because….
Answers will vary
*Would a number line help
you? Yes a visual is always
helpful.
- The teacher will show students
the right way to convert between
numbers clearing up any
misconceptions.
- Teacher will make sure all
students are recording in their
notebooks or their foldables
- Teacher needs to go in depth
about rational numbers and
explain why fractions and some
square roots are considered
rational numbers and give
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Unit 1
Value and Magnitude of Rational Numbers
Grade 8
detailed examples of fractions
and square roots that are rational
on top of decimal and whole
number example.
Phase ___Explain_(Day 2)
Compare and order rational numbers
Materials:
-Teacher created stations (not provided, make according to your class needs)
-Recording document for stations
Activity:
1. Students will need to be put into groups upon arrival to class.
2. Within their groups the students will need complete the stations provided by
the teacher.
3. The four stations will consist of :
Station 1: Order the rational number from least to greatest
Station 2: Use <,>,= symbols to compare the rational numbers
Station 3: Match the fractions, decimals and percent’s
Station 4: Order the rational numbers from greatest to least
*Teachers will make stations how they see fit in their own classroom
What’s the teacher doing?
-
-
-
The teacher will be monitoring
the student groups. Make sure
they are working on the stations
as directed.
The teacher will also be
asking/answering questions for
those struggling groups or
individual learners.
Teacher should also be watching
for those students that are not
getting it the ones depending on
their group
What are the students doing?
-
-
The students are working
together in their groups to
complete the stations
The students are asking their
group members and their teacher
for help.
Phase _Elaborate (Day 3)
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Unit 1
Value and Magnitude of Rational Numbers
Grade 8
Applications for ordering rational numbers
Materials:
-Ordering and Comparing Rational Numbers (handout section)
Activity:
1. Distribute the Ordering and Comparing Rational Numbers handout.
2. Place students in pairs and allow them time to work together to complete
the handout.
*Require students to justify their thinking. Don’t just allow them to quickly
complete the three questions and turn it in. Make them show and tell why.
What’s the teacher doing?
-
The teacher is monitoring the
pairs to check for understanding.
The teacher is also monitoring for
students to be on task.
What are the students doing?
-
The students are working
together to apply what they know
from previous lessons
Phase: Engage/Explain (Day 4)
Materials:
- Powers of 10 Video linked below
- Interactive journals or paper for foldables
- Dry erase boards and markers
Activity:
EngageWatch Powers of 10 Video
http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/
Lead class discussion on the purpose of the video. Then show the following
number on the board: 2,190,000,000,000,000
Ask students to try and say this number. Once they have tried show them how that
number would be written in Scientific Notation. 2.19X 10 15
Then show students the following number: .000000008
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Unit 1
Value and Magnitude of Rational Numbers
Grade 8
Ask students to try and say this number. Once they have tried show them how that
number would be written in Scientific Notation. 8 X 10-9
Practice several examples on white boards or in Interactive Journals as a class
and individually. Practice going from Scientific Notation to Standard Form and vice
versa.
ExplainCreate a 4 flap foldable as a class over important vocabulary. Include the word,
definitions, and examples.
Outside of
Foldable
Base
Exponent
Powers
Inside of Foldable
Definition:
In a power, the
number that is the
common factor.
Definition:
In a power, the
number of times
the base used as
a factor.
Example:
In 103, the base is
10.
Example:
In 103, the
exponent is 3.
What’s the teacher doing?
EngageTeacher is providing intro video of
Powers of 10. After video teacher leads
discussion over what is happening
during video. Then teacher provides
examples of times people may use
Scientific Notation. Teacher provides
examples for students to practice
Scientific Notation on white boards or in
Interactive Journal.
Definition:
A product of
repeated factors
using an
exponent and a
base.
Scientific
Notation
Definition:
A compact way of
writing numbers
with absolute
values that are
very large or very
small.
Example:
Example:
3
The power 7 is
5,500 is 5.5 X 103
read seven to
.0055 is 5.5 X 10-3
third power or
seven cubed.
What are the students doing?
EngageStudents will participate by watching
intro video, and then they will participate
in class discuss over video.
Students will practice Scientific Notation
as a class on white boards or in
Interactive Journal.
Students will create a foldable together
as a class over important vocabulary.
ExplainTeacher provides instruction and
assistance on creating 4 flap foldable.
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Unit 1
Value and Magnitude of Rational Numbers
Grade 8
Phase: Explore/Elaborate (Day 5)
Materials:
- Scientific Notation Matching Cards (handout section)
- Least to Greatest Scientific Notation Tiles (handout section)
- Recording sheet or interactive journals
Activity:
Use Scientific Notation Matching cards. Students will work with a partner to
match Scientific Notation cards with the correct Standard Decimal Notation.
After students have been given enough time to match the cards, lead a class
discussion over the answers. Have students share their results.
Use Least to Greatest Scientific Notation Tiles. Students will put the tiles in
order from least to greatest using what they know about Scientific Notation.
After students have been given enough time to order the cards, lead a class
discussion over the answers. Have students share their results.
What’s the teacher doing?
What are the students doing?
During these activities the teacher is
walking around the classroom
facilitating the activity. Teacher will
guide students if necessary and work
with students who are struggling in
order to better comprehend the topic.
Students are working with partners to
better understand Scientific Notation as
well as working together to discuss
what they have learned in class.
After students have been given enough
time on each activity, lead students in
class discussion as well as discussing
the correct answers.
Students will participate in class
discussion over what they have done
with their partner work.
Phase Evaluate (Day 6)
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Unit 1
Value and Magnitude of Rational Numbers
Grade 8
Activity:
Assess the students using the Performance Assessment.
Performance Assessment #1
Analyze the situation(s) described below. Organize and record your work for each
of the following tasks. Using precise mathematical language, justify and explain
each mathematical process.
1) Consider the following numbers:
a) Create a visual representation to organize and display the relationship between
the sets and subsets of numbers:




counting (natural) numbers
integers
rational numbers
whole number
b) Place the numbers in the correct set or subset within the visual representation.
c) Record two additional numbers that belong in each set of counting (natural)
numbers, integers, and rational numbers within the visual representation.
d) Place all of the numbers recorded within the visual representation in ascending
order and verify the order using a calculator.
Performance Assessment #2
Provide access to the Internet or another resource to very larger and very small
numbers.
Analyze the situation(s) described below. Organize and record your work for each
of the following tasks. Using precise mathematical language, justify and explain
each mathematical process.
1) Using the Internet or another resource, find a very large number greater than
one billion in standard decimal notation and a very small number less than onehundred thousandths in standard decimal notation (e.g., the distance from earth to
the moon, the diameter of a cell, etc.)
a) Explain the context in which each number was used.
b) Convert both numbers into scientific notation.
2) Consider the following numbers:
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Unit 1
Value and Magnitude of Rational Numbers
Grade 8
18.0909 x 103
0.98 x 10-8
2.09 x 105
-5.3848 x 10-8
7.34 ÷ 104
a) Identify which of the numbers is written in the correct form of scientific notation.
Explain why each number is or is not in the correct form of scientific notation.
b) Convert the numbers written in the correct form of scientific notation to standard
decimal notation.
What is the teacher doing?
-
The teacher is monitoring the
students on the assessment
she/he has chosen for the
students.
What are the students doing?
-
Showing the teacher what they
have mastered in this unit.
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