Unit 1
Grade 8
Value and Magnitude of Rational Numbers
5E Lesson Plan Math
Grade Level: 8
Subject Area: Math
Lesson Title: Unit 01: Value and
Lesson Length: 6 days
Magnitude of Rational Numbers
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…
 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
 order a set of rational numbers that arise from mathematical and real-world
situations including the use of quantifying descriptors such as
fastest/slowest, closest/farthest, 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
Unit 1
Grade 8
Value and Magnitude of Rational Numbers
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)
8.2C: Convert between standard decimal notation and scientific notation.
(Supporting)
B: Order a set of real numbers arising from mathematical and real-world contexts.
(Readiness)
ELPS:
C1(C) use strategic learning techniques such as concept mapping, drawing,
memorizing, comparing, contrasting, and reviewing to acquire basic and gradelevel vocabulary;
C1(H) 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.
C2(D) monitor understanding of spoken language during classroom instruction
and interactions and seek clarification as needed;
C2(E) use visual, contextual, and linguistic support to enhance and confirm
understanding of increasingly complex and elaborated spoken language;
C2(F) 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;
C3(D) speak using grade-level content area vocabulary in context to internalize
new English words and build academic language proficiency;
C3(H) narrate, describe, and explain with increasing specificity and detail as more
English is acquired;
C4(H) read silently with increasing ease and comprehension for longer periods;
C4(J) 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 needs; and
C5(B) write using newly acquired basic vocabulary and content-based grade-level
vocabulary;
C5(G) narrate, describe, and explain with increasing specificity and detail to fulfill
content area writing needs as more English is acquired.
Misconceptions:
Unit 1
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Grade 8
Value and Magnitude of Rational Numbers
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.)
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Underdeveloped Concepts:
Some students may think that a number can only belong to one set (counting
[natural] numbers, whole numbers, integers, or rational numbers) rather than
understanding that some sets of numbers are nested within another set as a
subset.
Vocabulary:
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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
Unit 1
Grade 8
Value and Magnitude of Rational Numbers
subsets of integers, whole numbers, and counting (natural) numbers (e.g., -
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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 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
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Multiplicative identity
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Set of num
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Base-10 place value system
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Number line
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Subset of
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Descending
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Repeating decimal
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Terminati
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Exponent
Unit 1 Lesson 1
List of Materials:
Venn diagram with “clue” Numbers (poster size)
Let’s get “Rat”ional numbers (these will be used again in ordering numbers)
Tape
Calculator, Journal, Pencil, blank ticket out slip
Unit 1 Lesson 2
List of materials:
Large number line -3 to +3
“Rat”ional numbers
Teacher generated list of numbers to covert for notes
Compare and Order Rational Numbers
HW: Part 2: Applications of Rational Numbers
Student Dry Erase Boards
Place Value Charts
The Powers of 10
Investigating Scientific Notation Notes
Ticket Out-Scientific Notation
Ticket out-Where do I fit and The Rule
Good Clips:
 OPTIONS for your choice
 Holt real world example grade 8 new textbook Unit 1, Module 2 Sci
Unit 1
Grade 8
Value and Magnitude of Rational Numbers
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Note
Schmoop: http://www.shmoop.com/video/scientific-notation Good for
accelerated students
Colin Dodd: https://www.youtube.com/watch?v=AWof6knvQwE Ok for
most students
https://www.youtube.com/user/bartlebytheeducator Very good for ESL
https://www.youtube.com/watch?v=HtXTKrigYqk synote OK but busy
Brain Pop Scientific Notation subscription required
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Applications of Scientific Notation
Reflecting Scientifically
Power point Adding and Subtracting Coefficients, Bases and Powers
Round Robin Scientific Notation Powers and Recording Document
Performance Assessment 1 and 2
INSTRUCTIONAL SEQUENCE
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Day 1
Copy or draw poster of Venn Diagram to be placed in desired location.
Copy and cut out Venn Diagram Sections for Assessment portion
Copy and cut out numbers that will be used (do not use percents in this
unit)
*enrichment-use irrational cards or blank cards to create extension
Place word wall vocabulary on word wall to refer to during the lesson
Decide and prepare for how you will show and speak the vocabulary EX:
power point, written notes, overhead, document camera, printed notes
Prepare “Ticket out” area
Phase: Engage
10 minutes (time can be arranged
according to individual class or bell
schedule)
Activity:
 Prepare classroom by placing the Venn Diagram in a prominent location.
 As students enter the room, give each of them a “Rat”ional number
 Instruct them to place the number in the correct location on the diagram,
using their knowledge and the “clue” numbers already listed.
What’s the teacher doing?
Monitoring vocabulary
Modeling compare and contrast
Similar characteristics
Asking Guiding Questions
How are these numbers related?
They can all go on the Venn
Diagram. Answers are varied for this
question.
Why did you place them into this
What are the students doing?
Placing the numbers in location
Discussing merit of placement
Self-correcting
Peer-correcting
Unit 1
Grade 8
Value and Magnitude of Rational Numbers
location on the Venn Diagram?
This is not a fraction, this is negative,
this is positive.
Are there any numbers that can into
more than one location?
Yes, 3 is a whole number and a
counting number.
Informally assessing
Phase: Explore
15 minutes (time can be arranged
according to individual class or bell
schedule)
Activity:
 Have the students group to discuss whether the numbers are in the correct
location. Can they be placed elsewhere? Is this the best or only place?
 Hand out the “duplicates” to groups, numbers that are in more than one set,
and have the groups place these in the correct location.
 Facilitate discussion how are these numbers related, alike, not alike
What’s the teacher doing?
What are the student’s doing?
Monitoring conversations
Guiding correct placement
Analyzing placement
Discussing duplicates
Forming opinions
Justifying with technology
Using calculator to prove terminating,
repeating, show square root
Phase: Explain
15 minutes (time can be arranged
according to individual class or bell
schedule)
Activity:
 Draw Venn Diagram in journal
 Label at least three numbers in each category
 Clarify notes on set, subset, terminating and repeating decimals, natural,
counting, integers.
 Enrichment: Use the irrational cards and discuss why they are not in any of
the subsets used. (Belong to the set of Real Numbers R, one set above
rational)
What’s the teacher doing?
What are the students doing?
Showing key vocabulary words on word
wall
Show and state the definition (power
Drawing in journal
Labeling and defining numbers
Unit 1
Grade 8
Value and Magnitude of Rational Numbers
point)
Checking for understanding
Phase: ELABORATE
5 min or less (time can be arranged
according to individual class or bell
schedule)
Activity:
Pull out 3 additional numbers and have the students quickly discuss location on
diagram. Have them tell you or come up and show you where they go.
What’s the teacher doing?
What are the students doing?
Show numbers
Listen and correct communications
Discussing
Placing
Verifying
5 minutes (time can be arranged
according to individual class or bell
schedule)
Phase: EVALUATE (Mini)
Activity:
 Have each student choose 1 previously unused number and determine
which subset/s it would be placed in and justify their reasoning.
What’s the teacher doing?
What are the students doing?
Answering questions
Checking for understanding
Making sure name is on cut out
Choosing a number, analyzing the set
and subset/s, using organized
information to present justification.
Placing it in pocket (ticket out)
**assess students numeracy in
preparation for next lesson, ordering
rational numbers
Unit 1
Grade 8
INSTRUCTIONAL SEQUENCE
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Value and Magnitude of Rational Numbers
Day 2
Prepare a large number line for the students to utilize (0) in middle
Have ready all positive and negative numbers from previous lesson
Place word wall vocabulary on word wall to refer to during the lesson
Decide and prepare for how you will show and speak the vocabulary EX:
power point, written notes, overhead, document camera, printed notes
Note that there will be HOMEWORK
Phase: Engage
10 minutes (time can be arranged
according to individual class or bell
schedule)
Activity:
Prepare classroom by placing the
number line on the floor or board.
As students enter the room, give each
of them a number from the “Rat”ional
Numbers sheet
Instruct them to place the number in the
correct location on the number line
What’s the teacher doing?
Monitoring placement
Modeling compare and contrast
Similar characteristics
Asking Guiding Questions
What do you notice about 1 and -1 in
relation to zero? They are the same
distance from zero.
What about 1.5 and negative 1.5 in
relation to zero? They are the same
distance from zero, they are on the
other side of the one.
Informally assessing integer knowledge,
in relation to zero
Phase: Explore
Activity:
 Have the students group to
discuss whether the numbers are
in the correct location.
What are the students doing?
Placing the numbers in location
Discussing merit of placement
Self-correcting
Peer correcting
5 minutes (time can be arranged
according to individual class or bell
schedule)
Unit 1
Grade 8
Value and Magnitude of Rational Numbers
What’s the teacher doing?
What are the student’s doing?
Monitoring conversations
Analyzing placement
Discussing duplicates
Forming opinions
Justifying with technology
Guiding correct placement with well
thought questions
Guiding calculator to prove terminating,
non-repeating
Phase: Explain
Activity:
 Use Compare and Order
Rational Numbers to determine
location of rational numbers in
relation to each other and on a
number line.
What’s the teacher doing?
Showing how to best use calculator to
determine placement
20 minutes (time can be arranged
according to individual class or bell
schedule)
What are the students doing?
Using numbers, equality and inequality
symbols to place numbers in relation to
each other
Checking for understanding
Phase: ELABORATE
Using a number line to visualize
location of and proximity of various
rational numbers
15 minutes
Activity:
 Teacher directed notes if
required
 How to convert mixed numbers
to whole numbers
What’s the teacher doing?
What are the students doing?
Using a previously chosen set of mixed,
improper and decimal rational numbers
Taking notes?
Unit 1
Grade 8
Value and Magnitude of Rational Numbers
to convert into best form for ordering
Phase: EVALUATE
 Homework sent home
 Can do a quick HW check next
day
Homework:
Activity:
 Part 2 Applications of Rational
Numbers
**Will be checked as warm up next day
What’s the teacher doing?
What are the students doing?
Answering questions
Checking for understanding
Clarifying misunderstandings
Making necessary corrections
PHASE: ENGAGE
DAY 3
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Applications 20 min or less
Check Calculators for setting scientific notation
Prepare word wall for lesson
Review video clips to choose one you like
1 copy of place value chart (blank) for each student for journal (cut
apart)
Make 1 copy of Powers of 10 for each student
Phase Engage
10 minutes (include 5 min HW check)
Unit 1
Grade 8
Value and Magnitude of Rational Numbers
Activity: Have one very large magnitude number written on the board and
one very small magnitude number written on the board.
EX: 1,234,567,891,234
EX: .00220033
What’s the teacher doing?
 Asking what the numbers are in
words.
 Listening to students and
clarifying that they are able to
articulate large and small
magnitude numbers correctly.
 Ask them to consider how they
know the correct verbiage.
 **This is the place value
discussion
 Ask them to think of an easier
way to write or say these
numbers.
 Discuss hundreds versus
hundredths, real world examples
of how mistakes could be
made.(medicine, dosages,
population etc.)
What are the students doing?
 Using pencil and paper to decide
the names (place value) of the
two numbers.
 Discussing the fact that these are
difficult numbers to use in every
day or scientific conversation.
 Hundreds sounds like
hundredths, easy to make a
mistake.
Phase Explore
Activity:
 Place value chart
5 minutes
What’s the teacher doing?
What are the student’s doing?
 Placing chart in journal
 Put numbers in correct locations
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Hand out and monitor placement
of chart in journal
Write three numbers on board
Unit 1
Grade 8
Phase Explain
Value and Magnitude of Rational Numbers
3-7 minutes
Activity:
Video Clip and discussion
Good Clips:
 Holt real world example grade 8 new textbook Unit 1, Module 2 Sci
Note
 Schmoop: http://www.shmoop.com/video/scientific-notation Good for
accelerated students
 Colin Dodd: https://www.youtube.com/watch?v=AWof6knvQwE Ok for
most students
 https://www.youtube.com/user/bartlebytheeducator Very good for ESL
 https://www.youtube.com/watch?v=HtXTKrigYqk synote OK but busy
 Brain Pop Scientific Notation subscription required
What’s the teacher doing?
What are the students doing?
Monitoring students comprehension of
video or videos
Phase: Elaborate
Watching video
20 minutes
Activity:
The powers of 10 Questions 1-23
Partner or group of three
What’s the teacher doing?
What are the students doing?
Monitoring appropriate use of calculator
Working together to use technology
Clarifying the use of the ^ and the –
** the ^ and (-) key are very
important in algebra.
Working together to check answers
(decimal placement)
Phase: Evaluate
Working together to answer short
response
5 minutes
Activity: Question 24
Independently
What’s the teacher doing?
What are the students doing?
Monitor written response answers
Clarifying their thoughts
Unit 1
Grade 8
Value and Magnitude of Rational Numbers
Phase Engage
5 minutes
Activity: Warm-Up Have the students work together to place the 2 numbers into
scientific notation format **They may not have yet grasped the concept. That is
OK. This is a learning experience.
What’s the teacher doing?
What are the students doing?
Monitoring for understanding
Using skills or technology to place the
numbers into what they think the
answer will be
Checking to see who might be paired
with who
Ask a few correct students to describe
how they arrived at their answer
Showing the white board to teacher
Discussing with peers
If no one is correct, that is OK, ask what
they think they can do instead.
Phase Explore
25 minutes
Activity:
 Investigating Scientific Notation Notes
What’s the teacher doing?
Working with partners to guide them in
the correct direction
Explaining E (TI Calc’s)
Monitoring that they remember
^ and -
What are the student’s doing?
Working with partner/s to complete the
notes
Checking number answers with
technology
Answering short response
Phase Explain
10 minutes
Activity:
 Class discussion
What’s the teacher doing?
Facilitating discussion
Why do you think we use scientific
notation? To write and say very large
or very small more accurately.
Clarifying misconceptions
What are the students doing?
 Comparing answers to short
response across groups
Unit 1
Phase: Evaluate
Grade 8
Value and Magnitude of Rational Numbers
5 min
Activity:
 Ticket Out -Standard form versus Scientific Notation
What’s the teacher doing?
What are the students doing?
Monitoring and offering feedback on
ticket out work
Independently converting 4 numbers
into either standard or scientific form
INSTRUCTIONAL SEQUENCE
DAY 3
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Prepare or use Slide Show of 5 or more real world objects and their
magnitude in scientific notation
 Prepare copy of where do I fit for student journal 1 per student
 Prepare copies of Applications of Scientific Notations or Reflecting
Scientifically (your choice)
Phase: Engage
10 minutes
Activity:
 Show slide show of objects
 Have students convert scientific notation into standard form verbally as a
whole group
What’s the teacher doing?
What are the students doing?
Showing slides
Viewing
Facilitating corrective techniques
discussion
Converting numbers into standard form
Phase: Explore
5 minutes
Activity: Where do I fit? Top half of Page
Bottom of page Ticket out
What’s the teacher doing?
Monitoring for understanding
Are we just adding zero’s? No, we
are adding or removing place value.
What are the student’s doing?
Converting rational numbers
Converting scientific notation into
standard form
Ordering numbers on the number line
Unit 1
Grade 8
Phase: Elaborate
Value and Magnitude of Rational Numbers
20 minutes
Activity:
 Applications of Scientific Notation or Reflecting Scientifically (one
could be used for HW)
 Work independently
What’s the teacher doing?
What are the students doing?
Monitoring appropriate use of calculator
Working independently to use
technology
Clarifying the use of the ^ and the Assisting struggling students
Working independently to check
answers (decimal placement)
Phase: Evaluate
Working together to answer short
response (if any on sheet)
5 minutes
Activity:
 Write the “Rule” (Standard number less than 1 negative exponent, more
than 1, positive exponent
What’s the teacher doing?
What are the students doing?
Monitoring
INSTRUCTIONAL SEQUENCE
Reviewing notes to arrive at conclusion
for when exponent is positive or
negative
Day 4
 Check Calculators for setting scientific notation
 Prepare notes for adding and subtracting using scientific notation
 Make one copy of carousel sheets for students to work with
 Place carousel sheets around the room according to your needs
Phase: Engage
5 minutes
Activity: Have a word problem subtracting scientific notation numbers together on
the board. Do not have them convert at this time. Just a straightforward
application problem is needed. EX:
The Nile River is the longest river in the world. The river is 4.195 x 103 miles
in length. The Rio Grande river is 1.896 x 103 miles long. How much longer
is the length of the Nile River than the Rio Grande?
A. 2299 x 103 mi
B. 2.299 × 10-3 mi
C. 2.299 × 103 mi
D. 2299 × 10 mi
Unit 1
Grade 8
Value and Magnitude of Rational Numbers
What’s the teacher doing?
What are the students doing?
Watching as the students try a variety of
ways to solve the problem
Using a calculator to solve
Using pen and paper to solve
Checking answer with technology
Phase Explore
Activity:
 Round Robin
What’s the teacher doing?
Monitoring student product
Checking for reasonableness
25 minutes
What are the student’s doing?
Phase Explain
Moving from page to page answering
and justifying
10 minutes
Activity:
 Go over answers
What’s the teacher doing?
What are the students doing?
Group students based on what you saw
while observing
Phase: Elaborate
Discussing answers in groups
5 minutes
Activity:
 Choose 2 problems, 1 addition and one subtraction that require conversion
What’s the teacher doing?
What are the students doing?
Working out, step by step, the 2
problems the students struggled with
the most
Placing these 2 examples into their
journals for notes
Phase: Evaluate
HW Review for Unit Exam
PA 01
PA 02
Unit 1
Grade 8
Value and Magnitude of Rational Numbers