5E Lesson Plan Math
Grade Level: 8
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 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 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 grade-level vocabulary
ELPS.c.1Hdevelop 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.2D monitor understanding of spoken language during classroom instruction and interactions and seek
clarification as needed
ELPS.c.2E use visual, contextual, and linguistic support to enhance and confirm understanding of
increasingly complex and elaborated spoken language
ELPS.c.2Flisten 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.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 needs
ELPS.c.5B write using newly acquired basic vocabulary and content-based grade-level vocabulary
ELPS.c.5G narrate, describe, and explain with increasing specificity and detail to fulfill content area writing
needs as more English is acquired.
Misconceptions:
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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.)
Underdeveloped Concepts:
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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.
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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 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:
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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:
Rational Numbers Handout (Includes Definitions)
Numbers Venn Diagram
Birthday Order Activity
Rational Numbers Card Set
Four Posters
Working with Scientific Notation
Converting Scientific Notation and Standard Form
Scientific Notation Activities
Investigating Scientific Notation
Ordering Scientific Notation
INSTRUCTIONAL SEQUENCE
Phase One: Engage the Learner
Day 1 Activity1:
View Colin Dodds - Number Types (Math Song) (http://youtu.be/m94WTZP14SA) on You
Tube
What’s the teacher doing?
What are the students doing?
Shows the video
Watching and listening to the video
Defining terms
Phase Two: Explore the concept #1
Day 1 Activity 2:
Create a Venn Diagram for identifying number types
What’s the teacher doing?
What are the student’s doing?
Facilitates the students identifying the different type
of numbers by creating an anchor chart (sets of
numbers) and (Subsets of numbers)
Make anchor charts identifying and explaining the
different type of numbers (students create in small
groups)
Ask - How are counting (natural) numbers, whole
numbers, integers, and rational numbers related?
Ask - How can a number belong to the same set of
numbers but not necessarily the same subset of
numbers?
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Counting (Natural) Numbers
Whole Numbers
Integers
Rational Numbers
Complete the Venn Diagram Numbers Model (each
students does an individual copy for their notebook)
Phase Three: Explore the concept #2
Day 1 Activity 3:
Birthday Order Activity using a vertical number line
What’s the teacher doing?
What are the students doing?
Passing out note cards
Students will create a fraction using their birthday
month and date.
Giving instructions for writing fractions using
birthdays
Ask how do you turn a fraction into a decimal?
Students should answer divide the numerator by the
Students will turn their personal fraction into a
decimal.
Students will check their work by using a calculator.
denominator. Make sure students show their work.
What happens when a fraction keeps repeating?
What do you do? Remind students about using the
repeating bar and show the difference between a
repeat decimal and a terminating decimal.
Students will place themselves in order from least to
greatest.
Explain the difference between ascending and
descending order.
Explain how to use the basic functions on the
calculator. Teach procedure.
Ask - How is place value used to order a set of
numbers?
Ask what it is called when you go in ascending order
(least to greatest) and descending order (greatest to
least).
Ask – What process can be used to order a set of
numbers?
Ask – How can the ordering of a set of numbers be
justified with and without a calculator?
Vertical number line – how does it look?
Phase Four: Explain the Concept and Define the Terms
Day 2 Activity 1:
Rational Numbers Card Activity
What’s the teacher doing?
What are the students doing?
Review words from yesterday
 Counting (Natural) Numbers
 Whole Numbers
 Integers
 Rational Numbers
 Ascending/descending order
 Ordering numbers
Students will get two note cards to write the
definitions down of ascending order and descending
order.
How else can ordering be identified in a question?
Examples: fastest to slowest, longest to shortest,
etc…
Pass out Rational Numbers Cards
(Direct students to cut the cards apart and place the
cards in order in ascending order)
Phase Five: Elaborate on the Concept
Students cut cards apart
Students place cards in order according to directions
from the teacher
Explain how they know the cards are in correct order
Day 3 Activity 1:
Rational Numbers Card Activity
Poster Activity
What’s the teacher doing?
What are the students doing?
Ask - How did you know what set the number
belongs in?
students fill in blank note cards
identify the type of number
Four posters needed and titled
 Counting (Natural) Numbers
 Whole Numbers
 Integers
 Rational Numbers
Give each student 4 sticky notes
How does a vertical number line compare to a
horizontal number line?
place them in order
Students write down an example of each number
type
Students place their sticky notes on the appropriate
poster and make sure the numbers are in correct
order according to the poster
Phase Six: Engage the Learner/ Explore the concept #1
Day 4 Activity 1:
View the Powers of Tens
www.powersof10.com
Investigate the Powers of Ten (Using the calculator)
What’s the teacher doing?
What are the students doing?
Show the website that demonstrates the powers of
tens
Students go to the website and they make
observations and predictions
Have students use calculator to multiply by different
powers of ten. (Use the same number like 612.235
times 10 to whatever power – remember to use
negative powers as well)
Students use the calculator to see what happens when
multiplying by a negative and positive exponent
What happens to the decimal when you multiply by a
positive exponent? Decimal moves to the right
What happens to the decimal when you multiply by a
negative exponent? Decimal moves to the left
Teach basic calculator usage for scientific notation
Phase Seven: Explore the concept #2
Day 4 Activity 2:
Converting Scientific Notation and Standard Form
Create a foldable explain converting between forms
What’s the teacher doing?
What are the students doing?
Facilitates by walking around and making
sure students are completing the table
Completing the table using the calculator as
a guide
Discusses using the calculator in normal
mode verses the scientific mode
Notice the difference on the calculator
between normal mode and scientific mode
Create a foldable explaining going between
Scientific notation and standard form
Phase Eight: Explain the Concept and Define the Terms
Day 5 Activity 1:
Scientific Notation Activities (Card Activity or Spinner Activity)
Investigating Scientific Notation
What’s the teacher doing?
What are the students doing?
Card Activity – teacher creates a set of scientific
notation cards and gives one to each student
Students move to the front of the room when called
to order themselves according to directions given
Students spin the spinner
Spinner Activity – teacher gives the display number
Investigating Scientific Notation – walking around
seeing if there are still any problems converting
numbers between scientific and standard form
Students express their number in scientific notation
as well as standard form.
Students justify why certain numbers are in scientific
notation and other numbers are not
Phase Nine: Elaborate on the Concept
Day 6 Activity 1:
Ordering Scientific Notation
Scientific Notation Note Card
What’s the teacher doing?
What are the students doing?
Teacher monitors students ordering scientific
numbers
Ordering numbers
Pass out Note Card
Scientific Notation Note Card
 a way of writing large or small numbers by
using powers of 10
 only one significant digit, non zero, to the
left of the decimal
 example: 3,500,000 = 3.5 X 10 6
 example: 0.035 = 3.5 X 10 - 2
Phase Ten: Evaluate students’ Understanding of the Concept
Day 6 Activity: 2
Rational Numbers and Scientific Notation Quiz
Students work on the performance indicators from IFD
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 numbers
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.
Standard(s): 8.1A, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.2A, 8.2D
ELPS ELPS.c.1C, ELPS.c.2D, ELPS.c.3D, ELPS.c.3H, ELPS.c.4H, ELPS.c.4J
Performance Assessment #2
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 one-hundred 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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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.
Standard(s): 8.1A, 8.1D, 8.1F, 8.1G, 8.2C
ELPS ELPS.c.1H, ELPS.c.2D, ELPS.c.2E, ELPS.c.2F, ELPS.c.3D, ELPS.c.3H, ELPS.c.4H, ELPS.c.4J,
ELPS.c.5B, ELPS.c.5G
What’s the teacher doing?
What are the students doing?
Monitor students as they complete quiz.
Students will complete the rational number and
scientific notation quiz.
Monitor students as they work on the performance
indicator to determine if any re-teaching is necessary
prior to the unit assessments.
Display understanding of the topics and skills taught
in this unit by completing the performance indicator.