5E Lesson Plan Math
Grade Level: 6th
Lesson Title: Unit 2: Ordering Fractions,
Decimals, and Integers
THE TEACHING PROCESS
Subject Area: Math
Lesson Length: 5 days
Lesson Overview
This unit bundles student expectations that address sets and subsets of numbers, generating
equivalent forms of rational numbers, as well as comparing and ordering rational numbers and
integers. 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 their understanding of equivalency by generating and using
equivalent forms of fractions, decimals, and percents. The negative aspect of the number line is
introduced as students explore the concept of integers and negative rational numbers. Students
locate an integer or rational number on a number line and use its location to compare and order a
set of numerical values, which may be presented in various forms. The number line may be used
as a tool to assist in comparing or ordering a set of numbers; however, students are also expected
to order a set of rational numbers arising from mathematical and real-world contexts using any
strategy, such as place value, number sense, or comparisons to benchmarks. Students 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. This is the first time students classify a
number as a counting (natural) number, whole number, integer, or rational number. Although the
focus of operations in Grade 6 is with integers and positive rational numbers, students are
expected to classify, compare, and order both positive and negative numerical values.
Unit Objectives:
Students will…
 continue their understanding of equivalency by generating and using equivalent forms of
fractions, decimals, and percents.
 explore the concept of integers and negative rational numbers.
 locate an integer or rational number on a number line and use its location to compare and
order a set of numerical values, which may be presented in various forms.
 expected to order a set of rational numbers arising from mathematical and real-world
contexts using any strategy, such as place value, number sense, or comparisons to
benchmarks.
 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.
 classify a number as a counting (natural) number, whole number, integer, or rational
number.
 expected to classify, compare, and order both positive and negative numerical values.
Standards addressed:
TEKS:
 6.1A: Apply mathematics to problems arising in everyday life, society, and the workplace.
 6.1C: 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.
 6.1D: Communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate.
 6.1E: Create and use representations to organize, record, and communicate mathematical
ideas.
 6.1F: Analyze mathematical relationships to connect and communicate mathematical
ideas.
 6.1G: Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
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6.2A: Classify whole numbers, integers, and rational numbers using a visual representation
such as a Venn diagram to describe relationships between sets of numbers. (Supporting)`
6.2C: Locate, compare, and order integers and rational numbers using a number line.
(Supporting)
6.2D: Order a set of rational numbers arising from mathematical and real-world contexts.
(Readiness)
6.4G: Generate equivalent forms of fractions, decimals, and percents using real-world
problems, including problems that involve money. (Readiness)
ELPS:
 ELPS.c.1A - use prior knowledge and experiences to understand meanings in English
 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.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.3C - speak using a variety of grammatical structures, sentence lengths, sentence
types, and connecting words with increasing accuracy and ease as more English is
acquired
 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.4D - use prereading supports such as graphic organizers, illustrations, and
pretaught topic-related vocabulary and other prereading activities to enhance
comprehension of written text
 ELPS.c.4H - read silently with increasing ease and comprehension for longer periods
 ELPS.c.5B - write using newly acquired basic vocabulary and content-based grade-level
vocabulary
Misconceptions:
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Some students may think that negative integers with larger absolute values are greater
than negative integers with smaller absolute values.
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.
Some students may think that a percent may not exceed 100%.
Some students may think that a percent may not be less than 1%.
Some students may not realize which operation is easier to use when converting between
number forms.
Some students may confuse decimal place values when converting decimals to fractions.
Some students may have difficulty recognizing the part and the whole in problem
situations.
Some students may believe every fraction relates to a different rational number instead of
realizing equivalent fractions relate to the same relative amount.
Some students may multiply a decimal by 100 moving the decimal two places to the right
when trying to convert it to a percent rather than dividing by 100 and moving the decimal
two places to the left.
Some students may try to convert a fraction to a decimal by placing the denominator in the
dividend, rather than the numerator.
Some students may think that is equivalent 0.78.
Vocabulary:
 Counting (natural) numbers – the set of positive numbers that begins at one and increases
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by increments of one each time {1, 2, 3, ..., n}
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
Percent – a part of a whole expressed in hundredths
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.
Positive rational numbers – the set of numbers that can be expressed as a fraction , where
a and b are whole numbers and b ≠ 0, which includes the subsets of whole numbers and
counting (natural) numbers (e.g., 0, 2, etc.)
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.
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
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Ascending
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Improper fraction
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Proper
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Compare
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Interval
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Repea
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Descending
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Less than
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Set of
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Decimal
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Magnitude
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Subse
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Denominator
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Mixed number
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Termin
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Equal to
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Number line
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Tick m
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Equivalent
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Numerator
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Venn d
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Fraction
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Open number line
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Whole
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Greater than
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Part
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List of Materials:
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Interactive math journal
Pencil
Scissors
Glue
Crayons
4 sheets of copy paper
Stapler
Markers
INSTRUCTIONAL SEQUENCE
Phase: ENGAGE
Activity: Materials needed for today: interactive math journal, crayons
Write the following words on the board: integer, whole number, irrational number, rational number,
and natural number. Ask students if they are familiar with any of the terms. Allow 1-2 minutes to
discuss with a shoulder partner what they think the words mean.
When time is up, allow a few to share their thoughts.
To introduce the vocab go to www.thatquiz.org
You may need to create an account in order to access the slides and quiz.
Search for – The Real Number System, click on Warren, Aaron-Port Chester Middle
School….Lesson – The Real Number System. At the top of the screen, click Take this test now.
Go through the slides discussing each one with the students. Have them write in their journals the
words, definition, and examples for each type of number. There are questions to review what they
have learned, go through those. Discuss why each number is classified in one or more of the
categories. Answer any questions that may arise.
Once you have finished, hand out the Real Number Graphic Organizer, and tell students they will
use their journal to fill this out. Give a few minutes for them to complete this activity. Check their
work as they go along. As a class, you will outline the different types of numbers. Students will
need to get out a red, blue, green, orange, and purple crayon. Have students take the red crayon
and outline the smallest box and label it with Natural Numbers, counting numbers and have them
put examples. Follow the same for each box (starting out with the smallest):
 Natural Numbers (Red): counting numbers, examples
 Whole Numbers (Blue): Natural numbers + Zero, ex.
 Integers (Green): Whole Numbers and their opposites, ex.
 Rational Numbers (Orange): Integers + Fractions, *Decimals must be terminating or
repeating, ex.
 (rectangle to the side) Irrational Numbers (Purple): Non-repeating and non-terminating
decimals, *cannot be expressed as a fraction of integers.
Discuss with students the relationship between the numbers in the number system.
Next we will look at comparing and ordering rational numbers using a number line.
ASK: How do you compare and order rational numbers? You can write them as equivalent
decimals and then compare them.
Students will watch a YouTube video that shows how this will be done.
https://www.youtube.com/watch?v=qOarSbiiSzs
Go through a few examples together.
 ½; 0.6, 9/10
 5/25; ¼; 0.321; 7/11
Use the following problem as an exit ticket: Compare and order 6/10; 4/10; 9/10
What’s the teacher doing?
Phase: EXPLORE
What are the students doing?
Activity: Materials needed for today: 4 sheets of copy paper, markers, stapler, handout
(Comparing and Ordering Rational Numbers)
Students will participate in a folding activity with the Real Number system. There is a video on
YouTube that shows how to create it. Real Number System Foldable by Carrie Mersch.
http://www.youtube.com/watch?v=vVVzl7SV5f0
Students will need 4 sheets of paper, markers, and a stapler available for them.
After completing the fold activity, you will do some examples on the board using number lines.
Hand out the explore activity (Comparing and Ordering Rational Numbers) for comparing and
ordering rational numbers.
Point out to students that the scale used for the number line is tenths. Every other fraction on the
number line has a denominator of 5 because the labels are in simplest form. For example, 2/10
simplifies to 1/5.
Exit Ticket: Students will take 2-3 minutes at the end of class to complete a KWL write activity.
Have the students do a quick write of What I Know, What I Want to know, and What I have Learned
so far. They will hand this to the teacher on their way out.
What’s the teacher doing?
What are the student’s doing?
Phase: EXPLAIN
Activity: Materials needed for today: individual whiteboards, dry erase
marker, eraser for board, homework page (Homework – Rational Numbers)
Draw a Venn Diagram, like shown below, on the board.
Rational Numbers
Integers
Whole Numbers
Use the Venn Diagram to determine to which set or sets each number belongs. Place the numbers
in the diagram. You can have kids come up to the board and write the numbers where they think it
goes. If their placement is incorrect, discuss why they chose that place and then explain the
correct placement to them.
 106
(Whole Numbers)
 -5
(Integers)
 5/7
(Rational Numbers)
 -0.4
(Rational Numbers)
Ask: In a Venn diagram, explain what it means when a number is within a particular circle. It
means that the number is part of the group represented by the circle. For example, a number
within the integers circle in an integer.
Ask: The Venn diagram shows the Whole Numbers circle within the integers circle. What does
that tell you about whole numbers? About integers? Name an integer that is not a whole number.
It means that all whole numbers are integers. Not all integers are whole numbers. -2 is an integer
but not a whole number.
Point out to students that part of the definition of a rational number is that the denominator, b,
cannot equal zero. This is because division by zero is undefined. It is possible to divide 0 pizzas
between 3 people; each person would get 0 pizzas. But 3 pizzas shared by 0 people is
meaningless.
Pass out whiteboards and markers to students. Have students work individually to write each
rational number as a/b. Do one at a time. Check each students work after each number.
 1 3/8
 0.75
 12
 -9
Answers:
 11/8
 75/100
 12/1
 -9/1
***Have the students keep the boards/markers, but place to the side, they will need it again.
Ask: How do you decide which number to use for the denominator when you are rewriting a
decimal as a fraction? You use the place value of the digit farthest to the right. For example, if the
decimal has 2 places, use 100 for the denominator.
Remind students that when writing a negative integer as a fraction, they need to include the
negative sign with the fraction.
Ask: How can you compare two fractions? Compare their equivalent decimals or rewrite them with
common denominators and compare the numerators.
Ask: How can you compare a fraction with a decimal? Rewrite them so both are decimals or both
are fractions.
Using the whiteboards/markers, you will give the students some examples to order.
 0.3, 2/5, 0.85, 0.09, ¾, 3/20 (least to greatest) 0.09, 3/20, 0.3, 2/5, 3/4, 0.85
 0.4, 1/3, 5/6 (least to greatest) 1/3, 0.4, 5/6
 -0.5, 1 ¼, 0.25, 3/8 (least to greatest) -0.5, 0.25, 3/8, 1 ¼
Use this problem as your exit ticket: 0.85, 3/5, 0.15, 7/10 (least to greatest) 0.15, 3/5, 7/10, 0.85
Ask students if there are any questions about today’s lesson because they will have homework to
complete for tonight.
Pass out homework.
What’s the teacher doing?
What are the students doing?
Phase: ELABORATE
Activity: Materials needed for today: individual whiteboard, dry erase
marker, eraser for board, handout (“Express” Fractions and Decimals)
Ask: Have you ever seen a sign that said “50% off” or one that said “1/2 off”? Which is a better
sale? Remind students that to compare two numbers, both need to be in the same form. Have
students rewrite 50% and ½ as fractions with the same denominator and compare the numbers.
Students should conclude that the two numbers are equivalent. Repeat the activity with another
pair of numbers, such as 20% and ¼.
You will do some examples on the board with the students and then allow time for extra practice on
whiteboards.
The following problems should be worked out on whiteboards by the students.
Write each fraction as a decimal and as a percent.
9/25 – 0.36, 36% 7/8 – 0.875, 87.5% 5/8 – 0.625, 62.5%
Write each percent as a fraction and as a decimal.
72% - 18/25, 0.72 25% - 1/4 , 0.25 500% - 500/100, 5/1=5
Students will complete the “Express” Fractions and Decimals either in class or for homework
depending on time.
What’s the teacher doing?
What are the students doing?
Phase: EVALUATE
Activity:
Students will complete the Performance Assessment for Unit 2.
Mathematics Grade 6 Unit 02 PA 01
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) Beginning on February 10, 2011, the average temperature in Nowata, Oklahoma was -31°F. For
seven consecutive days, the average temperature was recorded in the table below.
a) Create a visual representation, such as a Venn diagram, to organize and display the
relationships between the sets and subsets of numbers:
 counting (natural) numbers
 integers
 rational numbers
 whole numbers
b) Place the temperatures from the table above in the correct set or subset within the visual
representation.
c) Compare the temperatures and order them from coldest to warmest. Justify your comparison by
locating each temperature on a number line.
2) On February 12, the temperature fluctuated above and below 0°F several times. For
of
the day, the temperature remained below 0°F.
a) Generate an equivalent decimal and fraction to represent the part of the day the temperature
remained below 0°F on February 12.
If time permits, you can either review the Performance Assessment together as a class or if you
have laptops or a computer lab available, the students can play a game together
http://www.shodor.org/interactivate/activities/FractionFour/
there is also a math war game that they will be able to play….
Preparation:
● Cut index cards to make 40 playing cards.
● Write each number in the table on a card.
To Play:
● Play with a partner.
● Deal 20 cards to each player face-down.
● Each player turns one card face-up. The player with the greater number
wins. The winner collects both cards and places them at the bottom of
his or her cards.
● Suppose there is a tie. Each player lays three cards face-down, then a
new card face-up. The player with the greater of these new cards wins.
The winner collects all ten cards and places them at the bottom of his
or her cards.
● Continue playing until one player has all the cards. This player wins
the game.
The Index cards should have the following numbers on them:
75% ¾
1/3
3/10
0.75 66 2/3% 12.5% 40%
0
30%
5%
27/100
1
0.01
1/20
1/8
What’s the teacher doing?
0.3
25%
0.4
0.25
100%
¼
4%
0.5%
0.04
1/100
0.05 33 1/3%
2/5
0.333. . . 27%
0.125 1/25
1/200 0.005
0.666. . .
What are the students doing?
0.27
2/3
1%
0%