Gr 6 Unit 1 Resource B
Grade Level: 6th
Subject Area: Math
Lesson Title: Unit 1 Equivalent Forms
Lesson Length: 10 days
of Fractions, Decimals, and Percents
THE TEACHING PROCESS
Lesson Overview
This unit bundles student expectations that address representing and generating equivalent
forms of fractions, decimals, and percents as well as solving real-world problems involving
fractions, decimals, and percents. According to the Texas Education Agency, mathematical
process standards including application, a problem-solving model, 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 extend their mathematical foundations of equivalency within rational
numbers to include percents as a new notational system. Concrete and pictorial models,
including 10 by 10 grids, strip diagrams, and number lines are used to represent multiples of
benchmark fractions and percents. Additionally, percents are represented with concrete and
pictorial models, fractions, and decimals. Students continue their understanding of
equivalency by generating and using equivalent forms of fractions, decimals, and percents to
solve real-world problems, including those involving money. Percents less than or greater
than 100%, including percents with fractional or decimal values such as 8.25% or
are
encompassed within this unit. Students apply their understandings of percents to solve realworld problems that involve finding the whole given a part and the percent, the part given the
whole and a percent, and the percent given the part and the whole. Methods for solving realworld problem situations involving percents, such as the use of proportions or scale factors
between ratios, are not included in this unit. Additionally, computations within this unit are
restricted operational capabilities from Grade 5 which include sums and differences with any
positive rational numbers, products with factors limited to a whole number by a whole
number, a decimal by a decimal, or a whole number by a fraction, and quotients limited to
whole number dividends and divisors, a decimal dividend by a whole number divisor, or
whole number and unit fraction dividends and divisors.
Unit Objectives:
Students will…
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extend their mathematical foundations of equivalency within rational numbers to
include percents as a new notational system
represent multiples of benchmark fractions and percents. using concrete and pictorial
models, including 10 by 10 grids, strip diagrams, and number lines. Additionally,
percents are represented with concrete and pictorial models, fractions, and decimals
continue their understanding of equivalency by generating and using equivalent forms
of fractions, decimals, and percents to solve real-world problems, including those
involving money. Percents less than or greater than 100%, including percents with
fractional or decimal values such as 8.25% or
are encompassed within this
unit.
apply their understandings of percents to solve real-world problems that involve
finding the whole given a part and the percent, the part given the whole and a
percent, and the percent given the part and the whole. Methods for solving real-world
problem situations involving percents, such as the use of proportions or scale factors
between ratios, are not included in this unit. Additionally, computations within this unit
are restricted operational capabilities from Grade 5 which include sums and
differences with any positive rational numbers, products with factors limited to a
whole number by a whole number, a decimal by a decimal, or a whole number by a
fraction, and quotients limited to whole number dividends and divisors, a decimal
dividend by a whole number divisor, or whole number and unit fraction dividends and
divisors.
Standards addressed:
TEKS:
6.1A Apply mathematics to problems arising in everyday life, society, and the
workplace.
6.1B Use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution.
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.
6.4E Represent ratios and percents with concrete models, fractions, and decimals.
(supporting)
6.4F Represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and
multiples of these values using 10 by 10 grids, strip diagrams, number lines, and
numbers. (Supporting)
6.4G Generate equivalent forms of fractions, decimals, and percents using real-world
problems, including problems that involve money. (readiness)
6.5B Solve real-world problems to find the whole given a part and the percent, to find
the part given the whole and the percent, and to find the percent given the part and the
whole, including the use of concrete and pictorial models. (Readiness)
6.5C Use equivalent fractions, decimals, and percents to show equal parts of the same
whole. (Supporting)
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 gradelevel vocabulary
Elps.c.2D monitor understanding of spoken language during classroom instruction and
interactions and seek clarification as needed
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.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 gradelevel 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 percent may not exceed 100%.
Some students may think that a percent may not be less than 1%.
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 think the value of 43% of 35 is the same value of 43% of 45
because the percents are the same rather than considering that the wholes of 35 and
45 are different, so 43% of each quantity will be different.
Underdeveloped Concepts:
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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 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:
Percent – a part of a whole expressed in hundredths
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Positive rational numbers – the set of numbers that can be expressed as a
fraction
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, 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.)
Strip diagram – a linear model used to illustrate number relationships
Related Vocabulary:
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10 by 10 grid
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Denominator
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Multiple
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Area model
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Equivalent
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Number
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Place value
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Fraction
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Numera
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Benchmark fraction
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Fraction circle
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Part
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Benchmark percent
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Fraction notation
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Proper f
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Decimal
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Improper fraction
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Whole
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Decimal notation
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Mixed number
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Whole n
List of Materials:
 Decimal and Percent Pizza slices. www.worksheetfun.com for free fraction
circle templates to create pizza slices and pizza box models.
 Pizza boxes with original fractions to match drawn inside.
 Coins printed from the following http://www.eprintablecalendars.com/coins/
 10 x 10 grid https://www.teachervision.com/tv/printables/scottforesman/Math_4_TTT_12.pdf
INSTRUCTIONAL SEQUENCE
Phase: Engage
Suggested DAY 1
Activity:
Students will use their prior knowledge of equivalent fractions to match the pieces of each
fraction decimal and percent. Prior to the lesson you have made 2 pizza slices of each of
the following fractions ½, ¼, 1/3, ¾, 1/10, 1/5 and 4/4. One piece will have the decimal
of each of these fractions, one will have the percent of each of the previous fractions.
One student will be holding a pizza that is missing one of these fractional parts from
his/her pizza. Students with pizza slices are to match their pizza to the missing pizza and
announce to the pizza holder their part is equal to the missing fractional part (“I have 50%
and it is equal to ½”). Once both pizza slices are placed in the empty space, one on top of
the other, the box will be closed to indicate that their pizza is complete. After class has
completed the activity they will discuss with their group the following questions:
Why do you think the two slices of pizza belong in this group?
Besides matching the pictures, create another method of proving your fraction, percent
and decimal are equivalent to each other.
Think about the reasonableness of your answer.
Choose another fraction, decimal and percent and see if your method works.
Once they have discussed in groups, discuss their findings as a class.
What’s the teacher doing?
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Assigning parts to each student.
Monitoring student’s discoveries
and discussions.
Asking questions during class
discussion to help guide their
discussion.
What are the students doing?
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Using prior knowledge of
equivalent fractions to match their
percent and decimal to the proper
fraction.
Creating a method within a group of
why they chose to make their
match.
Testing their method on other
fractions to see if it works on all
fractions.
Phase: Explore
Activity:
Before giving a technical explanation of the relationship between fractions, decimals, and
percents, it is important to point out to the students that they are each different numerical
ways of writing the same thing (example: 1/4=0.25=25%). We will begin with a handson activity using coins. In their interactive notebook or on a piece of paper, have students
break their paper into 4 sections titled: COINS, FRACTIONS, DECIMALS, and
PERCENTS. Begin by asking the question “Who can tell me which one of our coins has
a picture of George Washington on the front?” Someone will respond with a quarter.
Direct students to cut a quarter from the coins page and paste underneath the “coins”
heading. Ask “Can anyone tell me the representation of the quarter in fraction form?”
Call on someone to come to your sample and represent a quarter in fraction form. “1/4!
So let’s fill that in under our fraction section. Very good! Now for a tougher question…
why does ¼ represent 25 cents?” This question may strike up some conversations so be
prepared. If they don’t answer, say “Because it takes 4 quarters to make a dollar, and we
just have one of them!” Point out that the numerator of 1 represents how many quarters
we have and the denominator of 4 represents the group of quarters needed to make one
dollar. Move them to the next column. Ask “who can come up with a way of
representing the quarter in decimal form?” If they have trouble getting started, say
“Think of how you write 25 cents using the decimal point.” Have someone come up and
write a quarter in decimal form. “0.25! That is correct!” After completing the decimal
section, ask the question “Why does 0.25 represent 25 cents?” They may say because 25
is the value of the quarter, but try to get them to understand that 0.25 means 25
hundredths and that is one quarter of 100. With one column to go, this may be the most
difficult for them. If someone answers 25%, ask the question why does 25% represent 25
cents? You may have to remind them that percentages are based on 100. You then
remind them that 100 parts are used to find percentages because percent means per
hundred. Once complete review back over 25%=0.25=1/4.
Have the students continue the exercise working together collaboratively. Have them use
2 quarters (2/4=0.50=50%), 3 quarters (3/4=0.75=75%), and 4 quarters (4/4=1.0=100%).
Upon completion of the lesson, students should be comfortable with converting between
fraction, decimal and percent. If you want to extend it further, have them do on their
own, a dime, nickel and penny.
This could be used as an exit activity day 1 or warm up to get them started back day 2.
Students are each detectives trying to find a particular fraction. They are each given a
clue that will help them find their fraction. When they discover their fraction, they are to
go stand by their fraction which will be posted randomly on the wall or on the board.
You could time each group of 6 or have 4 sets of fractions located on each wall and have
it be a contest to see which group gets their 6 members to the proper fractions first.
Clue #1: You visited grandma over the weekend and were given fifty cents. This is
written in money form as .50 and is equivalent to what fractional part of a dollar?
Clue #2: You made a 50 on your test out of 100 questions. That means you got 50%
correct on the test. What fractional part of 100% is 50%?
Clue #3: You find twenty-five cents on the sidewalk outside your house. This is written
in money form as .25 and is equivalent to what fractional part of a dollar?
Clue #4: You pick a colored marble out of a bucket that has 4 marbles. You are told that
you selected blue which had a 25% probability. What fractional part of 100% is 25%?
Clue #5: You add a quarter that you found on the ground to fifty cents that grandma gave
you and you now have seventy-five cents. This is written as .75 in money format and is
equivalent to what fractional part of a dollar?
Clue #6: You run 75 yards on the 100 yard football field and can’t run any more. This
means that you ran 75% of what your coach asked of you. What fractional part of 100%
is 75%?
What’s the teacher doing?
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Guiding the discussion
Modeling the activity
What are the student’s doing?
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Phase: Explain
Creating a hands-on representation of
fractions/decimals/percents using coins.
Answering questions asked by the
teacher in a guided instruction.
Working together collaboratively to
complete their activity.
Suggested DAY 2
Activity: Separate students into groups and have them use a 10 x 10 grid to model
benchmark fractions and percents and show how they would represent various
equivalencies of the number.
You may want to do one with the whole group if you notice some students
struggling…For example shade in 40 squares. Ask “What decimal would this
represent?” They should easily notice that you have shaded 40 out of 100 and state
that it is 0.40. You could also point out that there are 40 squares shaded out of 100
so the fraction would be 40/100 and then discuss simplifying the fraction. From
there discuss percent being out of 100 and see if they can come up with the percent.
Use as many examples that you may need. You could start with a fraction, a decimal
and a percent; working an example of each type if needed. You may want to assign
a problem or problems for students to try on their own as a comprehensive check to
make sure they understand the concept.
Suggested DAY 3
Create fraction, decimal percent conversion folding notes page which should
include:
 Given a fraction, how they are to generate a decimal and percent
 Given a decimal, how they are to generate a fraction and percent
 Given a percent, how they are to generate a fraction and decimal
(You may want to include mixed numbers, improper fractions, and percents larger than
100 in your examples. You will address them later in this unit).
Once the folding notes are complete, give them some numbers and have them practice
going from one to the other using their notes.
Suggested DAY 4
Have students create at least 2 strip diagrams (linear models used to illustrate number
relationships).
Give problems and have students model the percent on the strip diagram. You could have
them mark with a pencil, or if you have laminated strips they can use a dry erase marker
to mark their percent.
0%
100%
Once several problems have been given and students are able to correctly represent the
percents, do some comparison problems and have students raise their hand (or some other
way of answering) to identify the larger percent when given fractions or decimals
represented in word problems. For example: “Kennedy ate ¼ of her cereal bar and Macy
ate 2/5 of hers. Which one ate more of their cereal bar?” They may convert to percents
and mark, or they could break each bar up by fractions and see which is larger.
Suggested DAY 5
Have students in groups of 3 or 4. Have one laminated number line per group. On note
cards have several different benchmark percents, fractions and decimals. Have the group
order their set of numbers. Once they have finished, give one red square of paper for
every one incorrect. Have them talk it out and decide which one or ones needs to be fixed
and correct. Have them continue working together until all numbers on the number line
are in the correct order. You may want to have several sets for the advanced learners,
once they complete one set correctly give them another one.
What’s the teacher doing?
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Encouraging students to use their
own observation of various models
to explore their own thought as to
how to make the conversions.
Providing teacher-led explanations
of how to convert between
fractions, decimals and percents.
Clear up any misconceptions that
students have at this point.
What are the students doing?
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Using different models to convert
fractions, decimals and percents.
Taking notes on the topic of
fraction decimal percent
conversions
Phase: Elaborate
Activity:
Suggested Day 6
Give students an Area Model for example a 10 x 4 grid as shown below.
You could then ask them to shade a number of squares, or their own design, or their
name, or you could assign each student a number.
Ask them to use the diagram (not an algorithm) to explain each of the following:
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The percent of area that is shaded.
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The decimal part of area that is shaded.
The fractional part of the area that is shaded.
Extend it further, give them a larger area (10x10), ask them to draw a picture using 3
colors and leaving some white. Have them find the decimal, percent and fraction of the
four different colors represented.
Suggested DAY 7
Now that they have a grasp of conversions, extend it. Using the same models as used in
past days, take it a step further: decimals (greater than one), fractions (improper and
mixed numbers), and percents greater than 100%.
Do center activities using 4 centers. Have students use the four models: 10X10 grid, area
model, number line, and strip diagrams to have students extend their knowledge to these
more advanced numbers.
Suggested DAY 8 & 9
Students are in groups of 2 or 3.
Assign a Frayer model topic to each group. Topics that go in the center block are:
Fraction to Decimal
Decimal to Fraction
Percent to Fraction
Fraction to Percent
Decimal to Percent
Percent to Decimal
Each student will use the four corners to
1) Explain how to convert their assigned topic.
2) Use a model of their choice to model their assigned topic.
3) Write a real life story problem involving their assigned topic.
4) Give the fraction, decimal and percent of the number in their story problem.
After completing their Frayer Model, they present it to the class.
What’s the teacher doing?
What are the students doing?
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Monitoring students work to check
for understanding.
Monitoring to help students stay on
task.
Phase: Evaluate
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Working together to apply newly
learned concepts
Utilizing newly learned terms in a
new context.
Creating new connections to their
prior knowledge of fractions,
decimals and percents.
Suggested Day 10
Activity: Assess the students using the Performance Assessment
What’s the teacher doing?
What are the students doing?
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Working to demonstrate their
knowledge of fraction, decimal,
percent conversions using concrete
models.
Fraction Strips
10 X 10 Grids
How to convert:
Word problem:
Model chosen:
Fraction:
Decimal:
Percent:
Outside Front of Folding Notes
One sheet of Paper
Tri-folded
Percent
Percent
To
To
Fraction
Decimal
Fraction
Fraction
To
To
Decimal
Percent
Decimal
Decimal
To
To
Percent
Fraction
Two outsides come together her to make center line
Cut on each horizontal line
Inside of Foldable
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Rewrite the % over 100
Simplify
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Divide the numerator by the denominator
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Move the decimal 2 places to the right
Add the % sign
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Remove the % sign
Move decimal 2 places to the left
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Convert the fraction to a decimal
Move the decimal 2 places to the right
Add the % sign
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Write the decimal over 100 if it has an
integer in the hundredths place, over 10 if
only in the tenths place
Simplify
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This is inside that you will see when flaps are opened
Performance Indicator—Unit 1
Analyze the problem situation(s) described below. Organize and record your work for each of the following tasks.
Using precise mathematical language, justify and explain each solution process.
The four 6th grade classes at Waxahachie Middle School are fundraising for their end of the year field trip. Each of
the classes has an individual class goal.
1) Mrs. Vasquez’s class has earned 45% of their class goal of $300 and Mrs. May’s class has earned 30% or
$150 of their class goal.
a)
For each class, represent the percent of money earned compared to the class goal with a concrete or
pictorial model, fraction, and decimal and explain the relationship between the representations.
b) Using benchmark fractions and percents, estimate and determine how much more each class needs to earn
to meet their individual class goals.
2) Mr. Wu and Mr. Green’s classes each have a class goal of $600 for their end of the year field trip. Mr.
Wu’s class has earned one-fifth of their class goal, while Mr. Green’s class has earned 23% of their class
goal.
a)
Generate an equivalent fraction, decimal, and percent of the money earned by each of the two classes, Mr.
Wu and Mr. Green, to determine which class has earned more money toward their individual class goal of
$600.
b) Using benchmark fractions and percents, estimate and determine how much more each class needs to earn
to meet their individual class goals.