Gr 6 Unit 1 Resource A
Grade Level: 6th
Subject Area: Math
Lesson Title: Unit 1—Equivalent Forms
Lesson Length: 10 days
of Fraction, 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 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.
Unit Objectives:
Students will…

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

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

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
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 Standard
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 Standard
6.4G Generate equivalent forms of fractions, decimals, and percents using real-world
problems, including problems that involve money. Readiness Standard
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 Standard
6.5C Use equivalent fractions, decimals, and percents to show equal parts of the same
whole. Supporting Standard
ELPS:
c.1A use prior knowledge and experiences to understand meanings in English
c.1C use strategic learning techniques such as concept mapping, drawing, memorizing,
comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary
c.2D monitor understanding of spoken language during classroom instruction and
interactions and seek clarification as needed
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
c.3D speak using grade-level content area vocabulary in context to internalize new English
words and build academic language proficiency
c.3H narrate, describe, and explain with increasing specificity and detail as more English is
acquired
c.4H read silently with increasing ease and comprehension for longer periods
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
c.5B write using newly acquired basic vocabulary and content-based grade-level
vocabulary
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 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:





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
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.)
Strip diagram – a linear model used to illustrate number relationships
Related Vocabulary:
10 by 10 grid
Area model
Place value
Benchmark fraction
Benchmark percent
Decimal
Decimal notation
Denominator
Equivalent
Fraction
Fraction circle
Fraction notation
Improper fraction
Mixed number
List of Materials:
Index cards—1 per student
STAAR Grade 6 Mathematics Reference Materials—1 set per student
Fraction Strips Handout—1 per two students
Completed Fraction Strips Handout—1 per student
Glue or glue sticks
Scissors
Blank $ Bills Handout—1 per two students
Plastic bags—1 per student
Counters—100 per student (May use anything to represent 100 cents)
Making “Cents” of Percents handout—1 per student
Colored pencils—at least 1 per student
Percent Bars handout—1 per student
Match the Cards handout—1 per 4 students
Blank Cards extra handout
Match the Cards Recording Sheet—1 per student
Adding machine tape—1 strip per student (different lengths 4” – 18”)
Yardsticks—1 per two students
Notebook paper—1 sheet per student
Performance Indicator Unit 1 handout—1 per student
INSTRUCTIONAL SEQUENCE
Phase: Engage
Activity:
Play 3 minutes 30 seconds of “Fraction Shuffle “by Jetstangs,
https://www.youtube.com/watch?v=6i5_EopdUGc#t=17. While viewing the video,
students write down math terms they see and/or hear on index cards. After viewing video,
discuss terms and definitions students know. Discuss how fractions help people learn
dance steps. Write equivalent fourths and eighths fractions.
What’s the teacher doing?
What are the students doing?
Give an index card to each student.
Instruct students to write any math term
they may see and/or hear from the video.
Play up to 3:30 of “Fraction Shuffle.”
Writing terms on index card.
Ask students what terms they wrote on the
card. Write terms on white board.
Telling teacher their terms.
Discuss definitions that students know.
Defining terms in own words.
Discuss any fractions the students saw in the Telling teacher the fractions.
video.
Play video again and allow students who
know the appropriated steps to dance.
Dancing and watching.
Ask:
Answering questions.

How do you learn dance steps?

Has anyone used the 8 count
method?
Explain what 8 count method is for those
who do not know.
Play video again and help students count the Counting 8 counts aloud.
8 counts aloud.
Discuss with a partner how the 8 count
method is related to fractions.
Discussing with partner.
Ask:
Answering questions.

How could we relate the 8 count
method to fractions?
Discuss equivalent.
Participating in discussion.
Discuss how the fourths fractions are
equivalent to eighths fractions.
Tell students to write equivalent eighths
fractions for fourths fractions on back of
index card.
Write equivalent fractions.
Play video again and teach students the
dance.
Dance and count.
Phase: Explore/Explain
Activity:
Prior to instruction, copy the handout, Fraction Strips, for each student. Cut 5 fraction
strips for each student.
Distribute a STAAR Mathematics Reference Materials chart with inch ruler to each
student.
This lesson is adapted from TESCCC, 2012, Mathematics Grade 6, Unit 1, Lesson 1.
What’s the teacher doing?
Ask

What labels are on your ruler? (Answers
may vary. Inches; cm; etc.)

What numbers are on your ruler?
(Answers may vary. 1; 2; 3; 4; 5; etc.)
What are the student’s doing?
Students view STAAR Mathematics Reference
Materials and answer discussion questions regarding
rulers.

What do you notice about the numbers
on your ruler? (One edge of the ruler is
numbered 1 – 12, inclusive; the other edge
of the ruler is numbered 1 – 30; etc.)

What do you notice about the distance
between each whole number on the side
labeled “Inches”? (The distance between
each number is an equal distance and each
distance is subdivided into small equal size
pieces.)

Find the 0 and 1 inch marks on your
ruler. How many equal size spaces are
between 0 and 1 on the inch edge of your
ruler? (8)

How many marks are between 0 and 1
inch edge on the edge of your ruler? (7)

What do you think the marks represent?
Explain your reason. (The distance
between each consecutive mark represents
one eighth because the marks between 0
and 1 divide 1 whole inch into 8 equal size
parts.)
Distribute handout Completed Fraction Strips and 5
strips to each student. Explain to students that they
will create fraction strips to model an enlarged
version of one-inch from their ruler.
Display one fraction strip.
Ask:

If this strip represents a “magnified”
inch, where do you place 0 and 1? (0 on
the left edge and 1 on the right edge.)
Instruct students to mark 0 and 1 on the handout and
glue strip to handout. Verify that students have
marked 0 at the left edge and 1 on the right edge.
Display another fraction strip.
Ask:

How can you mark the strip in two equal
parts? (Fold the rectangle in half and draw
a line on the fold.)

What does each part represent? (1 out of
two equal parts or ½ of the whole)
Marking strips.

How would you count if you begin at 0
and count each equal size part? (0-half, 1half, 2-halves)
Instruct students to glue their second strip and mark
0/2, ½, and 2/2 on the handout.
Gluing and marking strips.
Instruct students to repeat the process of folding,
gluing, and labeling fraction strips for fourths and
eights. Instruct students to count the equal size parts
for each fraction strip. Allow time for students to
complete the activity. Monitor and assess students to
check for understanding. Emphasize to students the
importance of stating the complete fraction name,
and not just the numerator, when counting the
fractional parts.
Ask:

Do you think all rulers are marked in
eights? (No.)

Why would someone need smaller units?
(Answers probably vary. Smaller units
would be a more accurate measurement.)

What fraction would you get if 1/8 was
folded in half? (1/16)
Answering questions.
Instruct students to fold, glue, and label the last strip.
Monitor and assess students to check for
understanding.
Folding, gluing, and marking strips.
Facilitate a class discussion to review the equivalent
fractions from the activity.
Ask:

What do you notice about the positions
for ½, 2/4, 4/8, and 8/16 on the fraction
strip ruler? (Answers may vary. These are
all equivalent fractions; if you draw a
vertical line through ½ all these equivalent
fractions would line up on the vertical line;
etc.)

What other equivalent fractions do you
notice on the fraction strip rulers?
(Answers may vary. ¼, 2/8, 4/16; etc.)

What do you notice about the positions
for 2/2, 4/4, 8/8, and 16/16 on the fraction
strips? (Answers may vary. These are all
equivalent fractions; if you draw a vertical
line through 1, all these equivalent fractions
would line up on the vertical line; these
fractions all represent 1 whole; etc.)
Answering questions.

What is another method you can use to
verify when fractions are equivalent?
(Multiply or divide the numerator and
denominator of a fraction by the same value
to generate an equivalent fraction.)
Instruct students to compare their completed handout
to their actual ruler.
Ask:



Making comparisons.
How is the fraction strip for eights
similar to the markings between 0 inch
and 1 inch on your ruler? (Answers may
vary. The distance from 0 to 1 represents
one whole unit; there are 8 equal size
spaces between 0 and 1; each space
represents 1/8 of the whole unit; etc.)
How is the fraction strip for eights
similar to the markings between 1 inch
and 2 inch on your ruler? (Answers may
vary. The distance from 1 to 2 represents
one whole unit; there are 8 equal size space
between 1 and 2; each space represents 1/8
of the whole unit; etc.)
What fraction of an inch is the first
consecutive mark after 0 on your ruler?
Second consecutive? (1/8 inch) (2/8 inch)
Instruct students to locate the mark on the ruler
between 0 inch and 1 inch to represent ½ of an inch,
¾ of an inch, 3/8 of an inch, and 1 inch. (1/2 = 4/8 →
4 consecutive marks after 0.) (3/4 = 6/8 which is 6
consecutive marks after 0.) (3/8 is 3 consecutive
marks after 0.) (1 = 8/8 which is 8 consecutive marks
after 0.)

What fraction of an inch would 7
consecutive marks after 0 inch on your
ruler represent? 2 consecutive marks?
(7/8) (2/8 or 1/4)

Locate the mark on your ruler between 0
inch and 2 inches to represent 1 ½ inch.
What are some other names for this
location? (Answers may vary 1 2/4; 1 4/8;
12/8; etc.)

What fraction would be 20 consecutive
marks after 0 on your ruler? (Answers
may vary. 20/8; 2 4/8; 2 1/2; etc.)
Facilitate a class discussion about how the markings
on a ruler are related to fractional parts of a whole.
Answering questions.
Answering questions.
Ask:

How can you use your ruler to draw a
line segment 3/8 of an inch? Justify your
response. (Start at 0 on the ruler and draw
up to 3 consecutive marks after 0. This is
3/8 inch.)
Instruct students to draw a line segment 3/8 of an
inch with their ruler. They should draw on the back
of their handout.

How can you use your ruler to draw a
line segment 2 ¾ inches? Justify your
response. (Start at 0 on the ruler and draw
up to the 2 inch mark and 6 consecutive
marks after 2 inches. This is 2 6/8 inch = 2
¾ inch.)
Instruct students to draw a line segment 2 ¾ inches
with their ruler.

How can you use your ruler to draw a
line segment 13/8 inches? Justify your
response. (Start at 0 on the ruler and draw
up to 13 consecutive marks after 0. This is
8/8 + 5/8 = 13/8 = 1 5/8 inch.)
Instruct student to draw a line segment 13/8 inches
with their ruler.
Review converting between improper fractions and
mixed numbers, if needed.
Improper fraction to a mixed number
23/5 = ______
Mixed number to an improper fraction
4 3/5 = _______
Phase: Explore/Explain
Drawing line segments using ruler and answering
questions.
Activity:
Relate dollars and cents to decimal values.
Prepare 5 dollars for each student before lesson.
Prepare bags of 100 counters to represent cents.
What’s the teacher doing?
What are the students doing?
Give students five one-dollar bills.
Have students exchange one dollar for 100
cents. (Use counters or other items to
represent cents if pennies and play coins are
not available.)
Exchanging one dollar for 100 cents.
Ask:
Answering questions.

How many cents are equal to one
dollar? (100) One dollar is
equivalent to 100 cents.

How many cents are equal to two
dollars? (200) One dollar is 100
cents so two dollars is 200 cents.

Three dollars? (300) One dollar is
100 cents so three dollars is 300
cents.
Tell students to fold one-dollar in half and
tear along fold. (Remind students not to
tear real money.) Students should represent
half with the counters also.
Folding one dollar into halves.
Ask:
Answering questions.

How many cents are equivalent to
half of one dollar? Two-halves?

How do you write 50 cents? One
cent? One hundred cents?

Are cents and decimals related?
How?
Tell students to fold one-dollar into fourths
and tear along folds. Some students may
need to use counters also.
Folding one dollar into fourths.
Ask:
Answering questions.

How many cents for one-fourth of
one dollar? Two-fourths? Threefourths?

How many cents for $1 and ½ of a
dollar? $1 and ¼ of a dollar?
Tell students to fold one-dollar into fifths
and tear along folds. Some students may
need to use counters also.
Folding dollar into fifths.
Ask:
Answering questions.

How many cents for one-fifth of
one dollar? Two-fifths? Threefifths? Four-fifths?

How many cents for $1 and 2/5 of
a dollar? $1 and 4/5 of a dollar?
Have students draw a number line on the
back on one dollar.and mark half and
fourths along bottom edge of number line.
Tell students to mark equivalent money
amounts on top of number line.
Have students draw a number line on the
back on another one dollar and mark fifths
and tenths along bottom edge of number
line. Tell students to mark equivalent money
amounts on top of number line.
Phase: Explore/Explain
Drawing number lines and labeling.
Activity:
Model fractions, decimals, money, and percents using 10 by 10 grids. Complete as a fourperson group activity.
Copy ‘Making “Cents” of Percents’ handout, one per student before lesson.
What’s the teacher doing?
What are the students doing?
Organize class into groups of four.
Number students in each group 1-4.
Distribute handout ‘Making “Cents” of
Percents’ to each student.
Ask:

How does the squares relate to
money?

What percent is represented by
the entire group of small squares?
Tell students to complete Problem 1.
Completing Problem 1.
Ask each student to give an answer for
fraction, decimal, money, or percent.
Student #1 gives the answer for fraction.
Student #2 gives the answer for money.
Student #3 gives the answer for decimal.
Student #4 gives the answer for percent.
Listen to student answers.
Check for understanding.
Tell students to complete Problem 2-5.
Completing Problems 2-5. Students rotating
when giving the answers for fraction,
money, decimal, and percent.
Ask:
Answering questions.

What do you notice about the
problems and answers?
Instruct students to complete Problem 6.
Completing Problem 6. Continuing to
rotate when giving answers.
Ask:
Answering questions.

What fraction is represented?
Money? Decimal? Percent?

When would a person use a
percent less than 1?
Instruct students to complete Problem 7-8.
Completing Problems 7-8.
Ask:
Answering questions.

What fraction is represented?
Money? Decimal? Percent?

When would a person use a
percent greater than 100?
Instruct students to complete Problem 9-10.
Completing Problems 9-10.
Tell students to complete explanation on
last page of handout individually.
Explaining relationship between fractions,
decimals, money, and percents.
Phase: Explain/Explore
Activity:
Use percent bars to help answer real-world problems involving percent when given the
whole, part, or percent. Complete as a Think-Pair-Share activity.
Copy “Percent Bars” handout (1 per student) before lesson.
What’s the teacher doing?
What are the students doing?
Give each student a “Percent Bars”
handout.
Completing Problem 1.
Tell students to complete Problem 1.
Observe process students use.
Tell students to discuss the answer and
process used with a partner.
Discussing answer to Problem 1 and
process used.
Observe student discussion.
Ask several students to explain their process
to the class.
Explaining process.
Instruct students to complete handout using
Think-Pair-Share.
Completing handout using Think-PairShare.
Phase: Engage/Explore
Activity:
Copy and cut one set of “Match the Cards” per group of 4 students. Copy 1 “Match the Cards Recording
Sheet” per student before lesson.
Students match equivalent fractions, decimals, and percents.
Discuss converting fractions to decimals by dividing numerator by denominator.
Discuss difference in terminating and repeating decimals.
What’s the teacher doing?
What are the students doing?
Distribute set of cards to each group of students.
Tell students to group the equivalent fractions,
decimals, and percents they know.
Matching cards.
Ask:
Answering questions.

How do you convert a fraction to a
decimal?

Do you see a decimal with a bar over it?

What does the bar represent?
Tell the students to convert 1/3 to a decimal by
dividing numerator by denominator.
Dividing numerator by denominator to get repeating
decimal.
Instruct students to complete the matching activity
and record answers on “Match the Cards
Recording Sheet”.
Completing activity.
Phase: Elaborate
Activity:
Make flier to explain how to convert fractions, decimals, and percents.
Students will need blank paper and markers for this activity.
What’s the teacher doing?
What are the students doing?
Tell students to create a flier explaining how
to convert fractions, decimals, and percents.
Observe students as they complete flier.
Completing flier.
Instruct students to have another student
check the flier for understanding.
Phase: Elaborate
Checking fliers for understanding.
Activity:
Compare and contrast 50% of a number.
Cut different lengths of adding machine tape ranging 4 in. to 18 inches. Each student will
need one strip of tape.
What’s the teacher doing?
What are the students doing?
Give each student a strip of tape.
Tell students to measure adding machine
tape to the nearest 1/8 of an inch using a
yardstick. Students need to write
measurement at end of tape.
Measuring and recording.
Tell students to measure the length of 50%
of the tape. Student need to write down the
measurement on ½ of the tape.
Comparing measurement with a partner.
Instruct students to write a note on notebook
paper to the teacher comparing and
Writing a note to the teacher.
contrasting the value of 50%.
Phase: Evaluate
Activity:
Students work on the performance assessment from the IFD.
Provide concrete models for students to select, as needed.
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.
Standard(s): 6.1A , 6.1B , 6.1C , 6.1D , 6.1E , 6.1F , 6.1G , 6.4E , 6.4F , 6.4G , 6.5B ,
6.5C
ELPS.c.1A , ELPS.c.1C , ELPS.c.2D , ELPS.c.3C , ELPS.c.3D , ELPS.c.3H , ELPS.c.4
H , ELPS.c.4J , ELPS.c.5B , ELPS.c.5G
What’s the teacher doing?
What are the students doing?
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.
Fraction Strips
Completed Fraction Strips
Glue whole strip here
Glue halves strip here
Glue fourths strip here
Glue eights strip here
Glue sixteenths strip here
Blank $ Bills
$
$
$
$
$
$
$
$
$
$
Making “Cents” of Percents
1. Color one small square.
Fraction
Decimal
Money
Percent
Fraction
Decimal
Money
Percent
Fraction
Decimal
Money
Percent
2. Color ten small squares.
3. Color 25 small squares.
4. Color 50 small squares.
Fraction
Decimal
Money
Percent
Fraction
Decimal
Money
Percent
Fraction
Decimal
Money
Percent
5. Color 100 small squares.
6. Color ½ of a small square.
7. Color 8 1/4 small squares.
Fraction
Decimal
Money
Percent
Fraction
Decimal
Money
Percent
Fraction
Decimal
Money
Percent
8. Color 120 small squares.
9. Color 175 small squares.
10. Color 205 small squares.
Fraction
Decimal
Money
Percent
Explain how fractions, decimals, money, and percents are related.________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Percent Bars
For each problem, use a percent bar to model the situation. Place the information from the problem on
the percent bar. Use the percent bar to determine the answer.
1. Sam took a test which had 100 questions. All the questions had equal value. He answered 95 of
the questions correctly. What percent of the questions did Sam answer correctly?___________
0%
50%
100%
2. Julie took a test. All the questions had equal value. She answered 60 of the questions correctly.
This was 75% of the total questions on the test. How many questions were on the
test?________
3. Roberta took a test. There were 60 problems on the test. All the questions had equal value.
Roberta answered 55% of the questions correctly. How many questions did Jane answer
correctly?_________
4. Ben and Sally went to lunch. They left a 15% tip. If the total cost of their meal was $24.00, what
was the amount of tip they left?_____________
5. A candy inspector inspected 280 pieces of candy. Two hundred thirty-eight pieces passed his
inspection for packaging. What percent of the candy pieces did NOT pass
inspection?____________
6. The cheer squad had 3 seniors, 5 juniors, 2 sophomores, and 5 freshmen. What percent of the
team are freshmen?___________
7. Of the 320 seventh grade students at a local junior high, 70% ride a bus to school. How many
students ride a bus?_____________
8. Larry answered 85% of the questions on his math test correctly. There were 40 questions on the
test. All the questions had equal value. How many questions did Gary NOT answer
correctly?_______
9. On a candy package the nutrition facts shows 3 small pieces of candy contain 5% of the
recommended daily amount of carbohydrates. The amount of carbohydrates in the 6 small
pieces of candy is 24 grams. According to the information on the candy package, what is the
recommended daily amount of carbohydrates?_____________
10. The party planner sent out 72 invitations for a birthday party. Of the children invited, 63
attended. What percent of the children invited attended the party?
Match the Cards
Copy one set for each group of 4 students.
1/2
0.5
50%
1/4
0.25
25%
3/4
0.75
75%
1/3
0.3
33 1/3%
Match the Cards
1/5
0.2
20%
1/8
0.125
12.5%
2/5
0.75
75%
2/3
0.6
66 2/3%
Match the Cards
1/10
0.1
10%
3/10
0.3
30%
1/100
0.01
1%
5/6
0.83
83 1/3%
Match the Cards
1/1000
0.001
.1%
1 3/5
1.6
160%
2 7/8
2.875
287.5%
1 5/8
1.625
162.5%
Blank Cards
Match the Cards Recording Sheet
Fraction
Decimal
Percent
Performance Assessment—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.