Comparing and Ordering Fractions
Analyzing Elections
SUGGESTED LEARNING STRATEGIES: Marking the Text,
Summarize/Paraphrase/Retell, Create Representations,
Vocabulary Organizer
ACTIVITY
1.5
My Notes
• Comparing and ordering
fractions with like and unlike
denominators and numerators
• Writing equivalent fractions
Materials
• Number cubes
• Fraction strips/circles (optional)
• Colored paper (optional)
1. Work together to simulate this election.
a. In your group, roll a number cube until you have 23 votes.
Organize your data in this table.
Chunking the Activity
#1–3
#4–5
Answers may vary. Sample answers shown.
Betty (2)
Carla (3)
Deon (4)
Total
Votes
4
8
7
4
23
Comparing and
Ordering Fractions
Activity Focus
Every West Middle School homeroom must elect a student council
representative. Since Mr. Fare’s homeroom students do not know
each other yet, he has asked interested students to volunteer. Andy,
Betty, Carla, and Deon decide to volunteer.
To simulate a regular election, each of the 23 students in his
homeroom will roll a number cube to vote. A 1 is a vote for Andy.
A 2 is a vote for Betty. A 3 is a vote for Carla. A 4 is a vote for Deon.
If 5 or 6 is rolled, the student continues to roll until 1, 2, 3, or 4
is rolled.
Andy (1)
ACTIVITY 1.5 Investigative
#6–8
#9
#10–15
#16
#17
#18
Introduction Marking the Text,
Summarize/Paraphrase/Retell
b. Who did your group elect as the homeroom representative?
12 Create Representations,
Answers may vary. Sample answer: Betty
Debriefing Check that each
group of students is correctly
collecting data. You may need
to discuss what occurs when
students roll a 5 or 6. Students
use the last column in the table to
ensure that their group counted
23 votes. A class discussion
following 1b may include a short
explanation of the possibility
of a tie.
© 2010 College Board. All rights reserved.
2. List the names of the candidates in order of most to least
number of votes. Next to each name, write the number of votes
he or she received.
Answers may vary. Sample answer: Betty 8
Carla 7
Andy 4
Deon 4
3. What fraction of the total votes did each candidate receive?
Write the fractions in order from greatest to least.
8
Answers may vary. Sample answer: Betty ___
23
7
Carla ___
23
4
___
Andy
23
4
Deon ___
23
MATH TERMS
The number of votes each
candidate received can be
written as a fraction or as a
ratio of the number of votes
received to the total number of
votes. These ratios are called
rational numbers.
3 Use this question to check
Unit 1 • Number Concepts
© 2010 College Board. All rights reserved.
025-032_SB_MS1_1-5_SE.indd 25
25
12/16/09 5:43:49 PM
TThe Math Terms box has an informal description of rational
n
numbers.
The actual definition of a rational number is a
p
number ex
expressed as __
q, where p and q are integers and q is not zero.
TEACHER TO
TEACHER
that students understand what
the numerator and denominator
in each fraction mean. Students
may use the table instead of the
fractions to find their answers.
Be certain that the connection
between the numbers of votes,
from most to fewest, and the
fractions of the total votes, from
greatest to least, is established. If
possible, discuss student answers
that reflect both the table and the
fraction methods.
Unit 1 • Number Concepts
25
4 Marking the Text Check to
see that students understand how
to order fractions with a given
common denominator.
ACTIVITY 1.5
continued
Comparing and Ordering Fractions
Analyzing Elections
SUGGESTED LEARNING STRATEGIES: Marking the Text,
Quickwrite
My Notes
5 of the
4. In the election in Mr. Fare’s homeroom, Andy received ___
23
7
8 of
total votes, Betty received ___ of the total, Carla received ___
23
23
3 of the total. Who was elected?
the total, and Deon received ___
23
5 Quickwrite, Guess and
Check This question allows
students to understand the need
to use a common denominator
to compare fractions. Before
continuing, you may ask students
to quickly make a prediction of
who won the election. Point out
that they are using the Guess and
Check strategy and will check
their answers later.
Carla
The 300 students at West Middle School held a traditional election
for student council officers. Eden, Frank, Gabrielle, and Hernando
ran for president.
3 of the votes,
4 of the votes, Frank received ___
5. Eden received ___
15 1
10
2 of
Gabrielle received ___
of the votes, and Hernando received __
5
30
the votes. Why is it more difficult to decide who won this election than it was for the election in Question 4?
6 A common fractional unit
is the unit fraction of which
each fraction is composed.
For example, _27_ and _57_ are both
composed of sevenths, so the
common fractional unit is _17_.
The fractions do not have a common denominator.
To make it easier to compare the results from this election, you
can rewrite these fractions as equivalent fractions with a common
denominator.
6. What common denominator do all the fractions in Question 4
share?
7 Activating Prior Knowledge,
Create Representations This
question is intended to activate
students’ prior knowledge of
writing equivalent fractions by
making drawings.
© 2010 College Board. All rights reserved.
ACTIVITY 1.5 Continued
The common denominator is 23.
The LCD is simply the LCM for two
or more different denominators.
The LCM of 6 and 8 is 24, so you
use 24 as the LCD to write
1.
1 and __
equivalent fractions for __
8
6
7. You can draw a model to compare fractions. Use this method to
3 of the votes to Hernando’s __
2 of the votes.
compare Frank’s ___
5
10
a. What is the least common denominator, or LCD, of these
two fractions? (Hint: Look for the least common multiple, or
LCM, of 5 and 10.)
The LCD is 10.
26 SpringBoard® Mathematics with Meaning™ Level 1
12/16/09 5:43:57 P
0
© 2010 College Board. All rights reserved.
025-032_SB_MS1_1-5_SE.indd 26
26 SpringBoard® Mathematics with Meaning™ Level 1
Comparing and Ordering Fractions
ACTIVITY 1.5
Analyzing Elections
continued
7 (continued) Part e serves as
SUGGESTED LEARNING STRATEGIES: Create Representations,
Quickwrite, Self Revision/Peer Revision, Think Aloud, Summarize/
Paraphrase/Retell, Vocabulary Organizer
a review of writing inequality
expressions using symbolic
notation. Be sure to point out
the Writing Math signal box to
students, as many will need a
review on what the symbols
mean.
My Notes
b. Draw a rectangle in the My Notes space. Then divide it into
the number of equal parts you found in Part a.
2.
c. Shade your rectangle to represent __
5
2.
d. Write an equivalent fraction for __
5
4
__2 = ___
5
8 Quickwrite, Self Revision/
Peer Revision, Debriefing This
question leads students to finding
a common denominator for all
four fractions, so that they can
compare all of them at once.
Part b gives students a reason for
finding a more efficient method
for comparing fractions than
making drawings.
10
2 to write an inequality
e. Use the equivalent fraction for __
5
comparing the votes for Frank and Hernando. Who received
more votes?
3 ; Hernando received more votes.
4 > ___
___
10
10
8. Next compare the votes for Eden and Gabrielle.
a. Can you use 10 as the common denominator to compare
their votes? Explain your reasoning.
WRITING MATH
The symbols <, >, ≤, and ≥ are
inequality symbols. Remember,
each symbol opens towards the
greater number and points to
the smaller number: 5 > 1.
Answers may vary. Sample answer: No, because neither
30 nor 15 is a factor of 10.
Paragraphs Think Aloud,
Summarize/Paraphrase/Retell,
Vocabulary Organizer
b. One way to compare all four students’ votes is to find how
many of the 300 votes each candidate received. Would you
want to draw a model to do this? Why or why not?
© 2010 College Board. All rights reserved.
Answers may vary. Sample answer: You could, however,
it would be difficult to draw rectangles cut into 300 equal
pieces. The numbers are too big for accurate sketches.
You can use the Property of One to find equivalent fractions.
3,
2 , __
When you use the Property of One, you multiply a fraction by __
4 , and so on. This is the same as multiplying the fraction by the2 3
__
4
3 , __
4 , describes the number 1 in
2 , __
number 1. Each of the fractions, __
2 3 4
a different way.
1 , you
To use the Property of One to find an equivalent fraction for __
2
multiply this way.
3 = _____
1 × 3 = __
3
1 = __
1 × 1 = __
1 × __
__
2 2
2 3 2×3 6
1 are each
Notice that the numerator and denominator of __
2
multiplied by 3.
MATH TERMS
The Property of One for
fractions states that if the
numerator and the denominator
of a fraction are multiplied by
the same number, its value is
not changed.
Unit 1 • Number Concepts
PM
025-032_SB_MS1_1-5_SE.indd 27
© 2010 College Board. All rights reserved.
ACTIVITY 1.5 Continued
27
12/16/09 5:44:00 PM
MINI-LESSON: Finding Equivalent Fractions
Use five strips of different colored paper, all of the same length. Fold one
strip into halves, one into thirds, one into fourths, and one into sixths. (To
form sixths, fold into thirds, then fold each third in half.) Leave one strip
unfolded to represent the number 1.
Have students match the strips to help rename the fractions, draw a
sketch of their strips, and complete the fraction for each problem below.
1 = __
2
a. __
3
6
1 = __
2
b. __
4
2
3
1 = __
c. __
2
6
6
3
4 = __
2=1
d. __
= __
= __
4
6
3
2
Unit 1 • Number Concepts
27
ACTIVITY 1.5
continued
Comparing and Ordering Fractions
Analyzing Elections
9 Think/Pair/Share This question
b
b
SUGGESTED LEARNING STRATEGIES: Think/Pair/Share,
Simplify the Problem, Quickwrite, Self Revision/Peer Revision
My Notes
9. Use the Property of One to rename all four fractions to find the
fraction of the 300 total votes each student received.
4 = ____
___
80
15 300
b. Frank
3 = ____
90
___
10 300
c. Gabrielle
1 = ____
10
___
30 300
2 = ____
120
__
5 300
d. Hernando
b
b×n
a×n
other words, the fraction _____
is
b×n
a_
_
equivalent to the fraction .
b
10. Compare the renamed fractions. Then list the original
fractions from least to greatest.
3 , __
4 , ___
2
1 , ___
___
30 15 10 5
Students may not be ready to
understand this explanation
that uses variables as the
numerator and denominator,
but this question gives them an
opportunity to work with the
Property of One on some specific
numerical examples.
Now explore some ideas about common denominators.
11. You changed each fraction to an equivalent fraction with a
common denominator of 300. Why did this make it easier to
compare the fractions of the total votes for each candidate?
Once the denominators are the same, you can simply
compare the numerators.
12. List other common denominators that could be used to write
equivalent fractions for comparing the presidential election
votes at West Middle School.
0 Guess and Check Check
student guesses from Question 5.
Answers may vary. Possible common denominators are 30,
60, 90, 120, 150, 180, 210, 240, 270, 330, 360, …
a Simplify the Problem,
Quickwrite, Self Revision/Peer
Revision Students see a need for
finding common denominators.
bd Simplify the Problem,
Quickwrite, Self Revision/
Peer Revision In Question 12,
students list as many other
common denominators as they
can find, leading to a discussion
in Question 13 about the least
common denominator. Be sure
to elicit this term if the students
do not, and ask students to use
either their Math Notebooks or a
vocabulary organizer to add it to
their list of terms. Discuss how to
find the LCD and if it is important
to use it instead of a different
common denominator.
a. Eden
© 2010 College Board. All rights reserved.
requires students to use the
Property of One. The Property of
One states that any fraction __a can
b
be expressed by a different yet
equivalent fraction by multiplying
by an appropriate representation of
the number 1. The number 1 can
be represented in fraction form as _nn_.
The Property of One says that
a×n
_a_ = _a_ × 1 = _a_ × _n_ = _____
. In
n
13. Choose one of the common denominators you listed in
Question 12 that you think may be easier to work with than
300 to compare the fractions. Explain your choice.
Answers may vary. Sample answer: I chose 30 as the
common denominator, as it is easier to work with smaller
numbers.
14. Change each fraction from Question 9 to an equivalent
fraction with the denominator you chose in Question 13.
Answers may vary. Sample answer:
8 , ___
3 = ___
9 , ___
4 = ___
1 = ___
1 , __
2 = ___
12
___
15
30 10
30 30
30 5
30
28 SpringBoard® Mathematics with Meaning™ Level 1
025-032_SB_MS1_1-5_SE.indd 28
12/16/09 5:44:04 P
0
Suggested Assignment
CHECK YOUR UNDERSTANDING
p. 32, #1–5
UNIT 1 PRACTICE
p. 58, #31–34
Often it helps students to understand the Property of One
if they draw a 1 around the fraction as they multiply. For
example:
TEACHER TO
TEACHER
2_ = __
2
_1_ × ___
__
3
2
6
28 SpringBoard® Mathematics with Meaning™ Level 1
© 2010 College Board. All rights reserved.
ACTIVITY 1.5 Continued
Comparing and Ordering Fractions
ACTIVITY 1.5
Analyzing Elections
continued
e Debriefing
SUGGESTED LEARNING STRATEGIES: Create Representations,
Look for a Pattern
My Notes
Fraction of
Votes
Eden
4
___
Frank
Gabrielle
Hernando
Fraction
Fraction
Final Rank in
(Denominator of 300) (Denominator You Chose) Election (1st–4th)
15
3
___
10
1
___
30
2
__
5
80
____
8
___
300
30
90
____
9
___
300
30
10
____
1
___
300
30
120
____
12
___
3
EXAMPLE 1 Debriefing Now
that students understand the
Property of One, they apply this
knowledge to look for ways to
make this method even more
efficient when comparing two
fractions at a time. When students
find a common denominator by
multiplying the two given denominators, they are multiplying one
denominator by the other.
2
4
1
30
300
16. Explain how you determined the final ranking.
Answers may vary. Sample answer: I used the numerators.
Two ways to compare fractions are to rewrite the fractions using a
common denominator or to use cross products.
You do not have to find the LCD
to write equivalent fractions.
You can always find a common
denominator by multiplying the
denominators of the fractions.
EXAMPLE 1
5.
4 and ___
Compare __
5
4 ? ___
__
Step 1:
9 × 11 = 99
© 2010 College Board. All rights reserved.
9
11
Using a common denominator:
Step 2:
Step 3:
Multiply the denominators to find a
common denominator.
Write equivalent fractions.
Compare the fractions.
9 11
Thus, as they use the Property
of One, they are also multiplying
each numerator by the denominator of the other fraction. When
fractions have common denominators, only the numerators must
be compared. By only finding the
numerators, the students can save
time when comparing.
5 = ___
45
4 = ___
44 and ___
__
9
99
11
99
45 , so __
5
44 < ___
4 < ___
___
99
99
9
11
Using cross products:
Step 1:
Compare the products found by
multiplying the numerator of one
fraction by the denominator of the
other fraction.
4 × 11 = 44
4
__
5 × 9 = 45
5
___
Many teachers refer to cross
products as “cross-multiplication.”
It is important that students see
this pattern and understand why
cross-multiplication works as a
method for comparing before
they are allowed to use it.
9
11
5
4 < ___
44 < 45, so __
9 11
TRY THESE A
3.
2 and __
a. Compare __
7
9
5
__
___
b. Compare and 7 .
9
13
5 > ___
3 , b. __
2 < __
7
a. __
9 7
9 13
Unit 1 • Number Concepts
PM
025-032_SB_MS1_1-5_SE.indd 29
© 2010 College Board. All rights reserved.
A
After
Question 15 is a
g
good place for additional
practice w
with using common
denominators to compare and
order fractions.
TEACHER TO
TEACHER
15. Use this table to organize your data for the election results.
Candidate
ACTIVITY 1.5 Continued
29
12/16/09 5:44:06 PM
MINI-LESSON: Understanding the Property of One
If students are struggling with the Property of One and why it works, use
the following guided questioning.
• By what number can you multiply another number without changing
the value of the other number?
• By what number can I multiply 5 in order to get 5?
• Give five examples of this.
• Will this work with fractions and decimals too? Give an example.
• How many different ways can you write 1 using fractions?
• What does it mean to write an equivalent fraction?
1 of a pizza, is that more, less, or the same as eating __
2 of it?
• If you eat __
4
2
Unit 1 • Number Concepts
29
ACTIVITY 1.5
continued
Comparing and Ordering Fractions
Analyzing Elections
Connect to History
Compare the fractions of votes
received by the candidates in the
1860 presidential election. List the
order, from most to fewest votes,
in which the candidates placed.
SUGGESTED LEARNING STRATEGIES: Identify a Subtask,
Simplify the Problem, Create Representations
My Notes
As president of the Student Council, Hernando wants to speak with
all the student groups about their concerns. The guidance counselor
gave Hernando the following data:
8
• ___
15 of the students take part in music.
1 of the students are in the art club.
• __
6
___
• 16
33 of the students participate in sports.
4 of the students are in academic clubs.
• __
9
Stephen A. Douglas:
1,382,713
________
4,689,568
John C. Breckinridge:
212,089
________
1,172,392
Hernando decides to speak first with the groups that have the most
participants. To do so he must order these fractions. He knows that
a common denominator for them would be very large, so he asks
his math teacher, Ms. Germain, if there is an easier way to order
the fractions.
1,865,593
Abraham Lincoln: ________
4,689,568
296,453
John Bell: ________
2,344,784
17. Ms. Germain decides to explain the concept with less
complicated fractions. She starts by asking Hernando to
represent each of these unit fractions.
g Identify a Subtask,
Simplify the Problem, Create
Representations (a, b), Group
Presentation (b) This question
introduces students to using
common numerators to compare
fractions. Additionally, this
method reinforces the relationship
between numerator and
denominator. Before beginning,
you might ask students to find
the common denominator for
these four fractions (26,730 is a
common denominator; the LCD is
990) so that they can appreciate
Hernando’s conclusion that the
common denominator is, indeed,
a very large number. Part b is a
good question to use the group
presentation strategy.
a. Shade each rectangle to show the fraction.
1
3
© 2010 College Board. All rights reserved.
ACTIVITY 1.5 Continued
1
4
1
2
1
5
b. She tells Hernando that he can also use number lines to
compare the fractions. Graph each fraction on the number
lines below.
1
3
1
4
0
1
0
1
1
2
1
5
0
1
0
1
30 SpringBoard® Mathematics with Meaning™ Level 1
H
Help
students understand why it is not mathematically
aaccurate to shade a number line from zero to the given
fraction This
T is a misconception about graphing on a number line
fraction.
that may confuse students later on when they graph inequalities.
Shading includes all points along the shading. Students should place
only one point on each number line.
TEACHER TO
TEACHER
30 SpringBoard® Mathematics with Meaning™ Level 1
12/16/09 5:44:11 P
0
© 2010 College Board. All rights reserved.
025-032_SB_MS1_1-5_SE.indd 30
Comparing and Ordering Fractions
ACTIVITY 1.5
Analyzing Elections
continued
SUGGESTED LEARNING STRATEGIES: Quickwrite, Self Revision/
Peer Revision, Questioning the Text, Identify a Subtask, Create
Representations
Differentiating Instruction
Using concrete objects, such as
breakfast bars, may help students
to understand that the more parts
a whole is divided into, the smaller
each part is. So, the more people
you share something with, the
smaller the piece of it you will get
for yourself.
My Notes
1,
1 , __
c. Use your work from Parts a and b to order the fractions __
3 4
1 from greatest to least.
1 , and __
__
5
2
__1 , __1 , __1 , __1
2 3 4 5
d. Each of the four fractions you just ordered has the
same numerator. Tell Hernando how he can use just the
denominators to order the fractions.
Answers may vary. Sample answer: When the numerators
are the same, the fraction with the smallest denominator will
be the largest fraction.
g (continued ) Quickwrite, Self
Revision/Peer Revision (d)
4 , and ___
4 , ___
4 , __
4 from
e. Use mental math to order the fractions __
5 11 7
25
greatest to least.
4 , ___
4
__4 , __4 , ___
5 7 11 25
Hernando can see that the fractions he wants to order do not have
either a common numerator or a common denominator.
You may recall that mental math
is working a problem in your
head without writing it on paper.
18. He thinks that it will be easier to find a common numerator
for them rather than a common denominator.
© 2010 College Board. All rights reserved.
8 , __
1,
a. What is the least common numerator of the fractions ___
15 6
16
4?
___, and __
33
9
CHECK YOUR UNDERSTANDING
p. 32, #5–9
b. Change each of the fractions above to an equivalent fraction
with the common numerator found in Part a.
16 , __
16 , ___
16 = ___
16 , __
16
8 = ___
1 = ___
4 = ___
___
30 6
96 33
33 9
36
UNIT 1 PRACTICE
p. 58, #35–39
c. Order the fractions in Part b from least to greatest using the
number line below.
1
6
0
4
9
h Question the Text, Identify
a Subtask, Create Representations (c), Debriefing This is a
good question for questioning
the text by either the student or
the teacher. Ask students why
Hernando thinks that finding a
common numerator would be
easier.
Suggested Assignment
16
15
ACTIVITY 1.5 Continued
8
15
16
33
1
d. In what order will Hernando talk with the student groups?
music, sports, academic clubs, art club
Unit 1 • Number Concepts
© 2010 College Board. All rights reserved.
PM
025-032_SB_MS1_1-5_SE.indd 31
31
12/16/09 5:44:15 PM
MINI-LESSON: Comparing Fractions
Ask pairs of students to create a set of fraction cards. Students then play
Try to Get the Whole Deck as an engaging way to practice comparing
fractions. They can use the methods they learned in Example 1. Each
player lays a card down and whoever has the greater fraction wins the
two cards. Play continues until one player has won the entire deck. Use
this time to re-teach in a small group those students who were struggling
with comparing fractions.
Unit 1 • Number Concepts
31
ACTIVITY 1.5 Continued
Comparing and Ordering Fractions
ACTIVITY 1.5
continued
Analyzing Elections
Answer Key
2.
CHECK YOUR UNDERSTANDING
Write your answers
answers on
on notebook
notebook paper.
paper.Show your work.
6. Your school is holding a mock election for
Show your work.
president. 250 students vote.
1. A jar is filled with 70 centimeter cubes.
There are 15 red, 9 green, 21 yellow,
20 purple, and 5 orange. Write the
fractions for each color in order from
least to greatest.
2. Draw and shade rectangles and then order
the fractions from greatest to least.
3 __
7 , __
__
,1
8 4 2
3a. 18
5
15
7 = ___
14 and __
b. __
= ___
9
18
6
18
5
c. __
6
4. Answers may vary. Sample
answer: An LCD is simply an
LCM for 2 or more different
denominators.
5. Player 1
10 of the total votes.
Candidate 1 receives ___
50
9 of the total votes.
Candidate 2 receives ___
25
4 of the total votes.
Candidate 3 receives ___
10
5 of the total votes.
Candidate 4 receives ____
125
Rank the candidates by the number of
votes each received, from least to greatest.
3
__
4
1
__
2
7
__
8
7 and __
5.
3. Consider the fractions __
9
6
a. What is the LCD for these fractions?
b. Use the LCD you just found and the
Property of One to write equivalent
5.
7 and __
fractions for __
9
6
c. Which fraction is greater?
6. Candidate 4, Candidate 1,
Candidate 2, Candidate 3
4. What is the difference between an LCD
and an LCM?
7. Computer games, play sports,
watch TV, read. Explanations
may vary. Sample answer:
Since the numerators are
the same, I can compare the
denominators. The larger the
denominator, the smaller the
fraction.
5. Two students are playing a game with
fraction cards. Each player lays a card
down and whoever has the greater amount
wins the two cards. Who wins this pair?
7. The table below shows the fraction of
students who voted for each after-school
activity. Use mental math to order the
activities from most popular to least
popular. Explain your thinking.
Computer
Games
1
__
2
Read
1
___
12
Watch
TV
1
__
6
Play
Sports
1
__
4
© 2010 College Board. All rights reserved.
5
9
15
1. orange ___
, green ___
, red ___
,
70
70
70
20
21
___
___
purple 70 , yellow 70
8. Use common numerators to compare the
weekly growth of the plant. In which week
did the plant grow the most? Explain how
you reached your conclusion.
Week
1
Player 1
Player 2
2
11
14
3
4
3
Growth
(in.)
3
___
11
6
__
7
12
___
13
9. MATHEMATICAL Describe the steps for
R E F L E C T I O N comparing and ordering
fractions with unlike denominators.
3
12
= ___
8. Week 1: ___
11
44
6
12
Week 2: __
= ___
7
14
The plant grew the most in
Week 3.
32 SpringBoard® Mathematics with Meaning™ Level 1
025-032_SB_MS1_1-5_SE.indd 32
9. Answers may vary. Sample answer: Start by making either the
numerators or the denominators the same so that you can
compare the fractions. To do this, find a common denominator
or common numerator and use it to write equivalent fractions.
If you use common denominators, compare the numerators—
the greater the numerator, the greater the fraction. If you use
common numerators, compare the denominators—the smaller
the denominator, the greater the fraction.
32 SpringBoard® Mathematics with Meaning™ Level 1
12/16/09 5:44:19 P
© 2010 College Board. All rights reserved.
12
Week 3: ___
13