Mixed Numbers and Improper Fractions
Mood Rings, Part 1
ACTIVITY
1.6
SUGGESTED LEARNING STRATEGIES: Summarize/Paraphrase/
Retell, Vocabulary Organizer
My Notes
Tyrell and four of his friends from West Middle School went
to a craft fair and they all decided to buy mood rings. When
discussing their ring sizes with the ring maker, they learned about
anthropometry. Did you know that the average length around a
1 inches and the average length
woman’s ring finger is about 2 ___
16
9 inches?
around a man’s ring finger is about 2 ___
16
Before they can buy their rings, the friends must first measure
their ring fingers.
CONNECT TO SCIENCE
Anthropometry is the study of
the measurement of the human
body in terms of its dimensions.
People who design things for
others to use, such as bracelets
or rings, have to take typical body
measurements into account.
1. How big is your ring finger? To measure your ring finger wrap
a measuring tape snugly around the base of your finger. Record
1 of an inch.
your measurement to the nearest ___
16
2. This table shows the finger sizes of the five friends.
Tyrell
7 in.
1__
8
Bob
Jose
1 in.
2 __
4
Nisha
3 in.
1__
4
Ema
3 in.
2 ___
16
© 2010 College Board. All rights reserved.
a. Look at this measuring tape to determine Bob’s finger size.
Write your answer as a mixed number in the table above.
Remember, a mixed number is
the sum of a whole number and a
proper fraction.
0
2
1
3
1 inches are in 2 __
1 inches? Count the __
1 inches on
b. How many __
2
2
2
the diagram and write your answer as an improper fraction.
0
2
1
3
MATH TERMS
A positive improper fraction has
a value greater than or equal to
1. The numerator is greater than
or equal to the denominator.
c. Another way to see this is to use
a model. Name the shaded parts
of this diagram two ways.
Mixed Number: ______
(wholes + part)
Improper Fraction: ______
(total parts)
Unit 1 • Number Concepts
33
ACTIVITY 1.6
Mixed Numbers and Improper Fractions
continued
Mood Rings: Part 1
SUGGESTED LEARNING STRATEGIES: Think/Pair/Share,
Look for a Pattern, Quickwrite, Create Representations
My Notes
d. Complete this description of how to find the improper
fraction for the number of shaded halves:
There are ____ whole shaded circles with ____ shaded
halves in each. This gives me ____ shaded halves. Plus, there
is ____ shaded half in the last circle, making a total of ____
shaded halves.
e. Both the mixed number and the improper fraction in Part c
describe the same number. Write an equation that shows the
two are equal.
f. Without drawing a model, describe a method to use the
digits from the mixed number to find its equivalent improper
fraction. (Hint: Consider your description in Part d.)
3. Now convert Nisha’s finger size to an improper fraction.
b. Use a number line:
0
1
2
c. Use the method you discovered in Part e of Question 2. Did
you get the same answer as you did in Parts a and b?
4. Use your method from Question 2e to convert the other friends’
sizes to improper fractions.
a. Tyrell
b. Ema
c. Jose
34
SpringBoard® Mathematics with Meaning™ Level 1
© 2010 College Board. All rights reserved.
a. Use circles:
Mixed Numbers and Improper Fractions
ACTIVITY 1.6
continued
Mood Rings: Part 1
SUGGESTED LEARNING STRATEGIES: Identify a Subtask, Quickwrite
My Notes
5. You can use two methods to change from an improper fraction
to a mixed number: drawing a model or dividing.
WRITING MATH
9 . Then write a mixed number to represent
a. Draw a model of __
4
the whole and fractional parts of your model.
A fraction is a way of writing a
division problem:
9
__
= 9 ÷ 4.
4
b. Divide 9 by 4. Express the remainder as a fraction to get a
mixed number.
The five friends want to compare finger sizes to see whose ring
finger is the largest and whose is the smallest.
6. Nisha and Jose compare their finger sizes. Write an inequality
symbol in the circle to make the statement true. Explain your
thinking.
© 2010 College Board. All rights reserved.
Nisha
3
1__
4
Jose
1
2__
4
7. Next, Bob and Jose compare. Which of them has the larger ring
finger? Explain your thinking.
Bob
1
2 __
2
Jose
1
2 __
4
3 and 1 __
7 . Whose
8. Then Nisha and Tyrell compare their sizes of 1 __
4
8
finger is larger? Express your answer as an inequality. Explain
your thinking.
Unit 1 • Number Concepts
35
ACTIVITY 1.6
Mixed Numbers and Improper Fractions
continued
Mood Rings: Part 1
SUGGESTED LEARNING STRATEGIES: Quickwrite, Think/
Pair/Share, Create Representations, Debriefing
My Notes
9. You have compared the sizes of four friends, two at a time.
a. Use what you have learned to order the friends by their ring
finger sizes, going from smallest to largest.
b. Where does Ema fit into this order? Explain.
10. Ema tells her friends that they could order their fractions all
at once by using common denominators. Show how this can
be done.
11. Order the friends’ ring finger sizes from least to greatest on
the number line below. Label each point with each person’s
initial as shown for Bob.
1
CONNECT TO AP
Looking at the pattern of points
on a number line can help you
decide if the numbers are getting
close to a particular number.
Discovering such patterns is a
fundamental concept in advanced
math courses.
2
3
12. You now know different ways to order measurements. How
would you order the measurements of several other friends?
Describe your method.
Karen
Ahmed
Ileana
Keisha
Hunter
5
1__
8
7
__
5
2 ___
16
4
__
14
___
4
2
8
The finger sizes are easy to order since the fractions are all
1 ’s, or ___
1 ’s, __
1 ’s, __
1 ’s, like the increments on a ruler. However,
in __
2 4 8
16
98 , 1 ___
23 , and 2 ___
15 , 2 ____
2 , do not have
many numbers, such as 1___
31 100 44
71
denominators that are as simple to compare.
36
SpringBoard® Mathematics with Meaning™ Level 1
© 2010 College Board. All rights reserved.
B
Mixed Numbers and Improper Fractions
ACTIVITY 1.6
continued
Mood Rings: Part 1
SUGGESTED LEARNING STRATEGIES: Summarize/Paraphrase/
Retell, Create Representations, Quickwrite, Debriefing, Self
Revision/Peer Revision
To order numbers like these, think about how close each fraction
1 , 1, and so on. For example,
is to benchmark numbers, such as 0, __
2
15 is a little less than 1__
15
1 , because half of 32 is 16. Thus, place 1___
1___
31
2
31
1 mark.
just before the 1__
2
1
1 15
31
2
My Notes
MATH TERMS
Benchmark numbers are
numbers used as points of
comparison when estimating.
3
23 , and 2 ___
98 , 1 ___
2 on
13. Continue using benchmarks to order 2 ____
100 44
71
the number line above.
14. Summarize your findings on comparing and ordering mixed
numbers and improper fractions by discussing the following
cases.
© 2010 College Board. All rights reserved.
3 and 3 ___
1
a. Whole numbers are different: 2 ___
19
27
7
2 and 5 __
b. Whole numbers are the same: 5 __
3
9
32 and ___
27
c. Both are improper fractions: ___
5
4
3 and ___
13
d. One mixed number and one improper fraction: 6 __
5
2
Unit 1 • Number Concepts
37
ACTIVITY 1.6
Mixed Numbers and Improper Fractions
continued
Mood Rings: Part 1
CHECK YOUR UNDERSTANDING
Write your answers
answers on
on notebook
notebook paper.
paper.Show your work.
4. Order each of the following numbers
Show your work.
by placing them on a number line. Use
benchmark numbers to determine their
1. Convert the improper fraction to a mixed
placement.
number and the mixed number to an
improper fraction.
50
4
a. 7 __
b. ___
7
9
2. Mr. White’s students are playing a game.
He gives each student in a group a fraction
to help them decide the order in which
they will play. The person with the largest
fraction goes first, and so on. The table
below shows the fractions for the students
in one group.
Wyatt
3
1__
4
Kendra
8
2 ___
11
Miley
19
___
7
Bryson
9
__
5
10 , and __
8
11 , 2 __
2 , ___
1___
20 5 7
3
5. Compare.
9 and ___
53 and 7 __
3
47
b. ___
a. 8 ___
7
5
11
6
6. Order from least to greatest:
6 , ___
7 , 3 ___
24 , __
11
4 __
7 5 2 20
7. MATHEMATICAL Describe the three forms
R E F L E C T I O N in which fractions can be
written. Explain how to compare the three
forms. Give examples using different
forms of fractions.
3. Kim and Juan are measuring their wrists to
5 in.
purchase watches. Kim’s measures 5 __
3 in. Who has 8the
and Juan’s measures 5 __
4
larger wrist?
38
SpringBoard® Mathematics with Meaning™ Level 1
© 2010 College Board. All rights reserved.
List the order in which they will take their
turns.