


In mathematics, there is often more than one way to express a value or an idea. For
example, the statement, “Three out of ten students who are going on the field trip
have turned in their permission slips,” communicates the same portion as the
phrase, “30% of the students who are going on the field trip have turned in their
permission slips.” While three out of ten and 30% might look and sound very
different, they are both representations of the same portion of a whole. (In this case,
the whole is the entire number of students who are going on the field trip.)
Throughout this section, you have been representing numbers indifferent ways.
In Lesson 3.1.2, for example, you used a diagram and a percent ruler to express your
team’s guess about the portion of raisins in a jar. In this lesson, you will use a 100%
block to create models of the size of various numbers on the 100% block. Today you
will be investigating several ways to represent portions of wholes, including percents,
fractions, and decimals. As you work, keep these questions in mind:


How can I build it?
Is there another way to represent this portion?

What is the whole?



3-36. BUILD IT, DRAW IT, WRITE IT, SAY IT
In Section 2.2, you used a hundred block to represent the number 100. For your work
in this section, you will use this block to represent one whole or 100%, also described
as 1, as 100/100, or as one hundred out of one hundred. The block will be referred to
as the 100% block. Since a whole block represents 100%, 50% (50/100, 5 out of
every 10, or
) can be represented by the diagram right.


When the large square block represents 100%, what do each of the other blocks you
have worked with represent?
Obtain a set of Base Ten Blocks or use either of these: Base Ten Block (html5) or
Base Ten Blocks (GeoGebra: html5) and a copy of theLesson 3.1.3A Resource
Page from your teacher. For each of the portions listed below:

Build the portion on a 100% block.

Draw a diagram of the portion on your resource page.

Write the portion in at least two different equivalent representations.

Write out how you could use words to say or name the portion two different
ways.
e.
f.
g. 80 pieces out of 100 total pieces
h. 150%

3-37. Erik and Tate cannot agree on the amount shaded on the
100% block shown at right. Erik says, “It shows 2 tenths of the 100% block… and 3
hundredths of the block,” while Tate says, “It shows 23 hundredths of the whole
block.”
. What would you tell Tate and Erik? Justify your response with words and
pictures.
a. Another representation of the number shown on the 100% block above is a
decimal, which would be written as 0.23. Compare this number to how Erik
and Tate described the value. What similarities do you notice?

3-38. If 0.23 can be represented with 2 tenths and 3 hundredths, how can the number
0.19 be represented? What about 0.5? Get aLesson 3.1.3B Resource Page and draw
a picture of each of these numbers on the 100%-block diagrams. Explore using: Base
Ten Blocks

3-39. Jessa was working with a percent ruler when she had an idea. “Can we use this
idea for the other representations of a portion?” she asked.

Discuss this idea with your team. Decide how to label each end of the ruler (the 0%
end and the 100% end) if it is being used to measure fractions or decimals.

Draw a large percent ruler on your paper and mark each of the portions listed below
on the ruler.
. 80%
a.
b. 40%
c. 99 hundredths
d. 100%
e. 9 tenths
f. 3 tenths and 9 hundredths
g. 10 hundredths
h. 25 out of 100
i. 10 tenths

3-40. Suzie looked at the diagram below and wrote 134% =
. Is she correct?
Why or why not?


3-41. Use the diagram of
shown below to make sense of the following questions.
. Describe what would look like if it were built on a 100% block. What are
the largest pieces you could use? How many of these pieces would it take to
build the portion? What are the smallest pieces you could use? How many of
these pieces would it take to build the portion?
a. Write
as a fraction with a denominator of 10 and then with a denominator of
100. In other words,
show that
?
? What giant one would you use to
is equivalent to a portion of 100?
b. How could be written as a decimal? How is the decimal representation
related to the 100% block diagram that you described in part (a)?
c. What is another name for the decimal representation of
name relates to the 100% block.
? Explain how the

3-42. GUESS MY DECIMAL

Maya and Logan invented a new game called “Guess My Decimal.” One of them
thinks of a decimal and gives the other a clue to solve for the mystery decimal.
. Logan begins the game by saying, “First, I think of the 100% block as a one
block so I can make a decimal instead of a percent. Then my decimal can be
represented on the one block like this.” He pointed to the diagram at right.
What is Logan’s decimal?
a. It was Maya’s turn. She said, “My decimal is equivalent to
Maya’s decimal?
.” What is
b. Logan finishes the game with the following clue, “My decimal can be built by
combining 0.38 and 0.04.” What is Logan’s decimal?

3-43. Today you used 100% blocks to help connect percents and decimals.
. If
represents 100%, what do
a. If
represents 1, what do
and
and
represent?
represent?
b. Based on the pictures above, imagine what a one-thousandth block might look
like. How would it compare in size to the other three blocks? Explain.

3-44. Jonah began to wonder about other representations of
numbers on the 100% block. He calls the figure at right “twelve-and-a-half
hundredths.” Use his drawing to help answer the following questions.
. How could this be expressed as a percent?
a. What fraction of an entire 100% block is shaded? Is there more than one way
to write this fraction?
b. How could this number be written as a decimal?

100% Blocks

Base Ten Blocks can also be used to represent percents. The three basic blocks
represent 100%, 10%, and 1%, as shown below.

A percent is a way of expressing a number as a fraction out of 100. In the example
shown at right, 23 out of 100 squares are shaded to represent 23%. 23% can be
expressed as
, 0.23, or twenty-three hundredths.

3-45. An article in the local paper states that 30% of the students at Oak Grove
Middle School earned a place on the Silver Honor Roll. If there are 920 students at
Oak Grove, how many are on the Silver Honor Roll? Use a percent ruler to help you
decide. Show all of your work. Help (Html5)⇔Help (Java)

3-46. Given the following descriptions of portions, write each portion as a percent.
Use a 100% block to help you visualize the portions. Help (Html5)⇔Help (Java)
a. 3 tenths and 6 hundredths
b. 8 hundredths
c. 17 hundredths
d. 11 tenths

3-47. Maurice's gas tank can hold 60 liters of gas. On your paper, copy and label the
percent ruler below. Then use it to find how many liters are in the tank when it
is: Help (Html5)⇔Help (Java)
.
50% full
a.
full
b.
full

3-48. Which of the following fractions could you add together easily? Explain. Help
(Html5)⇔Help (Java)

3-49. Alex earns $7.75 a day by walking dogs for his neighbors. If he walks dogs for
12 days, how much money will he make? Show how you got your answer. Help
(Html5)⇔Help (Java)

3-50. Use the Lesson 3.1.3B Resource Page to shade in the amounts represented by
the following descriptions, and then write them in the stated form. Help
(Html5)⇔Help (Java)
a. Shade 7 hundredths, and write the portion as a percent.
b. Shade 7 tenths, and write the portion as a fraction.
c. Shade 28%, and write the portion as a fraction.
d. Shade 31.5%, and write the portion as a decimal.

3-51. Given the numbers 18% and 0.7, explain which number is larger by using words
and/or pictures. Help (Html5)⇔Help (Java)

3-52. Explain what 78.5% would look like on a 100%-block. Then write it as a
decimal. Help (Html5)⇔Help (Java)

3-53. What is the sum of
(Html5)⇔Help (Java)

3-54. Owen loves to eat hamburgers. He goes to his neighborhood grocery store to
buy ground beef and buns to make hamburgers at home. He buys a package of
hamburger buns for $1.29 and a package of ground beef for $5.82. He only has a $10
bill and wonders if he can buy some ketchup and mustard, too. The ketchup is $1.89,
and the mustard is $2.69. He does not have to pay sales tax on food. Help
(Html5)⇔Help (Java)
? Represent your ideas in multiple ways. Help
Does Owen have enough money to buy both the ketchup and the mustard? If he does,
how much money will he have left over? If not, then what could he buy and how
much would it cost?