Name____________________________________ Date________
a.
Fraction _____________
You have been working with various ways
to represent portions of a whole. These
multiple representations are shown in the
diagram at right. It is called a web. For
some problems, you might prefer to work
with a percent, while at other times, it
might make sense to use a fraction or a
decimal.
Today you will represent portions in multiple ways and consider
which of them allows you to work most efficiently. As you work
on today’s lesson, use these questions with your team to focus
your discussions:
b.
Fraction __________
Decimal _____________
Decimal
0.56
Percent _____________
Percent __________
In Words- three tenths and
one hundredth
In Words____________________
________________________________________________________________
c.
d.
Fraction
Fraction __________
Decimal _________
Decimal __________
 How else can I represent the same portion?
Percent _________
Percent
 How do I know the portions are equivalent (the same)?
In Words ________________ In Words ___________________
3-55. BUILD IT, WRITE IT, DRAW IT
Sometimes it is easier to compare portions when they are written
in a particular form. For example, 0.25 and 0.8 can be compared
easily when both are drawn on a 100% block or are both in
percent form. In this problem, your team will work with all of the
representations on the web and find ways to change one
representation into another. You may want to explore using Base
Ten Blocks. For each portion of a whole described below:
 Build the portion on top of a 100% block.
 Draw the representation on100 blocks.
 Write the portion as a percent, fraction, decimal, and as a
description in words.
3%
________________________ ____________________________
e. Place each of the portions described in parts (a) through (d) on a
number line. The number line should range from 0 and 1 be
marked in tenths.
f. Which representation (fraction, decimal, or percent) is most
convenient to use when placing values on a 0-to-1 number line?
Explain your choice. ___________________________________
____________________________________________________
3-56. LOCATION, LOCATION, LOCATION
_____________________________________________________
Sally was helping her younger sister Susie, who
had been absent from school, to understand
decimals.
When Susie came to the problem 0.37 + 0.7,
she got very excited. “I know, I know!” Susie shouted, “37 and 7
make 44, so the answer is 0.44!”
_____________________________________________________
“Well,” Sally said, “You’re right that 37 and 7 make 44, but 0.37
is not 37 and 0.7 is not 7. The value of numbers depends on
where they are located,” Sally explained, “That is why you have
to line up the place values, by lining up the decimal point, when
you add or subtract.”
b. Find the answer to 1.003 + 0.47.
3-58. Complete each of the following computations using your
understanding of decimal place value and representations of
portions.
a. 0.375 − 0.2
b. 18.6 + 0.04
c. 2.008 − 0.46
What does Sally mean? What explanation can you give
for lining up decimals when adding or subtracting?
Write a note to Susie explaining why 0.37 + 0.7 is not 0.44.
Include the correct answer and an explanation of what each
number in the problem represents. Hint: It might help to rewrite
each number as a sum of fractions or draw them with hundred
blocks.
_____________________________________________________
_____________________________________________________
_____________________________________________________
3-57. Susie’s next question impressed Sally. “So does that mean
that if I want to add 1.003 and 0.47, instead of adding 47
and 3, I need to add 470 and 3? Is this similar to adding
fractions, so I have to write them in equivalent forms?”
a. What do you think? Is Susie right? Use what you know about
representing these numbers with fractions, percents, and 100%
blocks to justify your answer.
_____________________________________________________
_____________________________________________________
3-59. Maya and Logan are playing “Guess My Decimal”
again. You will play along with them in parts (a) and (b)
below.
a. Maya challenges Logan by saying, “The decimal I’m thinking
of is what you would get if you subtract 0.01 from 0.3.”
Visualize what her number might look like on a 100% block.
What decimal is Maya thinking of?________
Explain how you know.
b. Logan continues the game with this challenge: “The decimal I
am thinking about is halfway between 18 hundredths and 3
tenths.” Help Logan solve this puzzle and show any work that
might help explain your thinking.