Lesson 3.1.3
3-36. BUILD IT, DRAW IT, WRITE IT, SAY IT
o
The 10 block is 10%, the 1 block is 1%.
b.
, 11%, 0.11, eleven percent, eleven hundredths
c. Students will need 2 columns (or equivalent) of the 100%-block covered,
20%,
,
, , 0.2, 0.20, twenty percent, two tenths, one fifth, twenty out
of one hundred total pieces
d. 80%, 0.8, 0.80,
,
,
, eighty percent, eight tenths
e. The students will need to use 1.5 100%-blocks, 1.5,
,
, , one hundred
fifty out of 100 total parts, one and one half, one hundred fifty percent
3-37. See below:
a. They are describing the same portion. 2-tenths are the same as 20-hundredths;
one way for students to show that is that two “tenths” blocks can be built with
20 “hundredths” blocks.
b. The 2 represents the number of “tenths” and the 3 represents the number of
“hundredths.”
3-38. 0.19 is represented with 1-tenth and 9-hundredths (or 19-hundredths). 0.5 is
represented with 5-tenths (or 50-hundredths).
3-39. Possible answers include: for fractions, 0 and
0.0 and 1.0. See percent ruler below.
or
or
; for decimals,
3-40. She is not correct. Percents are fractions over 100. 134% is more than 1,
but
is less than one.
3-41. See below:
a. It would take 4 tenths pieces or 40 hundredths pieces.
b.
.
. You would use
.
c. 0.4 or 0.40. The 4 is in the tenths place, which matches the number of tenths
pieces in the representation.
d. Four-tenths. Four-tenths is the same as 40-hundredths or 40%.
3-42. GUESS MY DECIMAL
a. Possible responses: 0.7 or 0.70
b. 0.6 or 0.60
c. 0.42
3-43. See below:
a. 10%, 1%
b. 0.10, 0.01
c. A one-thousandth block would be one-tenth of a one-hundredth block, so that
10 of them would fit in one of the small squares.
3-44. See below:
a. 12.5%
b.
or
or
c. 0.125
3-45. 276 students
3-46. See below:
a. 36%
b. 8%
c. 17%
d. 110%
3-47. See below:
. 30 liters
a. 42 liters
b. 24 liters
3-48. See below:
0.
Answers vary:
and
,
and
, and
and
have the same
denominator;
,
,
,
, and
have
denominators that are easy multiples of each other; students may identify fractions
that they can add together mentally, such as
that
,
; students may recognize
is equal to 1 and thus can be added easily to any other fraction or sum.
3-49. See below:
0. $7.75 · 12 = $93
3-50. See below:
. 7%
a.
or
b.
or
c. 0.315
3-51. See below:
0. 0.7 is larger than 18%, explanations will vary.
3-52. See below:
0. Drawings will vary, but the students should recognize that 78 squares and
another should be shaded, 0.785.
of
3-53. See below:
0. 2. See possible diagram below.
3-54. See below:
0. He does not have enough money, all of the items would cost $11.69. He could buy
either the ketchup, which would cost $9.80, or the mustard, which would cost $9.00.