Core Connections 1 (6th Grade Mathematics)
Chapter 3: Portions and Integers
Answer Key
Learning Targets Example Problems:
We are learning 3-12, 3-73 (a), and CL 3-133
to use the
multiplicative
identity to write
equivalent
fractions and to
rewrite fractions
as percents.
3-73. In this lesson, you looked for ways to convert between equivalent forms of
fractions, decimals, and percents. Using the portions web, write the other forms of the
number for each of the given portions below. Show your work so that a team member
could understand your process.
a. Write 4/5 as a decimal, as a percent, and with words/picture. [ 0.8, 80%, fourtenths]
b. Write 0.30 as a fraction, as a percent, and with words/picture. [ 30/100 or 3/10 , 30%,
thirty hundredths ]
c. Write 85% as a fraction, as a decimal, and with words/picture. [ 85/100 or 17/20 , 0.85,
eighty-five percent ]
d. Write one and twenty-three hundredths as a percent, as a decimal, and as a fraction
[ 1.23, 123%, 123/100 ]
We are learning 3-29, 3-31, 3-39, 3-40, 3-50, 3-51, 3-52, 3-55, 3-64, 3-131, CL 3-136, CL 3-138
to represent
portions
visually,
interpret visual
representations,
and determine
relative size of
portions given in
multiple
representations.
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.
a. Shade 7 hundredths, and write the portion as a percent. [ 7% ]
b. Shade 7 tenths, and write the portion as a fraction. [ 7/10 or 70/100 ]
c. Shade 28%, and write the portion as a fraction. [ 28/100 or 7/25 ]
d. Shade 31.5%, and write the portion as a decimal. [ 0.315 ]
3-55.
Write the portion as a percent, fraction, decimal, and as a description in words.
a. 3 tenths and 1 hundredth [ 0.31, 31%, 31/100 ]
b. 0.56 [ 5 tenths and 6 hundredths (or 56 hundredths), 56%, 56/100 ]
c. 21/25 [ 0.84, 84%, 8 tenths and 3 hundredths (or 83 hundredths) ]
d. 3% [ 0.03, 3 hundredths ]
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. [ See number line
below. ]
CL 3-138. Copy the number line below on your paper. Then label the following
numbers on the line in the appropriate locations.
a. 3/5
b. 120%
c. 0.07
d. 1 2/3
e. 83%
We are
converting from 3-33, 3-36, 3-45, 3-46, 3-64, 3-73, 3-109, CL 3-134
one
representation
of a portion to
others and
calculating
portions of given
wholes.
3-73. In this lesson, you looked for ways to convert between equivalent forms of
fractions, decimals, and percents. Using the portions web, write the other forms of the
number for each of the given portions below. Show your work so that a team member
could understand your process.
a. Write 4/5 as a decimal, as a percent, and with words/picture. [ 0.8, 80%, four tenths]
b. Write 0.30 as a fraction, as a percent, and with words/picture. [ 30/100 or 3/10 , 30%,
thirty hundredths ]
c. Write 85% as a fraction, as a decimal, and with words/picture. [ 85/100 or 17/20 , 0.85,
eighty-five percent ]
d. Write one and twenty-three hundredths as a percent, as a decimal, and as a
fraction. [ 1.23, 123%, 123/100 ]
We have a basic
understanding
of adding
positive and
negative
integers and
rational
numbers.
3-94, 3-106, 3-108, 3-111, 3-118, CL 3-140
3-94. Lucas’ frog is sitting at 2 on the number line.
a. His frog hops 4 units to the right, 6 units to the left, and then 8 more units to the
right. Write an expression (sum) to represent his frog’s movement.
[ 2 4 6 8 ]
b. Where does the frog land? [ 4 ]
c. What number is the opposite of where Lucas’ frog landed? [ –4 ]
3-111. Predict whether each answer below will be positive, negative, or zero. It may be
helpful to visualize a number line. After you have made each prediction, find the answer
to check your prediction. [ Predictions vary. ]
a. 5 10 [ –5 ]
b. (8) 2 [ 6 ]
c. 5 5 [ 0 ]
d. 4 15 [ 11 ]
3-118. Simplify the following expressions. Show your work.
a. 8.2310.9
b. 6 9
c. 8 34
d. 0 3
[ 19.13 ] [ –15 ] [ 1 ] [ –3 ]
e. 15 20
f. 9 14
h. 5 9
[ –5 ] [ 5 ] [ –4 ]