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Table of Contents
Introduction. ..................................................................................................... 5
Unit 1 Ratios and Percents............................................................................................... 7
6.RP.1
6.RP.3.a
6.RP.2, 6.RP.3.b
6.RP.3.d
6.RP.3.c
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Review
Ratios......................................................................... 8
Equivalent Ratios.................................................... 12
Rates........................................................................ 16
Measurement Conversions.....................................20
Percents................................................................... 24
Ratios and Percents................................................ 28
Unit 2 Operations. ............................................................................................................ 31
6.NS.2
6.NS.1
6.NS.3
6.NS.3
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Review
Dividing Whole Numbers....................................... 32
Dividing Fractions................................................... 36
Adding and Subtracting Decimals.........................40
Multiplying and Dividing Decimals.......................44
Operations...............................................................48
Unit 3 Factors and Multiples......................................................................................... 51
6.NS.4
6.NS.4
Lesson 1 Greatest Common Factors...................................... 52
Lesson 2 Least Common Multiples........................................ 56
Review Factors and Multiples.............................................60
Unit 4 Positive and Negative Numbers.....................................................................63
6.NS.5
6.NS.6.a, c
6.NS.6.b, c; 6.NS.8
6.NS.7.a, b
6.NS.7.c, d
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Review
Integers....................................................................64
Rational Numbers on Number Lines.....................68
Coordinate Graphing.............................................. 72
Comparing Integers................................................ 76
Absolute Value........................................................80
Positive and Negative Numbers.............................84
Unit 5 Expressions. ........................................................................................................... 87
6.EE.1; 6.EE.2.a, b
6.EE.1, 6.EE.2.c
6.EE.3, 6.EE.4
FLM CCSS Gr6_FM.indd 3
Lesson 1
Lesson 2
Lesson 3
Review
Writing Expressions................................................88
Evaluating Expressions...........................................92
Operation Properties.............................................. 96
Expressions........................................................... 100
10/4/10 3:19:30 PM
Unit 6 Equations and Inequalities............................................................................ 103
6.EE.5
6.EE.6
6.EE.7
6.EE.8
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Review
Equations and Inequalities.................................. 104
Writing Equations................................................ 108
Solving Equations................................................. 112
Representing Inequalities..................................... 116
Equations and Inequalities...................................120
Unit 7 Relationships Between Two Variables........................................................123
6.EE.9
6.EE.9
Lesson 1 Functions............................................................... 124
Lesson 2 Graphing Relationships........................................128
Review Relationships Between Two Variables.................132
Unit 8 Geometry..............................................................................................................135
6.G.1
6.G.2
6.G.4
6.G.3, 6.NS.8
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Review
Area.......................................................................136
Volume................................................................. 140
Nets and Surface Area......................................... 144
Coordinate Geometry...........................................148
Geometry............................................................... 152
Unit 9 Data and Statistics.............................................................................................155
6.SP.1
6.SP.2, 6.SP.3
6.SP.5.a–d
6.SP.5.a–d
6.SP.4
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Review
Collecting Data.....................................................156
Data Distributions.................................................160
Measures of Central Tendency............................ 164
Measures of Spread..............................................168
Representing Data................................................ 172
Data and Statistics................................................ 176
Practice Test............................................................................................................... 179
Glossary...................................................................................................................... 191
FLM CCSS Gr6_FM.indd 4
10/4/10 3:19:30 PM
Lesson
2
The product of
a number and its
reciprocal is always 1.
To multiply
fractions, multiply
the numerators.
Then multiply the
denominators.
8
2
4
234
 
​ 3 ​3  
​ 5 ​5 ​  
  
​5  
​ 15  ​
335
To change a mixed
number to a fraction
greater than 1,
multiply the whole
number part by the
denominator. Then
add the numerator.
This becomes the
new numerator of
the fraction. The
denominator stays the
same.
To change a fraction
greater than 1 to a
mixed number, divide
the numerator by the
denominator. Write the
remainder as a fraction.
36
Dividing Fractions
6.NS.1
To divide fractions, multiply by the reciprocal of the second fraction.
The numerator and denominator of a reciprocal switch places.
What is the reciprocal of each number?
5
1
 
​ 6 ​ ​  
 ​ 2
8
Switch the numerator and the denominator.
5
6
1
8
The reciprocal of ​  
 ​ is ​  
 ​.
5
6
The reciprocal of ​  
 ​ is ​  
 ​ 5 8.
1
8
2
2
1
As a fraction, 2 5  
​ 1 ​. The reciprocal of  
​ 1 ​is ​  
 ​.
2
3
3
What is the quotient of ​  
 ​ 4  
​ 8 ​?
4
3
First rewrite as multiplication using the reciprocal of ​  
 ​.
8
3
8
The reciprocal of ​  
 ​ is ​  
 ​, so the equivalent multiplication
8
3
3
8
expression is  
​ 4 ​3  
​ 3 ​.
Multiply and reduce to lowest terms if necessary.
3
8
24
​  
 ​ 3  
​ 3 ​5  
​ 12  ​5 2
4
3
3
The quotient of  
​ 4 ​4  
​ 8 ​5 2.
UNIT 2
Operations
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FLM CCSS Gr6_U2.indd 36
10/5/10 10:56:11 AM
Read each problem. Circle the letter of the best answer.
2
SAMPLE Travis has a 6-foot long rope. He ties a knot in the rope every  
​ 3 ​foot.
How many knots are tied in the rope?
A 4
B 8
C 9
D 12
The correct answer is C. To find the number of knots, divide 6
6
2
by ​  
 ​. First write 6 as the fraction ​  
 ​. Use it to write the division
1
3
6
6
2
2
problem:  
​ 1 ​4  
​ 3 ​. Multiply by the reciprocal of ​  
 ​ and reduce: ​  
 ​ 3
1
3
3
18
 
​ 2 ​5  
​  2  ​5 9 knots. Choice A is not correct because the numbers are
multiplied, not divided. Choices B and D are not correct because a
mathematical error was made.
5
1What is the reciprocal of ​  
 ​?
4
1
C  
​ 5 ​
4
D  
​ 5 ​
A​  
 ​
4
B​  
 ​
4
3
5
4 What is the quotient of  
​ 10  ​4  
​ 12  ​?
4
A​  
 ​
8
5
B​  
  ​
11
2Which number sentence shows the product
of a number and its reciprocal?
2
A​  
 ​ 3 0 5 0
7
2
7
B​  
 ​ 3  
​ 2 ​5 1
7
2
4
8 markers are placed equal distances apart
to help guide hikers. How far is one marker
from the next?
5
A​  
  ​ mi
10
1
C  
​ 32  ​mi
B​  
 ​ mi
5
2
D  
​  5  ​mi
32
D  
​ 25  ​
18
1
C 2 acres
2
D 2 ​  
 ​ acres
3
A​  
 ​ acre
3
B​  
 ​ acre
9
D  
​ 7 ​3  
​ 7 ​5  
​ 49  ​
4
3A hiking trail is  
​ 5 ​-mile long. A total of
4
evenly into 3 pieces. What is the size of
each piece of land?
2
2
C  
​ 6 ​
2
5A piece of land is  
​ 3 ​acre. It is divided
C  ​ 
 ​ 3 1 5  
​ 7 ​
7
2
5
1
1
6A bottle contains 8 cups of juice. The juice
3
is poured into glasses that hold  
​ 4 ​cup
each. How many glasses can be filled with
the juice?
2
A 6
C 10 ​  
 ​
3
B 8 ​  
 ​
4
3
D 12
UNIT 2
Operations
37
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FLM CCSS Gr6_U2.indd 37
10/5/10 10:56:12 AM
Read each problem. Write your answer.
3
1
SAMPLE Carmen walked 2 ​  
 ​ miles in ​  
 ​ hour. What was her average walking
4
2
speed, in miles per hour?
Answer ____________________________________
3
1
 ​ by ​  
 ​. Change the
To find the average walking speed, divide 2 ​  
4
2
1
23211
5
mixed number to a fraction: 2 ​  
 ​ 5 ​  
 
 
​5  
​ 2 ​. Now divide:
2
2
5
3
5
4
20
10
10
1
 
​ 2 ​4  
​ 4 ​5  
​ 2 ​3  
​ 3 ​5  
​  6  ​5  
​  3  ​. The fraction  
​  3  ​5 10 4 3 5 3 ​  
 ​. The
3
1
average walking speed was 3 ​  
 ​ miles per hour.
3
2
7It rained a total of  
​ 3 ​inch in 4 hours. What was the average amount
of rainfall each hour? Show your work.
Answer ________________________
8A recipe makes a total of 5 cups of pudding. A serving of pudding
3
is ​  
 ​ cup. How many servings of pudding does the recipe make?
4
Show your work.
Answer ________________________
1
9Horses are measured in units called hands. One hand equals  
​ 3 ​foot.
1
A horse is 5 ​  
 ​ feet tall. How tall is this horse in hands? Show your work.
3
38
Answer ________________________
UNIT 2
Operations
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FLM CCSS Gr6_U2.indd 38
10/5/10 10:56:13 AM
Read the problem. Write your answer to each part.
10Jada surveyed some students to see which tool they most favored for
communicating with friends. The results of her survey are shown in
this circle graph.
FAVORITE
COMMUNICATION TOOL
Text
Messages
5
12
1
5
Phone
1
20 Letters
1
3
E-mail
Part AWhat is the reciprocal of each fraction in the circle graph?
Answer ____________________________________
Part BA total of 50 students said they favored text messages
to communicate with friends. How many total students
did Jada survey? Show your work or explain how you
know.
What division
expression can be
used to answer this
question?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
UNIT 2
Operations
39
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FLM CCSS Gr6_U2.indd 39
10/5/10 10:56:14 AM