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Ohio
Master Ohio’s 15 most challenging mathematics skills with
SkillBridge. With lesson topics chosen based on actual state test
data, SkillBridge offers help in the skills that truly are the most
troublesome. As students move through each lesson, they are
equipped with guidance and connections that allow them to show
independent skill mastery by the end of the lesson. Ohio
references in each lesson offer a unique and familiar
point of entry into difficult skills.
Mathema
tics
Ohio’s 15 most challenging skills
in mathematics, grade 6
• Associative Property
• Input-Output Tables
• Multiples
• Identifying Triangles
• Factors
• Area
• Multiplying and Dividing
Fractions
• Volume
• Fractions and Percents
• Circle Graphs
• Ratios
• Proportions
• Range
• Probability
• Evaluating Expressions
Daniel Carter Beard Bridge in Cincinnati, Ohio
Catalog Number OHB2064W1
P.O. Box 2180
Iowa City, Iowa 52244-2180
ISBN 978-0-7836-6274-9
50599
STUDENT NAME
PHONE: 800-776-3454
FAX: 877-365-0111
www.BuckleDown.com
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Table of Contents
Associative Property (PA.D.3)................................................... 4
Multiples (NO.G.2b). .................................................................... 8
Factors (NO.G.2a)...................................................................... 12
Multiplying and Dividing Fractions (NO.H.11, NO.H.12).............. 16
Fractions and Percents (NO.D.5). ........................................... 20
Ratios (NO.D.5)......................................................................... 24
Proportions (NO.D.14)............................................................... 28
Evaluating Expressions (PA.G.6)............................................ 32
Input-Output Tables (PA.B.1)................................................... 36
Identifying Triangles (GS.D.3). ................................................ 40
Area (ME.C.3b)........................................................................... 44
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Volume (ME.C.3a)...................................................................... 48
Range (DP.F.4). ......................................................................... 52
Circle Graphs (DP.A.1). ............................................................ 56
Probability (DP.K.7).................................................................. 60
PA.D.3
OH
At the beginning of each lesson, you will see a box with the shape of
Ohio and an Academic Content Standard code in it. This code tells
you what is being covered in the lesson.
3
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PA.D.3
OH
Associative
Property
The associative property is a rule about the way
numbers are grouped. The associative property
states that the sum or product of a set of numbers is
the same even when the grouping is changed.
According to the order of operations, when you solve
an expression, you must complete any operations
inside parentheses first. The associative property
proves that moving the parentheses to change the
grouping of the numbers when you are adding or
multiplying will not change the answer.
The Rock and Roll Hall of
Fame Museum is located in
Cleveland, close to the shore
of Lake Erie.
(a  b)  c 5 a  (b  c)
(a 3 b) 3 c 5 a 3 (b 3 c)
The associative property of addition states that
the grouping of addends can change and the sum
will be the same.
Example 1
(18  12)  15 5 18  (12 
)
For the equation to be equal, the same addends
must be on each side of the equal sign. The
number 15 is missing on the right side of the
equation.
Check the answer by finding the sum of each
side. Add the numbers in parentheses first, to
follow the order of operations.
(18  12)  15 5 18  (12  15)
30  15 5 18  27
455 45
The missing number is 15. The associative
property of addition shows that you can group the
addends in any order and the sum is the same.
Write the missing number.
20  (26  23) 5
(20 
)  23
OH6 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW.
Build A Bridge 1
Write the missing number.
4
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The associative property of multiplication states that if the grouping of factors
is changed, the product will be the same.
Example 2
Use the associative property of multiplication to
find the equivalent expression.
Build A Bridge 2
A (7 1 10) 1 4
Use the associative
property of multiplication
to find the equivalent
expression.
B 7 • (10 • 7)
34 • (42 • 26) 5
C 7 • (10 1 4)
A (34  42)  26
D 7 • (10 • 4)
B 34 • (26 • 40)
(7 • 10) • 4 5
Check each answer choice to see if the same
three factors are being used. Then, check for the
same operation signs. Finally, compare the way
the factors are grouped.
C (34 • 42) • 26
D (34 • 42)  26
Choice D: 7 • (10 • 4) is the equivalent
expression.
So, (7 • 10) • 4 5 7 • (10 • 4).
OH6 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW.
Example 3
Which equation shows the associative property
of addition?
A (8 1 6) 2 9 5 8 2 (6 1 9)
B 8 1 (6 1 9) 5 (8 1 6) 1 9
C 8(6 1 9) 5 8(6) 1 8(9)
D (8 • 6) • 9 5 8 • (6 • 9)
You are looking for the associative property of
addition, so look for addition signs. Check each
answer choice to see if the same addends are
being used. Finally, compare the way the
numbers are grouped.
Choice B demonstrates the associative property
of addition: 8 1 (6 1 9) 5 (8 1 6) 1 9.
Build A Bridge 3
The associative property
only works for addition
and multiplication.
Consider (12 2 5) 2 3
and 12 2 (5 2 3). The
numbers are the same,
but the two expressions
are not equivalent.
The property does not
work for 24 4 (6 4 3) and
(24 4 6) 4 3 either. They
are also not equivalent.
Subtraction and division
are not associative.
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Guided PractiCE
1 Define the associative property.
2 Explain how to use the associative property of multiplication to write an
equivalent expression to 10 • (4 • 8).
3 Does the associative property work for subtraction? Give an example.
For Numbers 4–7, use the associative property to write the missing number.
6 26 • (
 19) 5
• (37 • 54) 5 (48 • 37) • 54
• 60) 5 (26 • 35) • 60 7 (81  18) 
5 81  (18  71)
For Numbers 8–10, use the associative property to find the equivalent
expression.
8 (15 • 29) • 52 5
A 15 • (29 • 15) B 15 • (29 • 52)
C 15  (29  52)
D 15  (29 • 52)
9 3.8  (4.1  2.4) 5
A (3.8  4.1)  2.4
B 3.8 • (4.1  2.4)
C (3.8  4.1) • 2.4
D 3.8 • (4.1 • 2.4)
10 172 • (86 • 93) 5
A 172  (86 • 93)
B (172 • 86) • 86
C (172 • 86) • 93
D (172  86)  86
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4 (13  11)  19 5 13  (
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Practice
For Numbers 1–4, use the associative property to write the missing number.
1 (42 • ) • 26 5 42 • (34 • 26)
3 (8.3 1 7.5) 1 9.4 5
2 (98 1 85) 1
5 98 1 (85 1 76)
1 (7.5 + 9.4) 4 36 • (62 • 21) 5 (36 • 62) •
For Numbers 5–7, use the associative property to find the equivalent
expression.
5 12.8 1 (15.2 1 17.1) 5
A 12.8 • (15.2 1 17.1)
B (15.2 1 15.2) 1 17.1
C (12.8 1 15.2) 1 17.1
D 12.8 • (15.2 • 17.1)
A (391 1 425) 1 391
B 391 1 (260 1 425)
C 391 1 (260 • 425)
D 391 • (260 • 425)
A 63 1 (39 • 69)
B (63 • 39) • 96
C 63 • (39 • 69)
D 63 1 (39 • 69)
6 (391 1 260) 1 425 5
OH6 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW.
7 (63 • 39) • 69 5
For Numbers 8–10, circle T for true or F for false for each equation.
8 T F
(20 1 28) 1 24 5 20 1 (28 • 24)
9 T F
(5.1 • 3.6) • 7.2 5 (3.6 • 3.6) • 7.2
10 T F
109 1 (213 1 391) 5 (109 1 213) 1 391
11 Six groups of visitors toured the Rock and Roll Hall of Fame Museum. Each
group had 8 visitors. Every visitor received 2 postcards on the tour. Which
expression shows the total number of postcards given out during the tours?
A 6 • (8 • 2) 5 (6 • 8) • 2
C (6 1 8) 1 2 5 6 • (8 • 2) B (6 1 8) 1 2 5 6 1 (8 1 2)
D 6 • (8 4 2) 5 (6 • 8) 4 2
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