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Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
Dazzling
Math Line
Designs
By Cindi Mitchell
S
C
H
O
L
A
S
T
I
C
PROFESSIONALBOOKS
N E W
Y O R K
•
T O R O N T O
M E X I C O
C I T Y
•
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L O N D O N
N E W
D E L H I
•
A U C K L A N D
•
H O N G
•
K O N G
S Y D N E Y
0.1
To my dad, George Neibler, for the endless hours
he spent at the kitchen table teaching me math.
(See Dad, I really was listening!)
Scholastic Inc. grants teachers permission to photocopy the activity sheets from this book for classroom use. No other part of this publication may
be reproduced in whole or in part, or stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying,
recording, or otherwise, without written permission of the publisher. For information regarding permission, write to Scholastic Inc., 555 Broadway,
New York, NY 10012.
Cover design by Pamela Simmons and Norma Ortiz
Interior design by Solutions by Design, Inc.
Interior illustrations by Cindi Mitchell
ISBN: 0-590-00085-3
Copyright © 1999 by Cindi Mitchell
All rights reserved.
Printed in the U.S.A.
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
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Contents
0.1
..........................................................5
Skills Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Introduction
Math Line Designs to Color
..................8
Holiday Glow (Number Theory: Divisibility) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Stardust (Number Theory: Divisibility) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Pattern Block Star (Decimals: Subtraction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Whirling Octagons (Decimals: Division by Decimals) . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Rising Star (Fractions: Addition With Unlike Denominators) . . . . . . . . . . . . . . . . . . . . . . 13
A Dozen Circles (Fractions: Subtraction With Unlike Denominators) . . . . . . . . . . . . . . . . . 14
Aztec Art (Fractions: Multiplication) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Tree Ornament (Fractions: Division) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Linked Together (Fractions: Equivalent Decimals and Percents) . . . . . . . . . . . . . . . . . . . . 17
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
Optical Illusion (Number Theory: Prime and Composite Numbers)
Stained Glass Window (Fractions: Subtraction of Mixed Fractions
With Unlike Denominators) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Gears (Fractions: Division of Mixed Fractions) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Paper Folding (Integers: Subtraction). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Star Wings (Integers: Division) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Poinsettia (Equations: Addition and Subtraction). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Hexagonal Flowers (Equations: Multiplication and Division) . . . . . . . . . . . . . . . . . . . . . 24
Starburst (Integers: Addition)
Math Line Designs to Create
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Patchwork Star (Decimals: Multiplication) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Nine Circles (Decimals: Equivalent Percents) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Puffy Cloud (Fractions: Equivalent Decimals) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Crochet (Fractions: Equivalent Decimals and Percents) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Four-Leaf Clover (Fractions: Renaming) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Dream Catcher (Fractions: Renaming) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Diamond (Fractions: Subtraction With Unlike Denominators) . . . . . . . . . . . . . . . . . . . . . . . 32
Emerging Triangle (Fractions: Division) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Letter Z (Decimals: Addition)
Octagonal Star (Fractions: Addition of Mixed Fractions With Unlike Denominators) . . . . . . 34
String Art (Fractions: Addition of Mixed Fractions With Unlike Denominators) . . . . . . . . . . 35
Starlit Sky (Fractions: Multiplication of Mixed Fractions) . . . . . . . . . . . . . . . . . . . . . . . . . 36
Birth of a Star (Fractions: Division of Mixed Fractions) . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Flaming Triangle (Percents: Discounts) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Zinnia (Percents: 10% Discounts) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Basket Weaving (Integers: Multiplication) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Explosion (Integers: Division) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Math Line Designs to Construct
How to Assemble the 3-D Constructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Triangular Pyramid (Number Theory: Divisibility) . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Dodecahedron (Decimals: Addition) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Rectangular Prism (Decimals: Subtraction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Trapezohedron (Decimals: Multiplication) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Triangular Prism (Decimals: Division by Whole Numbers) . . . . . . . . . . . . . . . . . . . . . . . 50
Pentagonal Prism (Decimals: Division by Decimals) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Octagonal Prism (Fractions: Renaming) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Rhombohedron (Fractions: Equivalent Decimals) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Cube (Fractions: Addition With Unlike Denominators) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Hexagonal Pyramid (Fractions: Multiplication) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Cuboctahedron (Fractions: Subtraction of Mixed Fractions with Unlike Denominators) . . . . 56
Cylinder (Fractions: Addition of Mixed Fractions with Unlike Denominators) . . . . . . . . . . . . 57
Cone (Fractions: Multiplication of Mixed Fractions) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Double Pentagonal Pyramid (Percents: 10% Discounts) . . . . . . . . . . . . . . . . . . . . . . . 59
Truncated Square Pyramid (Integers: Addition). . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Pentagonal Pyramid (Integers: Multiplication) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Icosahedron (Number Theory: Exponents)
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
Tree Topper (Percents: Discounts)
0.1
Introduction
that are suitable for framing. For these designs,
students need a ruler, a sharp pencil, and an eraser. Three of the activities require a compass.
Again, encourage students to solve all of the problems before they start drawing.
Designs to Construct (pages 45–61) are fun
and easy to make. Students complete math problems, then color the shapes based on the answers.
After coloring the
0.1
design, students simTrapezohedron
ply cut it out, then
fold and tape it
together. (Easy
assembly how-to’s
are provided on
pages 43 and 44.)
For these
designs, students
need crayons or colored pencils, scissors, and tape. The
finished products
are colorful three-dimensional designs that can be
hung on mobiles, used as holiday ornaments, or
given as gifts.
To help you use this book along with your
math curriculum, the chart on pages 6 and 7 organizes the activities by skill area and level. You can
see at a glance all of the activities that focus on a
specific math skill—for example, subtraction of
fractions with unlike denominators.
Many of the activity pages include a Taking it
Further problem. These problems are designed to
challenge students by allowing them to apply the
math operation used to complete the main design
activity. Answers to these problems can be found
on pages 62–64.
Don’t let students stop with these activities.
Invite them to create their own designs for their
classmates to color, create, and construct!
Name _______________________________________________________
DECIMALS
Multiplication
37.7
x 9.7
51.8
x 74.1
63.4
x 79.9
Figure 1
47.4
x 31.3
76.2
x 64.2
56.4
x 28.9
76.7
x 74.6
94
94
1,008
25
141
35
625
99
445
65
21
87
805
74
95
201
25
69
81
531
665
38
85
51
335
27
205
57
415
243
675
235
55
171
33
86
22
If the number
is divisible by
color the shape
5
2
green
orange
3
yellow
D a z z l i n g M a t h L i n e D e s i g n s Scholastic
ScholasticProfessional
ProfessionalBooks
Books
62
Finish the design by coloring the other shapes with the colors of your choice.
Taking It Further: Circle the numbers that are divisible by 9. (Hint: A number is divisible
by 9 if the sum of its digits are divisible by 9.)
324
5,364
4,592
147
6102
7055
10
Name _______________________________________________________
FRACTIONS
Equivalent Decimals and Percents
4%
62.5%
0.04
3
4
20%
0.625
0.20
1
2
80%
0.80
1
8
10%
0.10
3
5
45%
0.45
1
4
3
8
9
20
1
10
37.5%
Scholastic Professional Books
75%
Scholastic Professional Books
96.1
x 42
35.4
x 25.2
73.8
x 73.4
5.14
x 12.9
Figure 2
Solve the problems.
1. Then choose three colors that you like.
2. Write the name of one of the colors on each line below.
3. Color the design.
Finish the design by coloring
If the answer is between
color the shape
the other shapes with the
1 and 3,000
______________
colors of your choice.
3,001 and 6,000
6,001 and 9,000
______________
______________
Cut out the design and fold
it into a trapezohedron.
49
0.125
1
25
50%
85.9
x 61.7
22.5
x 12.9
0.60
5
8
12.5%
35.7
x 25.4
0.25
1
5
60%
67.1
x 69.4
0.375
4
5
25%
80.3
x 38.6
42.9
x 63
Dazzling Math Line Designs
N U M B E R T H E O RY
82
315
90.6
x 60.2
Flap A
Divisibility
711
88.3
1.53
Flap B
There are three different types of activities in this
book. Teaching tips for each type follow.
Designs to Color
(pages 8–24) are
Stardust
geometric shapes
with basic math
problems in them.
Students solve the
problems, then color
the shapes based on
the answers. The finished designs will
make a perfect addition to your bulletin
board. For these
designs, students
need crayons or colored pencils. Tell students to
solve all of the problems before they start coloring.
In the section
Designs to Create
Crochet
(pages 25–42) students also solve
math problems.
Then they draw
straight lines to connect the dots beside
the problems to the
dots beside their
answers. When all of
the dots have been
connected, beautiful
line designs emerge
Name _______________________________________________________
x
9.5
x 6.8
How to Use This Book
Dazzling Math Line Designs
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
M
athematics, like any other discipline,
requires practice to master the basic
skills. Sometimes this process can
become arduous and boring, especially for students in middle school grades. This book capitalizes on students’ natural love of art and design.
When they begin to see the connection between
art and math, their eyes light up and mathematics
becomes more than a row of tedious problems on
the page. I hope that by working with the designs
on these pages, your students will discover and
enjoy the creative side of mathematics.
0.50
0.75
Connect the dot beside each fraction to its equivalent decimal and percent.
Taking It Further: Each pie has a piece missing. Draw a line between the missing
percentage and its equivalent fractional piece.
20%
1
2
1
4
25%
40%
50%
1
5
2
5
29
5
0.1
Skills Matrix
The chart on these two pages organizes the activities in this book by skill area.
TITLE OF ACTIVITY
Number Theory: Prime and Composite Numbers
Optical Illusion
8
Number Theory: Divisibility
Holiday Glow
9
Number Theory: Divisibility
Stardust
10
Number Theory: Divisibility
Triangular Pyramid
46
Number Theory: Exponents
Icosahedron
45
Decimals: Addition
Letter Z
25
Decimals: Addition
Dodecahedron
47
Decimals: Subtraction
Pattern Block Star
11
Decimals: Subtraction
Rectangular Prism
48
Decimals: Multiplication
Patchwork Star
26
Decimals: Multiplication
Trapezohedron
49
Decimals: Division – Division by Whole Numbers
Triangular Prism
50
Decimals: Division – Division by Decimals
Whirling Octagon
12
Decimals: Division – Division by Decimals
Pentagonal Prism
51
Decimals: Equivalent Percents
Nine Circles
27
Fractions: Renaming
Four-Leaf Clover
30
Fractions: Renaming
Dream Catcher
31
Fractions: Renaming
Octagonal Prism
52
Fractions: Addition With Unlike Denominators
Rising Star
13
Fractions: Addition With Unlike Denominators
Cube
54
Fractions: Subtraction With Unlike Denominators
A Dozen Circles
14
Fractions: Subtraction With Unlike Denominators
Diamond
32
Fractions: Multiplication
Aztec Art
15
Fractions: Multiplication
Hexagonal Pyramid
55
Fractions: Division
Tree Ornament
16
6
PAGE
NUMBER
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
MATH SKILL
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
0.1
Fractions: Division
Emerging Triangle
33
Fractions: Equivalent Decimals and Percents
Linked Together
17
Fractions: Equivalent Decimals
Rhombohedron
53
Fractions: Equivalent Decimals
Puffy Cloud
28
Fractions: Equivalent Decimals and Percents
Crochet
29
Fractions: Addition of Mixed Fractions With Unlike Denominators
Octagonal Star
34
Fractions: Addition of Mixed Fractions With Unlike Denominators
String Art
35
Fractions: Addition of Mixed Fractions With Unlike Denominators
Cylinder
57
Fractions: Subtraction of Mixed Fractions With Unlike Denominators Stained Glass Window
18
Fractions: Subtraction of Mixed Fractions With Unlike Denominators Cuboctahedron
56
Fractions: Multiplication of Mixed Fractions
Starlit Sky
36
Fractions: Multiplication of Mixed Fractions
Cone
58
Fractions: Division of Mixed Fractions
Gears
19
Fractions: Division of Mixed Fractions
Birth of a Star
37
Percents: Discounts
Flaming Triangle
38
Percents: Discounts
Tree Topper
39
Percents: 10% Discounts
Zinnia
40
Percents: 10% Discounts
Double Pentagonal Pyramid
59
Integers: Addition
Starburst
20
Integers: Addition
Truncated Square Pyramid
60
Integers: Subtraction
Paper Folding
21
Integers: Multiplication
Basket Weaving
41
Integers: Multiplication
Pentagonal Pyramid
61
Integers: Division
Star Wings
22
Integers: Division
Explosion
42
Equations: Addition and Subtraction
Poinsettia
23
Equations: Multiplication and Division
Hexagonal Flowers
24
7
Name _______________________________________________________
N U M B E R T H E O RY
Prime and Composite Numbers
Optical Illusion
5
97
30
8
71
89
88
13
6
83
4
50
18
83
11
37
43
15
22
41
40
31
33
18
47
19
32
7
2
59
61
35
73
79
28
38
83
50
17
16
42
21
29
97
89
53
45
60
14
44
54
67
23
81
90
77
3
11
24
71
19
If the number in the shape is a prime number, color the shape blue.
If the number in the shape is a composite number, color the shape orange.
Finish the design by coloring the other shapes with the colors of your choice.
Taking It Further: Shade the prime numbers. Then read the message.
8
2
4
5
6
71
83
37
55
23
53
61
97
10
7
30
89
20
22
25
67
90
99
11
79
59
33
43
19
12
60
2
3
41
15
17
27
28
3
48
46
62
66
88
47
24
31
25
26
13
73
29
50
5
19
11
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
12
34
9
Name _______________________________________________________
N U M B E R T H E O RY
Divisibility
Holiday Glow
46 32
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
82
38
21 141
98
57
28
63
69
93
77
85
124
531
35
209
54
52
238
189
143
205
861
64
25
717
51
86
121
771 603
81
39
16
8
82
14 4
If the number
is divisible by
color the shape
11
5
3
2
yellow
red
orange
blue
Finish the design by coloring the other shapes with the colors of your choice.
Taking It Further: Circle the numbers that are divisible by 3.
175
654
1,701
2,519
825
9
Name _______________________________________________________
N U M B E R T H E O RY
Divisibility
Stardust
82
94
94
711
25
315
35
141
625
99
445
65
21
87
95
805
74
201
25
69
81
531
38
85
665
51
335
27
205
57
415
243
675
55
235
171
33
86
22
62
If the number
is divisible by
color the shape
5
2
3
green
orange
yellow
Finish the design by coloring the other shapes with the colors of your choice.
Taking It Further: Circle the numbers that are divisible by 9. (Hint: A number is divisible
by 9 if the sum of its digits is divisible by 9.)
324
10
5,364
4,592
147
6102
7055
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
1,008
Name _______________________________________________________
DECIMALS
Subtraction
Pattern Block Star
9.213
– 5.912
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
75.42
– 15.88
156.13
– 99.09
66.39
– 56.91
0.1
8.903
– 0.691
152.0
– 21.2
102.86
– 89.09
55.33
– 19.09
89.10
– 79.44
165.76
– 111.19
13.91
– 9.37
103.5
– 99.2
672.9
– 301.9
61.18
– 36.99
71.71
– 15.63
397.9
– 143.2
36.21
– 29.99
547.3
– 541.2
916.68
– 906.93
70.14
– 1.28
56.80
– 41.92
703.3
– 591.2
63.33
– 11.02
43.19
– 39.04
103.39
– 96.31
97.09
– 35.12
90.33
– 0.12
2.033
– 0.912
Solve the problems.
If the answer
is between
color the shape
0 and 10
11 and 99
100 and 999
red
blue
yellow
Taking It Further:
Fill in the missing numbers.
8.8 7
– 0.9 0
0
0
2.9 1
11
Name _______________________________________________________
Whirling
Octagons
DECIMALS
0.1
Division by Decimals
2.5 4.75
1.2 2.04
3.1 25.42
3.7 38.48
7.2 31.68
6.2 23.56
1.6 14.56
6.1 86.62
5.1 91.29
4.4 125.4
3.9 4.29
1.1 2.31
4.1 212.79
9.3 78.12
4.1 13.53
1.3 93.08
5.8 182.12
3.7 173.16
2.8 169.4
Solve the problems.
Finish the design by coloring the other
shapes with the colors of your choice.
If the number in the
tenths place is between
color the shape
0 and 4
5 and 9
gray
pink
12
Taking It Further: Matt Neibler was one of
5,000 people to ride in a 100-mile bike
ride called the Hilly Hundred. Matt was
different from the other riders, though. He
was only 11 years old. In preparation for
the ride, he rode his bike 787.5 miles
over a period of 15 weeks. How many
miles a week did he average?
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
8.3 13.28
Name _______________________________________________________
Addition With Unlike Denominators
Rising Star
+
1
3
5
15
+
+
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
5
21
1
7
+
+
+
+
+
1
2
3
4
7
8
2
3
+
+
1
12
2
5
9
10
1
4
4
9
6
7
2
6
2
12
+
+
3
5
2
10
1
4
2
8
1
8
1
4
+
+
FRACTIONS
4
20
1
4
+
1
8
1
9
1
15
3
21
4
9
1
3
+
1
6
15
24
Solve the problems. Rename the answers in lowest terms.
If the answer is
greater than 0 and less than or equal to
greater than
1
2
color the shape
1
____
2
and less than or equal to 1
greater than 1
orange
red
yellow
Finish the design by coloring the other shapes with the colors of your choice.
Taking It Further: Fill in the missing numbers in this sequence.
2
19 ,
27
76 ,
46
76 ,
65
76 , ____________, ____________, ____________
13
Name _______________________________________________________
Subtraction With Unlike Denominators
30
35
–
–
23
27
–
20
30
15
16
–
11
12
– 18
18
19
30
38
–
5
12
9
10
–
13
16
–
4
8
– 14
–
9
33
2
11
–
14
15
2
3
– 15
7
8
20
64
7
– 24
8
9
1
3
– 25
6
7
2
28
– 26
17
24
1
8
–
2
– 15
11
13
–
29
30
11
12
1
4
– 23
7
8
1
2
– 23
10
15
1
3
–
8
9
–
– 25
30
35
1
5
– 14
42
48
5
8
2
– 14
3
4
4
8
–
10
32
–
6
7
6
– 16
30
34
5
17
– 27
8
9
1
3
18
30
32
34
– 38
5
6
9
18
– 18
Solve the problems.
If the answer is
color the shape
1
000
2 or less
red
greater than
1
000
2
blue
Finish the design by coloring
the other shapes with the colors
of your choice.
14
Taking It Further: Find the missing fractions.
a. 56
– ___ =
1
3
b. 78
– ___ =
1
8
c. 23
5
– ___ = 12
d. 47
5
– ___ = 21
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
A Dozen
Circles
–
FRACTIONS
Name _______________________________________________________
Multiplication
Aztec Art
9
5
8
15
5
x 49
x
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
4
3
3
4
40
11
FRACTIONS
x
15
7
x 30
3
5
4
3
5
x
16
15
4
2
12
5
x
9
4
12
6
x
x 20
4
9
8
2
12
4
9
2
x 18
8
7
x 14
10
5
7
x 49
x 68
4
9
5
x 10
3
4
4
11
x 12
16
6
2
x 87
x
3
8
x
4
5
x
x
14
8
Use common factors
to simplify each equation.
Then find the product.
5
9
3
15
15
2
25
16
x
15
2
5
4
9
12
12
9
x 64
7
If the answer is
color the shape
greater than 0 and less than 1
greater than 1 and less than 4
greater than 4
black
orange
brown
3
7
1
8
6
7
x 10
3
x 22
16
x 21
4
x 38
x 18
4
Finish the design by coloring the other shapes with the colors of your choice.
7
Taking It Further: Ian has 8 of a box of salt. He will use
How much of the box of salt will he use?
1
4
of that to make a salt map.
15
Name _______________________________________________________
FRACTIONS
Division
Tree Ornament
÷ 38
1
5
÷ 2
7
7
10
4÷ 8
1
8
2
9
÷ 27
1
9
÷ 27
8
9
÷ 32
7
9
÷ 87
1
÷ 17
3
5
2÷ 9
5
6
÷ 32
2
3
÷ 45
5
6
2
3
÷ 6
7
8
6
11
÷ 67
3
4
4
5
1
7
÷ 5
1
2
÷ 2
2
÷ 27
÷ 3
÷ 17
4
5
÷ 13
7÷ 3
÷ 23
6
7
÷ 77
÷ 18
÷ 45
Solve the problems.
If the answer is
greater than 0 and less than
1
color the shape
1
00
2
red
greater than 000
2 and less than 1
green
greater than 1
yellow
Finish the design by
coloring the other
shapes with the colors
of your choice.
Taking It Further: Fill in the next three numbers in this sequence.
1
2,
16
4
2,
16
2,
64
2, ____________, ____________, ____________
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
1
6
Name _______________________________________________________
Linked Together
FRACTIONS
Equivalent Decimals and Percents
20%
5
40
12.5%
25%
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
0.60
60%
0.25
50%
0.5
4
32
0.125
0.50
3
24
9
72
8
32
6
10
5
10
2
16
0.6
6
48
2
8
20
100
If the fraction,
percent, or decimal
is equivalent to
color the shape
1
4
pink
1
8
1
2
green
yellow
1
5
blue
3
5
purple
Finish the design by coloring the other shapes
with the colors of your choice.
Taking It Further: Circle the numbers that are
equivalent to 15 .
0.2
4
5
3
4
0.20
2
10
0.21
5
25
1.25
17
Name _______________________________________________________
FRACTIONS
Subtraction of Mixed Fractions With Unlike Denominators
Stained Glass Window
–
2
27 5
– 21 14
1
7
16 6
5
– 1 12
1
2
–
2
8 7
8
5 21
3
37 9
– 29 23
30 7
5
– 26 14
1
51 5
– 43 58
2
19 15
– 9 23
– 9 12
4
11 8
5
– 10 16
3
7
4
13 8
4
35 14
– 23 56
30 10
– 26 45
12 8
– 11 34
1
33 9
5
– 19 36
45 4
– 38 78
3
21 3
– 15 26
20 15
– 8 56
3
52 11
– 44 57
7
59 33
9
– 49 11
3
18 12
– 16 58
Solve the problems. Rename the answers in lowest terms.
If the number is between
0 and 5
6 and 10
11 and 15
color the shape
black
gray
red
Finish the design by coloring the other shapes
with the colors of your choice.
18
Taking It Further: Fran needs 5 more
hours of physical activity to complete
her Presidential Sports Award. If she
3
swims for 1 4 hours, how many
more hours does she need?
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
2
2 3
5
1 6
Name _______________________________________________________
FRACTIONS
Division of Mixed Fractions
Gears
5
5
12
1
4
÷ 3
3
4
2
5
÷ 2
÷
1
2
2
3
2
4
7
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
6
7
1
3
÷ 2
5
6
2
7
3
3
4
÷
1
4
9
2
÷ 1
4
1
4
6
7
÷
2
5
1
4
÷ 1
2
3
2
5
÷ 3
6
3
7
÷
1
3
÷ 3
5
12
÷ 1
5
6
3
4
÷ 1
1
2
2
1
4
÷ 1
1
7
6 ÷ 2
1
6
2
3
4
1
2
2
÷
1
2
7
3
2
1
11
1
8
÷ 6
1
4
1
1
5
11
1
2
÷ 2
3
÷ 1
3 ÷ 1
1
3
4 ÷ 1
5
8
3
8
5
8
÷ 2
7
8
1
÷ 1
÷ 2
3
1
1
7
1
6
÷ 4
2
3
6
9 ÷ 4
1
9
÷ 5
2
3
2
6
1
1
2
÷ 1
1
4
Solve the problems.
Rename the answers in lowest terms.
If the answer is
color the shape
between 0 and 1
greater than 1 and less than 2
2 or greater
yellow
gray
purple
Finish the design by coloring the other shapes
with the colors of your choice.
1
Taking It Further: Lisa has 10 4
yards of fabric for banners that
she is making for the craft fair.
If she needs 14 yard of fabric
for each banner, how many
banners can she make?
19
Name _______________________________________________________
INTEGERS
Addition
51 + - 12
44 + - 29
15 + - 16
- 15 + - 26
- 7 + 33
- 11 + - 21
29 + - 6
35 + - 15
- 52 + 29
17 + - 28
- 45 + 16
- 15 + - 2
- 25 + 16
41 + - 39
15 + 3
- 39 + 11
69 + - 26
-1 + -3
30 + - 55
- 16 + 27
- 13 + 55
Solve the problems.
If the number is between
-50 and -25
- 24 and -5
-4 and 24
25 and 50
color the shape
yellow
orange
red
blue
Finish the design by coloring the other shapes with the colors of your choice.
Taking It Further: In the evening, the outside temperature was 37°F. Eight hours later the
temperature was -5°F. What was the temperature change?
20
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
Starburst
Name _______________________________________________________
INTEGERS
Subtraction
Paper Folding
10 – - 11
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
- 8 – - 34
-5 – 3
-4 – 7
-5 – 8
13 – - 2
-2 – -2
- 7 – - 22
- 1 – - 13
- 9 – - 20
-1 – 1
18 – - 4
- 15 – 7
- 2 – 10
-2 – 4
- 1 – - 12
- 3 – - 13
Solve the problems.
If the number is between
-30 and -10
-9 and 9
color the shape
purple
pink
Finish the design by coloring the other shapes with the colors of your choice.
Taking It Further: Place the number 13 or -13 on the lines below.
a. 18 – 31 = ______
- b. 2 – -11 =
______
c. - 9 – 4 = ______
d. -19 – -6 = ______
21
Name _______________________________________________________
INTEGERS
Division
Star Wings
-85
5
-45
-3-
-14
2
-18
-6
-60 ÷ 4
38
-212
-4-
-8
2
76
-4-
60
-2-
54
-3-
81
-9-
- 24 ÷ - 6
45 ÷ - 9
51
-3-
Solve the problems.
If the number is between
-40 and -15
-14 and 20
color the shape
green
red
Finish the design by coloring the other shapes with the colors of your choice.
Taking It Further: Place the number 7 or -7 on the lines below.
a.
22
49
-7
=
______
b.
-56
-8
=
______
c.
-14
2
=
______
d.
-21
3
=
______
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
-64 ÷ 4
Name _______________________________________________________
E Q U AT I O N S
Addition and Subtraction
Poinsettia
22 + n = 113
n – 6 = 34
n – 17 = 171
46 + n = 140
175 – n = 65
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
7 + n = 26
27 + n = 50
n + 150 = 268
318 – n = 143
n + 31 = 188
182 – n = 38
n + 9 = 88
n + 33 = 98
233 – n = 96
n – 120 =41
n – 52 = 104
n – 87 = 26
67 – n = 45
n – 41 = 9
157 – n = 20
n – 18 = 75
n – 36 = 152
n + 29 = 38
n + 16 = 100
Solve the problems.
If the answer is between
color the shape
1 and 50
51 and 100
101 and 150
151 and 200
red
green
pink
yellow
Taking It Further: Amelia had $0.45 when she left for school. She found some money on
the sidewalk and now she has $3.20. How much money did she find?
23
Name _______________________________________________________
Multiplication and Division
Hexagonal
Flowers
= 9
n
7
6n = 288
3n = 243
n
7
5n = 350
n
9
3n = 243
8n = 536
= 3
n
7
4n = 224
n
7
= 8
n
8
= 13
= 8
n
= 3
11
= 6
5n = 275
n
4
7n = 287
9n = 333
= 8
Solve the problems.
5n = 350
4n = 212
10n = 60
If the answer is between
color the shape
0 and 50
51 and 100
orange
yellow
Finish the design by coloring the other
shapes with the colors of your choice.
24
= 7
Taking It Further: What number am I?
When I’m divided by 5, I equal 15.
When I’m multiplied by 3, I equal 225.
What number am I?
______________
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
n
7
6n = 36
12n = 144
2n = 102
E Q U AT I O N S
Name _______________________________________________________
6.8
+ 3.1
0.1
Addition
Letter Z
2.7
+ 1.3
DECIMALS
1.5
+ 3.7
21.9
+ 1.9
68.6
+ 2.9
0.75
+ 1.83
9.82
+ 0.46
5.08
+ 3.12
4.0
9.9
Line A
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
5.2
71.5
23.8
2.58
8.20
10.28
65.6
6.43
7.5
4.37
67.5
33.95
12.52
8.08
+ 0.12
59.3
+ 6.3
2.09
+ 4.34
4.55
+ 2.95
1.98
+ 2.39
63.8
+ 3.7
32.16
+ 1.79
12.38
+ 0.14
Solve the problems.
Then connect the dot above or below each problem to the dot beside its answer on
Line A. The first line has been drawn for you.
Taking It Further: Fill in the missing numbers.
9. 4
+ 0.3 0
0
0
0
10.61
25
DECIMALS
Multiplication
Patchwork Star
15.9 x 2.5
0.1
1.18 x 4.9
2.78 x 9.1
5.75 x 4.7
8.93 x 8.8
12.7 x 6.1
12.1 x 3.1
4.19 x 1.4
Solve the problems. Then connect the dots beside the answers in the order given below.
5.782, 5.866, 25.298, 27.025, 37.51, 39.75, 77.47, 78.584, 5.782.
Taking It Further: Piedmont Park rents inline skates for $8.50 an hour. How much does it
cost to rent inline skates at this rate for 3 12 hours?
26
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
Name _______________________________________________________
Name _______________________________________________________
DECIMALS
Equivalent Percents
Nine Circles
0.1
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
0.1
0.45
0.85
0.15
0.75
0.25
0.51
0.49
0.39
0.9
0.33
0.09
0.05
You will need a compass to complete this design. Set your compass points as shown
below. Then write each decimal as a percent. If the percent is between 1% and 50%,
place your compass point on the dot beside that number and draw a circle.
(radius of the circle)
Put your compass here.
Place your pencil point here.
Taking It Further: John had $1.00. He gave 5% of his money to his sister and 15%
of his money to his brother. How much money did he have left?
27
Name _______________________________________________________
FRACTIONS
Equivalent Decimals
Puffy Cloud
2
5
2
3
2
8
1
8
3
8
7
8
1
4
1
3
17
25
9
10
1
7
4
10
4
15
1
5
2
7
3
4
3
16
You will need a compass to complete this design. Set your compass points as shown
below. Then write each fraction as a decimal. Extend the decimal to the thousandths
place. If the answer is between 0.01 and 0.50, place your compass point on the dot
beside that number and draw a circle. Watch a cloud form!
(radius of the circle)
Put your compass here.
Place your pencil point here.
Taking It Further: John was up at bat 50 times and had a total of 15 hits.
What is his batting average?
28
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
3
5
Name _______________________________________________________
Equivalent Decimals and Percents
Crochet
4%
62.5%
0.04
3
4
20%
0.625
0.20
1
2
80%
0.80
1
8
10%
0.10
3
5
45%
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
FRACTIONS
0.45
1
4
3
8
9
20
1
10
37.5%
0.375
4
5
25%
0.25
1
5
60%
0.60
5
8
12.5%
0.125
1
25
50%
75%
0.50
0.75
Connect the dot beside each fraction to its equivalent decimal and percent.
Taking It Further: Each pie has a piece missing. Draw a line between the missing
percentage and its equivalent fractional piece.
20%
1
2
1
4
25%
40%
50%
1
5
2
5
29
Name _______________________________________________________
FRACTIONS
Renaming
6
9
8
64
18
81
17
34
12
15
8
10
7
14
10
45
4
32
12
18
45
72
2
3
15
20
21
27
1
8
16
30
8
56
2
9
36
42
20
50
1
2
8
22
9
27
4
5
10
50
8
24
5
8
7
9
1
7
2
5
1
3
1
9
1
5
4
11
6
7
8
15
3
4
3
15
12
30
2
7
8
22
4
28
9
10
12
14
14
18
7
8
24
45
10
16
1
4
27
36
25
100
21
24
36
40
4
14
9
81
2
18
14
49
18
20
14
16
20
80
Connect the dot beside each fraction outside the square
to the dot beside its equivalent fraction inside the square.
Taking It Further: Complete the squares
so that each box adds up to 2.
a.
(Hint: Rename the fractions first.)
2
16
30
b.
3
4
6
8
10
12
2
8
4
24
c.
15
16
8
16
2
32
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
Four-Leaf Clover
Name _______________________________________________________
FRACTIONS
Renaming
Dream Catcher
17
34
8
11
12
48
24
36
7
9
15
20
26
28
3
5
21
35
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
65
70
12
16
105
135
56
77
12
18
75
150
1
4
2
8
47
94
2
3
16
22
49
63
3
4
13
14
30
50
Rename each fraction in lowest terms. Then connect the dot beside each fraction to the
dots beside its equivalent fractions. (Hint: Each fraction has two other equivalent
fractions.)
Taking It Further: Complete the squares with the following fractions so that each box
contains equivalent fractions.
5
10 ,
84
96 ,
7
28 ,
9
36 ,
12
48 ,
17
34
49
56 ,
, and
9
18 ,
14
16
1
2
1
4
7
8
.
31
Name _______________________________________________________
FRACTIONS
Subtraction With Unlike Denominators
5
6
8
15
– 23
5
6
2
9
9
14
– 45
7
8
– 14
27
56
5
6
7
18
– 13
4
4 – 9
3
10
8
17
9
16
13
15
2
9 – 11
– 13
1
6
8
9
– 23
6
7
1
30
3
– 14
12
14
5
8
– 38
8
9
3
6
– 12
Solve the problems.
Rename the answers
in lowest terms.
Then connect the dot
beside each problem to
the dot beside its answer.
5
5
5
3 9
7
– 10
15
16
31
102
– 38
9
8 11
Taking It Further: Fill in the missing fractions.
a.
9
10
–
b.
c.
–
17
30
32
– 16
1
2
5
16
3
4
–
3
8
d.
11
12
–
1
6
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
Diamond
Name _______________________________________________________
FRACTIONS
Division
Emerging Triangle
5
7
4
2 7
1
5
÷ 4
9
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
2
9
1
8
÷ 4
5
6
7
3
8
÷ 9
10
2
5
1
1 5
÷ 2
3
1
10
1
3
÷ 3
11
3
10
9
25
÷ 5
6
8
11
11
30
3
5
20
21
5
32
9
20
1
7
÷ 1
5
6
7
1
9
÷ 1
3
÷ 1
2
1
4
÷ 2
3
÷ 24
11
1
5
÷ 1
6
Solve the problems. Rename the answers as mixed fractions in lowest terms.
Then connect the dot beside each problem to the dot beside its answer.
Taking It Further: Fill in the missing fractions.
1
3
a. 7 ÷ ___ = 14
1
b. 2 ÷ ___ = 4
4
16
c. 5 ÷ ___ = 5
5
45
d. 6 ÷ ___ = 6
1
5
e. 3 ÷ ___ = 6
f.
5
8
÷ ___ = 10
8
33
Name _______________________________________________________
FRACTIONS
Addition of Mixed Fractions With Unlike Denominators
Octagonal Star
25
1
2
1 9 + 2 3
14 36
1
7
12 3 + 9 15
19
35 20
3
6 5
+ 6
11
10 15
2
7
1
7 6
11
21 18
+ 2 23
2
31
12 35
2 6
+ 8 25
4
7
5 9
3 9
3
+ 9 12
3
1
21 4 + 14 5
4
21 5
Solve the problems. Rename the answers in lowest terms.
Then connect the dot beside each problem to the dot beside its answer.
Taking It Further: Fill in the missing mixed fractions.
a.
1 13
c.
+ 2 4
7
+
5
34
b.
5
7
3 12
+
d.
5
4 16
+
5
5
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
1
1
8 9 + 13 2
5
9 6
Name _______________________________________________________
FRACTIONS
Addition of Mixed Fractions With Unlike Denominators
String Art
14
6
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
9
4
4
1
6
1
9
+ 13
+4
21
1
4
+ 7
1
10
+
1
7
+ 9
4
8
1
5
8
+ 9
1
15
8
5
12
1
2
17
4
9
1
12
16
1
3
1
3
3
3
5
3
12
23
5
8
19
9
14
17
19
21
16
1
8
+ 3
+ 7
1
2
3
9
10
14
8
15
16
13
3
4
6
7
24
14
1
8
+ 7
1
2
2
1
3
+ 17
1
2
7
1
5
+ 3
2
5
9
1
4
+ 7
1
3
4
15
2
12
4
7
Solve the problems. Rename the answers in lowest terms.
Then connect the dot beside each problem to the dot beside its answer.
1
3
Taking It Further: Paul rode his bike 10 4 miles on Monday, 5 4 miles on Tuesday,
9 18 miles on Wednesday, 5 12 miles on Thursday, and 6 34 miles on Friday.
How many miles did he ride in all?
35
Name _______________________________________________________
FRACTIONS
Multiplication of Mixed Fractions
Starlit Sky
1
1
1 2 x 3 4
1
2
2 5 x 1 5
1
1
3 8 x 2 4
1
1
3 3 x 2 9
3
1
2
1
4
1 2 x 3 7
x 2 45
1
1
2 8 x 3 2
1
3
5 4 x 3 8
Solve the problems. Rename the answers in lowest terms. Then connect the dots beside
the answers in the order given below.
4
7
8
, 7
7
16
, 3
2
25
, 5
5
14
, 7
1
27
, 7
1
32 ,
Taking It Further: Adam gets paid 4 12
How much will he earn if he works 3
36
9
1
2
4
5
, 5
1
15
, 17
23
32
, and 4
7
8.
dollars an hour for working at Burger Land.
hours?
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
1
4
1 3 x 3 5
Name _______________________________________________________
FRACTIONS
Division of Mixed Fractions
Birth of a Star
2
1
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
2
7
1
1
14
1
4
5
12
11
28
1
1
3
3
12
÷
2
12
3
7
÷
6
11
3
7
1
8
1
÷ 2
3
8
1
3
1
3
2
1
5
1
6
÷ 1
4
1
2
÷ 1
2
3
4
÷ 1
2
11
1
2
1
4
1
1
9
2
1
2
÷ 2
1
4
2
5
14
3
1
7
÷ 1
1
3
9 ÷ 1
3
2
1
5
2
4
27
56
1
3
6
2
1
1
2
2
1
5
1
8
÷ 1
1
6
3
1
9
÷ 2
1
3
7
1
4
÷ 3
1
8
1
2
÷ 1
1
4
÷ 2
1
6
÷ 2
÷ 1
1
4
5
6
3
4
2
3
4
8
Solve the problems. Rename the answers as mixed fractions in lowest terms.
Then connect the dot beside each problem with the dot beside its answer.
Taking It Further: The telethon needs students to answer phones for 4 12 hours.
1
If each student can work only 2 hour, how many students are needed?
37
Name _______________________________________________________
PERCENTS
Discounts
Flaming Triangle
40% of $820.00
20% of $1,640.00
20% of $72.00
10% of $7.00
1% of $25.00
15% of $185.00
10% of $53.00
10% of $22.50
5% of $45.00
20% of $26.50
20% of $138.75
25% of $1.00
25% of $88.00
50% of $1.40
30% of $48.00
10% of
$3,280.00
50% of
$656.00
$328.00 $14.40 $22.00 $27.75
$2.25
$5.30
$0.25
$0.70
$328.00
Compute the discount for each dollar amount. Then connect the dot beside each
problem to the dot beside its answer. The first line has been drawn for you.
Taking It Further: Below are the prices for three different CDs and their discounts.
Which CD is the least expensive?
a. $15.99 with 10% off
38
b. $18.99 with 20% off
c. $20.99 with 30% off
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
20% of $110.00
Name _______________________________________________________
PERCENTS
Discounts
Tree Topper
20% of $15.00
4% of $8.00
10% of $8.00
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
25% of $84.00
30% of $45.00
20% of
$152.00
40% of
$76.00
8% of $168.75
35% of $60.00
50% of $1.60
10% of $3.20
25% of $12.00
Compute the discount for each dollar amount. Then connect the dot beside each
problem to the dot beside the problem that has the same answer.
Taking It Further: Below are the prices for three different dartboards with their discounts.
Which dartboard is the least expensive?
a. $25.99 with 15% off
b. $22.50 with 25% off
c. $17.99 with 10% off
39
Name _______________________________________________________
PERCENTS
10% Discounts
Zinnia
$95.00
$108.90
$199.90
$13.90
$43.70
$7438.10
$201.30
$55.00
$1.70
$89.40
You will need a compass to complete this design. Set your compass points as shown
below. Then find 10% of each dollar amount. If 10% of each dollar amount is less than
$10.00, place your compass point on the dot beside that number and draw a circle.
Watch a flower bloom!
(radius of the circle)
Put your compass here.
Place your pencil point here.
Taking It Further: Tamika bought items that cost $1.75, $6.99, $4.19, and $5.27.
She used her 10% discount coupon. By using her coupon, how much money did she
save on the total purchase price?
40
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
$7.90
$63.50
Name _______________________________________________________
INTEGERS
Multiplication
Basket Weaving
-8 • 2
-8 • -8
-14 • 4
-12 • -4
12 • -3
-24 • -1
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
-4 • -3
-6 • -2
-12 • -2
-12 • 3
-8 • -6
-56 • 1
-2 • -32
-4 • 4
2 • -8
-8 • -8
-9 • -4
-6 • -8
-28 • -2
-8 • -3
-3 • -4
-1 • -12
-4 • -6
8 • -7
-1 • -48
-1 • -36
-32 • -2
1 • -16
Solve the problems. Then connect the dot beside each problem to the
dot beside the other problem that has the same answer.
Taking It Further: Fill in the missing numbers.
-5
a.
10
b.
x
x
20
-20
c.
x
20
4
d.
x
20
– 20
41
Name _______________________________________________________
INTEGERS
Division
Explosion
-44
144 ÷ -12
4
-36
-6
63 ÷ 9
24 ÷ -12
64 ÷ -4
-40 ÷ 5
-81 ÷ -9
-91 ÷ -7
42 ÷ -3
15 ÷ -5
-34 ÷ -17
54 ÷ 3
-16
4
85 ÷ -5
Solve the problems. Then connect the dots beside each answer in the following order.
-12, 18, 7, 13, 9, -16, 2, 6, -17, -11, -3, - 2, - 8, -14, 15, -4, and - 12.
Taking It Further: Place the number 4 or -4 on the lines below.
a. 24 ÷ 6 = _______ -
42
b. -24 ÷ 6 = _______
c. -24 ÷ -6 = _______
d. 24 ÷ -6 = _______
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
-75 ÷ -5
0.1
How to Assemble the 3-D Constructions
The activity pages that follow (pages 45–61) give students the opportunity to color designs based on
answers to mathematical problems and then construct them into three-dimensional shapes. While most
of the designs are self-explanatory, these two pages give complete construction directions. If you like,
enlarge the patterns on a photocopier before having students color and construct them.
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
Icosahedron (page 45)
Cut out the pattern along the outer
solid lines and fold along the
dotted lines. Tape each
unlettered flap to the
underside of the triangle
shape beside it. Tape flap A to
the underside of side A. Do the
same thing with the rest of the
lettered flaps.
Trapezohedron (page 49)
icosahedron
Cut out the pattern along the outer
solid lines and fold along the dotted
lines. Tape flap A to the underside
of figure 1. Tape flap B to the
underside of figure 2. Then carefully
tape the other flaps on figure 2 to the
underside of figure 1.
trapezohedron
Triangular Pyramid (page 46)
Cut out the pattern along the outer
solid lines and fold along the
dotted lines. Tape each flap to the
underside of a triangle shape.
triangular pyramid
Triangular Prism (page 50)
Cut out the pattern along the
outer solid lines and fold along
the dotted lines. Tape each
flap to the underside of a
rectangle shape.
triangular prism
Dodecahedron (page 47)
Cut out the pattern along the
outer solid lines and fold
along the dotted lines. Tape
each lettered flap in
alphabetical order to the
underside of the pentagon
next to it. Tape the numbered
flaps on figure 2 to the
underside of figure 1.
Pentagonal Prism (page 51)
Cut out the pattern along the outer
solid lines and fold along the dotted
lines. Tape each flap to the underside
of a pentagon or rectangle shape.
dodecahedron
Rectangular Prism (page 48)
Cut out the pattern
along the outer solid
lines and fold along
the dotted lines. Tape
each flap to the
underside of either
a rectangle or a
square shape.
rectangular prism
pentagonal prism
Octagonal Prism (page 52)
Cut out the pattern along the outer
solid lines and fold along the dotted
lines. Tape each flap to the
underside of an octagon or
rectangle shape.
octagonal prism
43
0.1
How to Assemble the 3-D Constructions
Rhombohedron (page 53)
Cut out the pattern along the
outer solid lines and fold
along the dotted lines. Tape
each flap to the underside
of a rhombus shape.
Cone (page 58)
Cut out the pattern along the outer
solid lines and fold along the dotted
lines. Tape each flap to the inside of
the cone.
cone
rhombohedron
Cube (page 54)
Cut out the pattern along the
outer solid lines and fold along
the dotted lines. Tape each flap
to the underside of a square
shape.
Cut out the pattern along the outer
solid lines and fold along the
dotted lines. Tape flap A to the
underside of side A. Do the same
thing with the rest of the flaps.
cube
Hexagonal Pyramid (page 55)
Cut out the pattern along the outer
solid lines and fold along the dotted
lines. Tape flap A to the underside
of side A. Do the same thing with
the rest of the flaps.
hexagonal pyramid
Cuboctahedron (page 56)
Cut out the pattern along the outer
solid lines and fold along the
dotted lines. Tape flap A to
the underside of side A. Do
the same thing with the
rest of the flaps.
cuboctahedron
Cylinder (page 57)
Cut out the pattern along the
outer solid lines and fold along
the dotted lines. Tape each flap
to the underside of the cylinder.
cylinder
44
double pentagonal pyramid
Truncated Square Pyramid (page 60)
Cut out the pattern along the outer solid lines
and fold along the dotted lines. Tape each
flap to the underside of the large square
shape. Fold down the small square and tape it
in place.
truncated square pyramid
Pentagonal Pyramid (page 61)
Cut out the pattern along the outer
solid lines and fold along the dotted
lines. Tape flap A to the underside
of side A. Do the same thing with
the rest of the flaps.
pentagonal pyramid
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
Double Pentagonal Pyramid (page 59)
Name _______________________________________________________
N U M B E R T H E O RY
Exponents
Icosahedron
A
B
3
2
2
12
3
9
6
3
3
C
6
2
20
3
9
8
2
4
7
2
3
4
5
2
12
3
7
2
4
x5
2
2
21
22
3
2
4
8
2
3
2
9
x2
2
12
3
6
1
7
3x
x3
2
19
3
5
2
x5
6
2
2
9
2
2
13
x2
2
19
x
2
2
16
2
2
2
1
x1
2
15
2
23
2
3
11
2
17
x3
2
7
31
x8
2
1
6
3x
A
C
Find the products.
between 0 and 200
between 201 and 400
between 401 and 600
601 or greater
3
5
3x
2
3
2
3
If the answer is
5
B
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
3
color the shape
red
gray
black
yellow
Cut out the design
and fold it into
an icosahedron.
45
Name _______________________________________________________
N U M B E R T H E O RY
Divisibility
Triangular
Pyramid
28
231
884
125
734
662
118
68
88
92
185
603
46
715
333
598
605
If the number is divisible by
2
3
5
81
584
752
145
423
436
205
273
135
865
681
404
715
55
819
668
295
441
596
325
902
115
color the shape
green
pink
yellow
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
225
Cut out the design
and fold it into a
triangular pyramid.
985
Name _______________________________________________________
DECIMALS
Dodecahedron
8
31. .9
1
2
+
C
0.1
Addition
Figure 1
D
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
57
27. .69
4
+2
7
42. .9
1
+1
27
0.5 09
.9
+ 2
B
37
48. .96
+ 6
Figure 2
E
27
29. .29
1
+3
A
8
7
3.7 8
3
.
+ 1
Solve the problems.
If the answer
is between
color
the shape
1 and 49
purple
50 and 100
yellow
Finish the design by
coloring the other
shapes with the
colors of your choice.
Cut out the design
and fold it into
a dodecahedron.
J
9
16. .8
8
+2
7
F
1
I
5
33. .7
6
+1
7
29. .3
9
+1
8
9.2 6
3
.
+ 8
2
G
8
43. .9
4
+
H
6
5
3
4
47
Name _______________________________________________________
DECIMALS
Rectangular Prism
Subtraction
0.1
605.4
– 113.2
489.8
– 312.3
781.5
– 133.3
3.41
– 1.96
918.7
– 219.9
811.0
– 317.5
659.09
– 112.11
–
698.5
– 279.0
Solve the problems.
If the answer in the
ones place is
color the shape
even
odd
black
purple
Finish the design by coloring the other
shapes with the colors of your choice.
48
Cut out the design
and fold it into a
rectangular prism.
969.2
69.7
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
905.0
– 408.8
Name _______________________________________________________
DECIMALS
Multiplication
Trapezohedron
37.7
x 9.7
51.8
x 74.1
63.4
x 79.9
Figure 1
47.4
x 31.3
76.2
x 64.2
56.4
x 28.9
76.7
x 74.6
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
0.1
88.3
x 1.53
90.6
x 60.2
9.5
x 6.8
Flap A
Flap B
x
80.3
x 38.6
42.9
63
67.1
x 69.4
35.7
x 25.4
85.9
x 61.7
22.5
x 12.9
x
96.1
42
35.4
x 25.2
73.8
x 73.4
5.14
x 12.9
Figure 2
1.
2.
3.
4.
Solve the problems.
Choose three colors that you like.
Write the name of one of the colors on each line below.
Color the design.
Finish the design by coloring
If the answer is between
color the shape
the other shapes with the
1 and 3,000
______________
colors of your choice.
3,001 and 6,000
6,001 and 9,000
______________
______________
Cut out the design and fold
it into a trapezohedron.
49
Name _______________________________________________________
Triangular Prism
553.8 ÷ 71
153.6 ÷ 32
Division by Whole Numbers
1002.3 ÷ 13
188.1 ÷ 19
124.6 ÷ 14
562.1 ÷ 11
600.6 ÷ 11
743.4 ÷ 14
1173.6 ÷ 18
378.3 ÷ 13
907.8 ÷ 51
695.2 ÷ 88
939.2 ÷ 16
1101.6 ÷ 18
1033.5 ÷ 15
664.3 ÷ 13
573.3 ÷ 21
183.6 ÷ 12
849.2 ÷ 11
192.6 ÷ 18
895.4 ÷ 11
Solve the problems.
If the answer is between
color the shape
0 and 30
31 and 80
red
green
Cut out the design and fold it into a triangular prism.
50
0.1
138.6 ÷ 33
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
706.2 ÷ 11
DECIMALS
Name _______________________________________________________
DECIMALS
Division by Decimals
Pentagonal Prism
0.1
50.6 ÷ 5.5
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
24.64 ÷ 3.2
28.6 ÷ 6.5
60.06 ÷ 9.1
314.9 ÷ 9.4
51.85 ÷ 8.5
126.72 ÷ 8.8
30.076 ÷ 7.3
80.91 ÷ 9.3
97.52 ÷ 4.6
82.34 ÷ 4.6
52.92 ÷ 5.4
17.69 ÷ 6.1
12.374 ÷ 2.3
1. Solve the problems.
2. Choose two colors that you like.
3. Write the name of one of the colors
on each line below.
4. Color the design.
If the answer has an
color the shape
even number in the tenths place
odd number in the tenths place
______________
______________
Cut out the design and fold it into a pentagonal prism.
51
Name _______________________________________________________
FRACTIONS
Renaming
Octagonal Prism
6
24
8
32
2
8
14
16
35
40
9
18
2
6
49
56
2
4
42
48
5
15
77
88
6
12
63
72
7
21
21
24
8
16
28
32
5
20
7
28
3
12
4
16
If the fraction
is equivalent to
color the shape
1
4
1
3
yellow
1
2
brown
7
8
orange
black
Finish the design by coloring the other
shapes with the colors of your choice.
52
Cut out the design and fold
it into an octagonal prism.
9
27
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
9
36
Name _______________________________________________________
FRACTIONS
Equivalent Decimals
Rhombohedron
9
20
16
20
30
50
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
68
80
1
4
32
80
46
50
10
20
93
100
Rewrite each fraction
as a decimal.
Extend the decimal
to the hundredths place.
3
10
22
50
45
60
44
80
94
100
8
20
4
4
45
100
54
100
79
100
83
100
76
100
5
10
51
100
33
100
44
100
22
50
2
10
20
40
2
4
32
50
2
5
1
4
72
100
37
100
89
100
6
10
9
10
3
5
70
100
7
20
98
100
3
4
If the answer is between
color the shape
0.01 and 0.35
0.36 and 0.75
0.76 and 1.00
green
yellow
pink
Finish the design by coloring
the other shapes with the
colors of your choice.
Cut out the design and fold
it into a rhombohedron.
53
Name _______________________________________________________
FRACTIONS
Addition With Unlike Denominators
+
3
2
7
9
54
3
1
12
7
7
+
18
7
9
1
8
9
16
+
1
7
+
blue
+
2
6
19
2
3
+
2
5
+
red
Finish the design by coloring
the other shapes with the
colors of your choice.
Cut out the design
and fold it into a cube.
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
+
7
8
+
6
+
10
1
3
1
9
1
5
9
9
2
7
3
10
1
greater than 1/2
2
1
3
11
1
1
4
1
+
2
+
5
1
1
3
1
3
+
1
less than or equal to
color the shape
1
1/2
2
1
2
5
+
+
2
9
7
+
4
1
12
+
+
4
13
Solve the problems.
Rename the answers in lowest terms.
If the answer is
8
4
9
+
1
1
8
1
1
+
8
1
2
+
7
4
7
5
1
2
+
1
16 3
+
5
8
1
4
+
16
9
12
8
1
1
Cube
Name _______________________________________________________
FRACTIONS
Multiplication
Hexagonal Pyramid
D
E
C
x 56
x 45
1
2
x 12
B
9
11
F
x 78
9
12
x 25
A
5
9
F
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
1
2
6
7
x 56
A
2
3
x 7
8
B
1. Solve the problems.
2. Choose two colors that you like.
3. Write the name of one of the colors
on each line below.
4. Color the design.
If the answer is
1
1/2or
2
less
1
greater than 1/2
2
E
2
5
x
2
3
3
8
15
16
x 3
7
11
4
1
9
9
x 10
x 8
9
x 5
6
C
D
color the shape
______________
______________
Finish the design by coloring the other
shapes with the colors of your choice.
Cut out the design and
fold it into a hexagonal pyramid.
55
Name _______________________________________________________
FRACTIONS
Subtraction of Mixed Fractions With Unlike Denominators
Cuboctahedron
A
7
A
9 9
5
8 7
2
3
–
– 6 23
3
C
9 18
E
C
4
12 5
– 1 19
– 9 16
J
E
5
D
13
F
– 5
9
11
1
3
– 9 23
– 2 58
4
12 7
– 2 12
2
9 3
4
20 12
6
9
I
F
B
7 4
K
– 7
5
3
16 6
I
– 9 14
K
9
5 10
7
9 8
22 9
– 4 12
–11 23
7
– 3 15
H
H
5
11 8
–
1
2
G
G
Solve the problems.
If the answer is
color the shape
greater than 0 and less than 4
orange
greater than 4 and less than 7
yellow
greater than 7 and less than 13
blue
Cut out the design and fold it into a cuboctahedron.
56
B
J
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
D
Name _______________________________________________________
FRACTIONS
Addition of Mixed Fractions With Unlike Denominators
Cylinder
2
8 5
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
+ 13 27
1
+
1
1
7 3
5 2
5 18
1
18
+ 2 38
+ 9 29
1
1
1
8 3
+
1
4 10
3 6
8 6
2
9
5
+ 3 12
+ 9 27
+
1
1
3
6 15
7 9
2 5
+ 9 23
+ 1 27
+ 1 16
1
1
1
2 8
+
7 15
4 4
+ 15 24
+ 8 25
+ 5 39
1
1
9 4
9 6
11 14
+ 9 78
+ 4 28
+ 1 27
Solve the problems.
Rewrite each answer as a
mixed fraction in lowest terms.
If the fractional part
of the answer is
color
the shape
1
less than 1/2
2
1
1/2or
greater
2
orange
green
1
7
1
1 8
1
2
5
1
2 6
+
2
3
1
17 5
+ 12 29
Finish the design by coloring the other
shapes with the colors of your choice.
Cut out the design and fold it into a cylinder.
57
Name _______________________________________________________
FRACTIONS
Multiplication of Mixed Fractions
Cone
Solve the problems. Rewrite each answer
as a mixed fraction in lowest terms.
If the answer is
than
than
than
than
1
2
3
4
and
and
and
and
less
less
less
less
than
than
than
than
2
3
4
5
blue
orange
red
yellow
Finish the design by coloring
the other shapes with the
color of your choice.
3
3
1 4 x 2 7
Cut out the design
and fold it into a cone.
1 x 1 8
3 2
1
3 5
x
1
1
3
4
2 6
x
2
3
5
1
7
1
8
x
2 1
2
9
10
58
4
5
1 1
3
x
1 1
4
1 7 x
9
1 1
3
1
5 2 x
3
3
1
3 1
1 1
2
1 1 x
3
x
x
1
1
1 8 x 1 4
5
8
4
9
9
x
1
1
1 4
2
3
x
5
4
6
x
1
8 8
x
5
4 7
9
5
7 6
x
3 4
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
greater
greater
greater
greater
color the shape
Name _______________________________________________________
PERCENTS
10% Discounts
Double Pentagonal
Pyramid
A
500
B
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
4850
780
470
A
C
198.40
1630.7
C
880
930
142.20
198
2500
489.40
B
740
440
244.1
598
E
E
337
820
F
9600
D
7500
D
F
Find ten percent of each number.
If the number in the tens place is an
color the shape
odd number
even number
pink
green
Cut out the design and fold it into a double pentagonal pyramid.
59
Name _______________________________________________________
INTEGERS
Addition
Truncated Square
Pyramid
8 + -5
-8 + -9
3 + -3
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
-7 + 6
3 + -7
7 + - 21
-5 + -5
6 + -5
-3 + -5
-4 + -16
5 + -8
9 + 12
-7 + -8
24 + -5
8 + - 27
- 7 + - 10
6 + -8
-5 + 17
Solve the problems.
If the answer is between
- 3 and 24
- 4 and - 27
7+4
color the shape
purple
green
Finish the design by coloring the
other shapes with the colors of your choice.
Cut out the design and fold it into a truncated square pyramid.
60
9 + - 23
-9 + -7
Name _______________________________________________________
INTEGERS
Multiplication
Pentagonal Pyramid
C
D
7 x - 11
12 x - 12
- 8 x 10
- 9 x 12
- 11 x 11
B
9x5
6 x - 11
E
- 3 x -4
6 x - 12
5 x -5
A
-12 x 8
-7 x 8
- 11 x 8
E
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
-8 x -9
A
-2 x 9
7 x -12
6 x -6
-7 x -3
Solve the problems.
If the answer is between
-144 and -61
-60 and -31
-31 and 0
B
-9 x -8
color the shape
1 and 30
black
red
orange
yellow
30 and 60
61 and 90
blue
purple
D
-7 x -7
C
Cut out the design and fold it into a pentagonal pyramid.
61
0.1
Answers for Taking It Further questions,
pages 8–42.
Page 19: Gears
41 banners
Page 8: Optical Illusion
The shaded blocks form the word yes.
Page 20: Starburst
42 degrees
2
4
5
6
71
83
37
55
23
53
61
97
10
7
30
89
20
22
25
67
90
99
11
79
59
33
43
19
12
60
2
3
41
15
17
277
28
3
48
46
62
66
88
47
24
31
25
26
13
73
29
50
5
19
11
Page 22: Star Wings
a. - 7, b. 7, c. - 7, d. - 7
Page 9: Holiday Glow
654, 1,701, 825
Page 23: Poinsettia
$2.75
Page 10: Stardust
324, 5,364, 6102
Page 11:
Pattern Block Star
Page 21: Paper Folding
a. - 13, b. 13, c. - 13, d. - 13
8.87
– 5.96
2.91
Page 12: Whirling Octagons
52.5 miles
Page 13: Rising Star
84 103 122
76 , 76 , 76
Page 14: A Dozen Circles
3
1
6
3
3
1
7
1
or
or
or
or
2 b. 8
4 c. 12
4 d. 21
3
a. 6
Page 24: Hexagonal Flowers
75
Page 25:
Letter Z
9.24
+ 1.37
10.61
Page 26:
Patchwork Star
$29.75
Page 15: Aztec Art
7
32 of a box
Page 16: Tree Ornament
256 1,024 4,096
2 , 2 ,
2
Page 17: Linked Together
2
5
0.2, 0.20, 10 , 25 ,
Page 18: Stained Glass Window
1
3 4 hours
62
Page 27:
Nine Circles
$0.80
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
Answers
Page 32: Diamond
1
13
3
3
a. 3 b. 16 c. 8 d. 4
Page 28:
Puffy Cloud
0.300
Page 29:
Crochet
20%
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
1
5
1
4
1
2
25%
40%
50%
2
5
Page 33:
Emerging Triangle
2
1
1
1
2
1
a. 3 b. 8 c. 4 d. 9 e. 5 f. 2
Page 30:
Four Leaf Clover
Page 34: Octagonal Star
6 or 3
a. 16
8
2
a. 3 3
3
b. 2 7
5
c. 1 12
11
d. 16
18 or 3
b. 24
4
16 or 1
c. 32
2
Page 31: Dream Catcher
1
2
5
10
1
4
7
28
7
8
49
56
9
18
17
34
9
36
12
48
14
16
84
96
Page 35: String Art
3
37 8 miles
63
Page 36: Starlit Sky
$15.75
Page 41: Basket Weaving
a. - 4, b. 2, c. - 1, d. - 5
Page 37: Birth of a Star
9 students
Page 38:
Flaming Triangle
a. $15.99 with 10% off = $14.39
Page 39: Tree Topper
c. $17.99 with 10% off = $16.19
Page 40: Zinnia
$1.82
64
Dazzling Math Line Designs: Grades 6-8 © Cindi Mitchell, Scholastic Teaching Resources
Page 42: Explosion
a. 4 b. - 4 c. 4 d. - 4