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0.1 0.1 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 • • 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 0.1 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