GRADE 6 100 Math Practice Pages New York • Toronto • London • Auckland • Sydney Mexico City • New Delhi • Hong Kong • Buenos Aires 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Text Credits: Practice Pages 3, 5, 7, 9, 38, 41, 46, 52, 54, 58, 62, 64, and 89 taken and/or adapted from Practice, Practice, Practice! Fractions & Decimals by Judith A. Muschla and Gary Robert Muschla © 2005 by Judith A. Muschla and Gary Robert Muschla; Practice Pages 6, 15–19, 21, 23, 27, 30, 33, 34, 37, 39, 40, 42, 45, 47, 49, 56, 59, 63, 65–67, 78, 82, and 96 taken and/or adapted from Tic-Tac-Math: Grades 5 & Up by Laura Meiselmann © 2005 by Laura Meiselmann; Practice Pages 10, 12, 14, 69, 71, 72, 75, 77, 80, 83, 85–87, 92, 94, and 95 taken and/or adapted from Practice, Practice, Practice! Algebra Readiness by Judith A. Muschla and Gary Robert Muschla © 2005 by Judith A. Muschla and Gary Robert Muschla; Practice Pages 20, 22, 29, 35, and 50 taken from 50 Fill-In Math Word Problems: Fractions & Decimals by Bob Krech and Joan Novelli © 2009 by Bob Krech and Joan Novelli; Practice Pages 24, 28, 36, 44, 48, 51, 53, 55, and 61 taken and/or adapted from Solve-the-Riddle Math Practice: Fractions & Decimals by Liane B. Onish © 2012 by Liane B. Onish; Practice Pages 43 and 60 adapted from Practice, Practice, Practice! Word Problems by Judith A. Muschla and Gary Robert Muschla © 2005 by Judith A. Muschla and Gary Robert Muschla; Practice Page 74 taken from 50 Fill-in Math Word Problems: Algebra Readiness by Bob Krech and Joan Novelli © 2009 by Bob Krech and Joan Novelli. Other Practice Pages from this workbook were previously published in: Morning Jumpstarts: Math, Grade 6. Scholastic Inc. grants teachers permission to photocopy the reproducible pages 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., 557 Broadway, New York, NY 10012. Edited by Mela Ottaiano Cover design by Lindsey Dekker Interior design by Melinda Belter ISBN: 978-0-545-79942-3 Compilation copyright © 2015 by Scholastic Inc. Illustrations copyright © by Scholastic Inc. All rights reserved. Published by Scholastic Inc. Printed in the U.S.A. 2 3 4 5 6 7 8 9 10 40 22 21 20 19 18 17 16 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Contents Introduction . . . . . . . . . . . . . . . . 5 Practice Page 27 • Multiplying 4-Digit by 2-Digit Numbers/ Word Problems . . . . . 33 Practice Page 1 • Writing Whole Numbers . . . 7 Practice Page 2 • Comparing Whole Numbers . . . . . . . . . . 8 Practice Page 3 • Place Value/Decimals . . . . 9 Practice Page 4 • Writing Decimals . . . . . 10 Practice Page 5 • Comparing Decimals . . . 11 Practice Page 6 • Comparing Fractions . . . 12 Practice Page 7 • Ordering Decimals . . . . 13 Practice Page 8 • Rounding . . . . . . . . . 14 Practice Page 9 • Rounding . . . . . . . . . 15 Practice Page 10 • Identifying Integers . . . 16 Practice Page 28 • Multiplying Decimals . . . 34 Practice Page 29 • Multiplying Decimals/ Word Problems . . . . . 35 Practice Page 30 • Multiplying Decimals/ Word Problems . . . . . 36 Practice Page 31 • Dividing With Mental Math and Estimation . . 37 Practice Page 32 • Dividing Multi-Digit Whole Numbers . . . . . 38 Practice Page 33 • Dividing Multi-Digit Whole Numbers/ Word Problems . . . . . 39 Practice Page 11 • Ordering Integers . . . . 17 Practice Page 12 • Comparing Integers . . . 18 Practice Page 13 • Absolute Value . . . . . 19 Practice Page 14 • Absolute Value . . . . . 20 Practice Page 34 • Dividing Decimals by Whole Numbers . . . . . 40 Practice Page 35 • Dividing Decimals by Whole Numbers/ Word Problems . . . . . 41 Practice Page 15 • Mixed Practice . . . . . 21 Practice Page 16 • Adding and Subtracting Practice Page 36 • Dividing Decimals by Practice Page 17 • Adding Whole Numbers/ Practice Page 37 • Dividing Decimals by Decimals . . . . . . . . 42 Whole Numbers . . . . 22 Decimals/Word Problems . . . . . . . . 43 Word Problems . . . . . 23 Practice Page 18 • Subtracting Whole Numbers/Word Problems . . . . . . . . 24 Practice Page 38 • Adding Mixed Numbers . . 44 Practice Page 39 • Adding Mixed Numbers/ Word Problems . . . . . 45 Practice Page 19 • Adding and Subtracting Decimals . . . . . . . . 25 Practice Page 40 • Subtracting Fractions and Mixed Numbers . . . . . 46 Practice Page 20 • Adding Decimals/ Word Problems . . . . . 26 Practice Page 41 • Subtracting Mixed Numbers . . . . . . . . 47 Practice Page 21 • Adding Decimals/ Word Problems . . . . . 27 Practice Page 42 • Subtracting Mixed Numbers/Word Problems . . . . . . . . 48 Practice Page 22 • Subtracting Decimals/ Word Problems . . . . . 28 Practice Page 23 • Subtracting Decimals/ Practice Page 43 • Adding and Subtracting Mixed Numbers/Word Problems . . . . . . . . 49 Word Problems . . . . . 29 Practice Page 24 • Adding and Subtracting Decimals/Word Problems . . . . . . . . 30 Practice Page 44 • Multiplying Whole and Mixed Numbers . . . . . 50 Practice Page 25 • Multiplying With Mental Practice Page 45 • Multiplying Fractions and Practice Page 26 • Multiplying 3-Digit Practice Page 46 • Multiplying Mixed Mixed Numbers . . . . . 51 Math and Estimation . . . 31 by 3-Digit Numbers . . . 32 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Numbers . . . . . . . . 52 Practice Page 47 • Multiplying Mixed Numbers/Word Problems . . . . . . . . 53 Practice Page 48 • Dividing Fractions by Fractions . . . . . . . . 54 Practice Page 49 • Dividing Fractions by Fractions . . . . . . . 55 Practice Page 50 • Dividing Decimals by Whole Numbers/ Word Problems . . . . . 56 Practice Page 51 • Dividing Mixed by Whole Numbers . . . . . 57 Practice Page 52 • Dividing Mixed Numbers 58 Practice Page 53 • Converting Fractions to Decimals . . . . . . . 59 Practice Page 71 • Order of Operations . . . 77 Practice Page 72 • Order of Operations . . . 78 Practice Page 73 • Writing Expressions . . . 79 Practice Page 74 • Writing Expressions/ Word Problems . . . . . 80 Practice Page 75 • Writing Expressions/ Word Problems . . . . . 81 Practice Page 76 • Simplifying Expressions . 82 Practice Page 77 • Evaluating Expressions . 83 Practice Page 78 • Evaluating Expressions . 84 Practice Page 79 • Evaluating Expressions . 85 Practice Page 80 • Writing Equations . . . . 86 Practice Page 81 • Writing Equations . . . . 87 Practice Page 54 • Converting Decimals to Practice Page 82 • Writing Equations/ Practice Page 55 • Converting Fractions Practice Page 83 • Writing Equations/ Percents . . . . . . . . 60 to Percents . . . . . . . 61 Word Problems . . . . . 88 Word Problems . . . . . 89 Practice Page 56 • Mixed Practice . . . . . . 62 Practice Page 84 • Solving Equations . . . . 90 Practice Page 57 • Calculating Percents . . . 63 Practice Page 85 • Solving Equations . . . . 91 Practice Page 58 • Calculating Percents . . . 64 Practice Page 86 • Writing and Solving Practice Page 59 • Calculating Percents/ Word Problems . . . . . 65 Practice Page 60 • Calculating Percents/ Word Problems . . . . . 66 Practice Page 61 • Calculating Percents/ Word Problems . . . . . 67 Practice Page 62 • Identifying Decimal Patterns . . . . . . . . . 68 Practice Page 63 • Identifying Decimal Patterns . . . . . . . . . 69 Practice Page 64 • Identifying Fraction Patterns . . . . . . . . 70 Practice Page 65 • Identifying Fraction Patterns . . . . . . . . . 71 Practice Page 66 • Factors, Primes, and Greatest Common Factor . . . . . . . . . . 72 Practice Page 67 • Multiples and Least Inequalities . . . . . . . 92 Practice Page 87 • Writing Rules for T-Tables . . . . . . . . . 93 Practice Page 88 • Identifying Ratios . . . . 94 Practice Page 89 • Solving Proportions . . . 95 Practice Page 90 • Calculating Rate . . . . . 96 Practice Page 91 • Graphing a Coordinate Plane . . . . . . . . . 97 Practice Page 92 • Graphing a Coordinate Plane . . . . . . . . . . 98 Practice Page 93 • Graphing a Coordinate Plane . . . . . . . . . . 99 Practice Page 94 • Calculating Area . . . . 100 Practice Page 95 • Calculating Area . . . . 101 Practice Page 96 • Calculating Averages . . 102 Practice Page 97 • Data Analysis . . . . . . 103 Common Multiple . . . . 73 Practice Page 98 • Data Analysis . . . . . . 104 Practice Page 68 • Exponents . . . . . . . 74 Practice Page 99 • Data Analysis . . . . . . 105 Practice Page 69 • Exponents . . . . . . . 75 Practice Page 100 • Data Analysis . . . . . 106 Practice Page 70 • Identifying Properties . . 76 Answer Key . . . . . . . . . . . . . . . . 107 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Introduction In today’s busy classrooms, it is vital to maximize learning time. That’s where 100 Math Practice Pages, Grade 6 comes in. The activities in this book are designed to review and reinforce a range of math skills and concepts students will build throughout the year. Each page provides focused, individual practice on an essential, grade-level skill students are expected to master, including multiplication, division, fractions, decimals, percents, ratios, numerical expressions, equations, geometry, and data analysis. Reviewing concepts students have already learned is a good way to keep their math skills sharp and to discover where revisiting a skill may be beneficial. You know your students best, so feel free to pick and choose among the activities and incorporate them as you see fit. The goal is to build automaticity, fluency, and accuracy so students can succeed in school. How to Use This Book The engaging activity Preview each activity page to ensure that students pages are a great have the skills needed to complete it. If necessary, way to help students: walk through its features with your class to provide an 3 reinforce key overview before you assign it and to make sure students academic skills understand the directions. Work out a model problem or and concepts two as a class. 3 meet curriculum The 100 practice pages can be used to enhance the standards curriculum during math time, to keep fast finishers on task anytime, or as homework. 3 prepare for You’ll find an answer key beginning on page 107. standardized tests If time allows, you might want to review answers with 3 succeed in school the whole class. This approach provides opportunities for discussion, comparison, extension, reinforcement, 3 become lifelong learners and correlation to other skills and lessons, Your observations can direct the kinds of review or reinforcement you may want to add to your lessons. Alternatively, you may find that having students discuss activity solutions and strategies in small groups is another effective way to deepen understanding. 5 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Meeting the Standards Completing the exercises will help students meet the College and Career Readiness Standards for Mathematics, which serve as the backbone for the practice pages in this book. These broad standards were developed to establish a framework of clear educational expectations meant to provide students nationwide with a quality education that prepares them for college and careers. The following list details how the activities in this book align with the standards in the key areas of focus for students in grade 6. Standards for Mathematics Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. C onstruct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeating reasoning. Mathematical Content 3 Ratios and Proportional Relationships 3 The Number System 3 Expressions and Equations 3 Geometry 3 Statistics and Probability 6 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 1 Writing Whole Numbers Name Date Super Summer Numbers W rite each number in standard form. 1. three hundred billion ten ___________________________________________________ 2. fifty-nine billion one hundred thirty _________________________________________ 3. six hundred six billion ______________________________________________________ 4. thirty-two trillion one hundred four _________________________________________ 5. seven trillion four hundred _________________________________________________ 6. five million twenty-four thousand twenty _____________________________________________________________________________ 7. twenty-four billion sixteen million ___________________________________________ 8. one hundred fifty-two trillion two billion five _____________________________________________________________________________ 9. ninety-seven million fourteen thousand eleven _____________________________________________________________________________ 10. forty-eight trillion nine hundred billion one thousand twenty-seven _____________________________________________________________________________ 7 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 2 Comparing Whole Numbers Name Date Dare to Compare Compare. Write <, =, or >. 1.788,000 _________ 780,000,000 2.606,666,000 _________ 606,000,666 3.87,000,000,000 _________ 970,000,000 4.585,500,000 _________ 585,005,000 5.300,000,099,000 _________ 300,001,000,000 6. fifty million _________ 50,000,000 7. four hundred four billion _________ 400,000,004 8. three trillion five hundred million _________ 3,500,000,000 9.1,000,000,370,000 _________ one trillion thirty-seven thousand 10. four hundred fifty trillion _________ 450,000,000,000 8 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 3 Place Value/Decimals Name Date Showtime! This city is home to the first movie theater to open in the U.S. What is the name of this city? I Answer: ______________________________ 9455312608 To answer the question above, write the number that represents the place value listed next to each decimal. Then write the corresponding letter in the space above its answer. The first one has been done for you. Hint: One letter will be used more than once. One letter will not be used. 4 I.0.643 ______ hundredths U. 4,284.01 ______ hundreds R. 0.6872 ______ tenths B. 9.78215 ______ ten-thousandths C. 1.4729 ______ hundredths G. 1.6403 ______ thousandths S. 123.48 ______ ones P. 526.96 ______ tenths H. 59.068 ______ thousandths T. 651.034 ______ tens To learn what year this theater opened, continue finding the given values for the following decimals. Correct answers (from top to bottom) will be the year. 1 82.013 2 0.04895 ______ ten-thousandths 3 0.62015 ______ thousandths 4 612.593 ______ tenths ______ hundredths 9 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 4 Writing Decimals Name Date Decimal Detective W rite each decimal in standard form. 1. eight tenths _______________________ 2. six hundredths _______________________ 3. sixty-three hundredths _______________________ 4. sixteen thousandths _______________________ 5. nine ten-thousandths _______________________ 6. one and two hundredths _______________________ 7. 12 hundred thousandths __________________________________________ 8. 60 and 9 hundredths __________________________________________ 9. 47 ten-thousandths __________________________________________ 10. 7 thousand and 22 thousandths __________________________________________ 3.951 10 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 5 Comparing Decimals Name Date Look to the East! The easternmost point in the United States is located in Maine. What is the name of this place? Answer: ____________ 9112 5 __________________ 101 6134 8 ___ ___ ___ ___ 14 7 3 12 To answer the question, use the signs >, <, or = to compare each pair of decimals. Write the letter of the larger decimal in the space above its problem number. If a pair of decimals is equal, write the letter E (for equal) above the problem number. 1 2 3 4 15.40 _______ 15.042 DH 5 0.075 _______0.0740 TM 6 0.8009_______ 0.81 LO 7 7.601 _______7.6010 CK 0.45 _______ 0.5 NU 8 12.54 _______ 12.539 YT 9 4.781 _______ 4.7672 W G 10 1.904_______19.03 VQ 11 0.004 _______ 0.00400 JP 0.37 _______ 0.295 SI 2.965 _______ 2.99 RA 12 0.0530_______ 0.04 D S 13 11.642_______ 11.75 14 11 KD 23.6404 _______23.64112 MH 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 6 Comparing Fractions Name Date Fractions Beyond Compare These fractions are simply gorgeous! Solve three problems in a row to get Tic-Tac-Math! Circle the fractions that are Circle the fractions that are Write three fractions that are greater than 2 . less than 2 . equivalent to 2 using the denominators 20, 44, and 72. 1 ___ 5 ___ 10 ___ 6 ___ 3 ___ 15 ___ 9 ___ 4 ___ 21 ___ 12 28 18 16 14 10 she eat if she wants to eat 2 ___ more: 4 of a pizza or 3 of a pizza? 4 ___ 7 60 29 6 ___ 18 14 ___ Marco studied for 16 of an hour, and Melissa studied for 3 ___ 4 1 ___ 15 ___ 6 56 ___ 50 Which amount of pizza should 3 ___ 1 ___ 4 Hortence is really hungry. 2 ___ 1 ___ of an hour. Who studied longer? 7 ___ 1 ___ Frangelica swam 2 2 laps at the pool, while her sister Bailey 2 ___ swam 2 4 laps. Who swam more? 3 ___ Bekah ran 5 of a mile and 2 ___ Jeff ran 3 of a mile. Who ran Paula Sue completed 8 of her homework, and Roberto skied 4 5 miles on the cross-country trails, while his more? Janet Lynn completed 20 of her homework. Who did brother Pascal skied 4 10 miles. Who skied a greater distance? 15 ___ 9 ___ a greater portion of her homework? 12 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 7 Ordering Decimals Name Date Let’s Go to a Movie The first “real” movie was produced in 1903. What was the name of this movie? Answer: THE __________________________________________ 123456 To answer the question, arrange each set of decimals in order from smallest to largest. Then arrange the letters of the decimals of each set in the same order. Write the letters in the spaces above their problem numbers. You will have to separate the letters into words. The first one has been done for you. 1 2 H. 1.010 T. 1.001 E. 1.101 T. 1.001 H.1.010 E. 1.101 _________________________________________________________________________ R. 4.245 E. 4.25 G. 4.205 _________________________________________________________________________ 3 T. 0.854 A. 0.853 T. 0.8539 _________________________________________________________________________ 4 A. 0.0082 R. 0.00802 I. 1.0820 _________________________________________________________________________ 5 O. 17.1020 R. 17.1002 N. 17.013 B. 17.120 _________________________________________________________________________ 6 E. 2.03254 B. 2.00325 Y. 2.3253 R. 2.325 _________________________________________________________________________ 13 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 8 Rounding Name Date Round ’em Up Complete each set of problems below. 1.Round each number to the nearest 1,000 and 100,000. Number Nearest 1,000 Nearest 100,000 390,000 400,000 1,844,938 1,845,000 1,800,000 24,061,562 24,062,000 24,100,000 389,900 2.Round to the place of the underlined digit. 30,948,007 _____________________ 92,807.045 _____________________ 1,286,000.372 __________________ 4,000,040,706 ___________________ 8,726,739.0283 _________________ 5,528,908,282 ___________________ 3.Round to the greatest nonzero place. 0.047 __________________________ 9.807 __________________________ 0.00872 ________________________ 44.4123 ________________________ 6,727.39 _______________________ 0.00526 ________________________ 14 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 9 Rounding Name Date Buzzing ’round R ound each decimal to the given place. Circle the correct answer. 1.Round 0.584 to the nearest tenth. 0.684 0.6 0.59 2.Round 6.0392 to the nearest hundredth. 7.00 6.049 6.04 3.Round 4.7503 to the nearest thousandth. 4.8004.7504.75 4.Round 29.546 to the nearest whole number. 29.5 30 30.5 5.Round 0.704788 to the nearest ten-thousandth. 0.7048 0.705 0.70479 6.Round 297.0432 to the nearest hundredth. 300 297.04 297.043 7.Round 12.407992 to the nearest ten-thousandth. 12.4079 12.408092 12.4080 8.Round 27.086 to the nearest whole number. 27.09 27.1 27 9.Round 6.38724 to the nearest ten-thousandth. 6.39006.38726.38704 10. Round 63.30156 to the nearest thousandth. 63.302 15 63.301 63.3016 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 10 Identifying Integers Name Date What’s in the Fridge? In 1851, the first patent for mechanical refrigeration was awarded to an American inventor. The basic process this man invented is still used today. What was his name? Answer: ________________ ________________________ 1234 5678910 To answer the question, find the point described in each problem on the number line and write it on the space next to each problem. Write the letter of the point in the space above its problem number. Hint: Some letters will be used more than once. Some will not be used. J T S N E I O R V HMDG -6-5-4-3-2-1 0 1 2 3 4 5 6 1 It is the smallest number that is pictured on the graph. ______________ 2 It is halfway between –1 and +1. ______________ 3 It is 3 units to the right of 0. ______________ 4 It is 3 units to the right of –6. ______________ 5 It is the largest number that is graphed. ______________ 6 It is neither positive nor negative. ______________ 7 It is 4 units to the right of –3. ______________ 8 It is 5 units to the left of +6. ______________ 9 It is 4 units to the left of +3. ______________ 10 It is halfway between –3 and –1. ______________ 16 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 11 Ordering Integers Name Date Order! Order! Complete each set of problems below. 1. Order the integers from least to greatest. –6 –2 –4 4 –9 40 –5 ___________________________________ –40 ___________________________________ 2. Order the integers from greatest to least. –9 –91 19 –17 7 –77 9 ___________________________________ 17 ___________________________________ 3. Write the integer that represents each of the following: a loss of $5 dollars ___________________________________ an increase in altitude of 400 feet ___________________________________ a dive to 75 feet below sea level ___________________________________ a rise in temperature of 6 degrees ___________________________________ 17 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 12 Comparing Integers Name Date Big Wings With a wingspan of nearly 10 feet, this seabird has the largest wingspan of any bird. What is the name of this bird? Answer: ___________________________ 147 8 3181012413 ___________________________ 159166 1112 517 To answer the question, use > or < to make each number sentence true. Write the letter beneath the sign in the space above the problem number. 1 > K 2 > D 9 0____–2 > S < G 10 12 < A 13 8____+5 < P 14 5____–6 < U 15 11____–15 > R > O < C 18 < R 8____+4 – > L < I 6____–5 – > S + > L 1____0 – + > N 2____0 2____+5 < N < W – > V 8 – > R 5 < L 4____–7 < O > A 7 11 +11____–12 3____+8 > S 4 < T – 3 6 8____+7 – < G 16 3____–8 + > B 17 18 < H 7____+2 – > M < S 2____–6 > E < A 2____+2 – > C < W 0____–3 > A < N 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 13 Absolute Value Name Date Absolutely Amazing! Write the absolute value of each number. –326 _________ –4.5 _________ 2 – ___ 5 _________ – 0.6 _________ –22 _________0 _________ –87 _________ –15 _________18 _________ 5 – ___ 8 _________ 2 ___ 3 _________75 _________ Complete the chart. Statement True or False? 1. A ny number on a number line is greater than any number to its left. 2. T he number –6 is to the left of –9 on the number line. 3. If x is a positive integer, then x > than 0. 4. A ny positive integer has a greater absolute value than any negative integer. 19 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 14 Absolute Value Name Date Fairy Tales The Grimm Brothers collected and published fairy tales, including “Cinderella,” “Rapunzel,” and “Rumpelstiltskin.” What were the full names of the Grimm Brothers? Answer: _______________ __________________ ____________ 54537024 15653 17 62 2523 24 and _____________________ ____________ 53 17 249824 12 2523 24 To answer the question, write the absolute value of the numbers and complete the number sentences below. Write the letter of each problem in the space above its answer. Hint: Some letters will be used more than once. Some will not be used. D. | + 6| = _______ S. | –16| = _______ E. | –8| = _______ R. | + 23| = _______ I. | + 17| = _______ U. | –15| = _______ C. | + 3| = _______ O. | + 14| – | –7| = _______ P. | –14| = _______ K. | –19| – | + 17| = _______ M. | –12| = _______ G. | + 52| + | –10| = _______ B. | 0 | = _______ W. | + 44| + | –9| = _______ A. | –5| = _______ L. | –18| + | 6| = _______ H. | + 9| = _______ J. | –64| – | 10| = _______ 20 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 15 Mixed Practice Name Date Absolutely Positive! Being negative isn’t so bad. Negative numbers are actually pretty cool. Solve three integer problems in a row to get Tic-Tac-Math! What is the absolute value What is the absolute value of –8? of –13? Fill in the box with <, >, or =. –3 Fill in the box with <, >, or =. Imagine a number line with 2 What is the sum of –3 and +7? negative numbers to the left 6 –5 of zero and positive numbers to its right. If you start on +7 and move three spaces to the right, on what number will you land? Find the sum: –4 + –3 + –11 Talia added –4 + –5 + 8 and What number should you add got –17. She made an error. to –8 to get +12? What error do you think she made? What is the correct answer? 21 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 16 Adding and Subtracting Whole Numbers Name Date Plus or Minus? Look at the signs. Then add or subtract. 1. 7,532 6. 67,312 – 38,350 2. 825 – 58 7. 89,429 + 65,752 3. 18,475 8. 741,508 + 20,676 4. 1,600 9. 2,945,062 – 834,173 5. 38,238 10. 3,813,455 + 794,567 + 3,269 + 3,941 – 443 + 37,882 22 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 17 Adding Whole Numbers/ Word Problems Name Date Make a Splash! M ake a splash by solving these addition word problems. 1.May DeSplash surfed 11,832 waves one summer, and 34,729 the next summer. How many waves did she surf in both summers? ________________ 2.Sandy Beach had 57,385 visitors one year, 49,275 the next, and 53,658 the next. How many visitors did Sandy Beach have in all three years? ________________ 3.Jose loves to read books. He read books that were 449 pages, 764 pages, 502 pages, and 393 pages this summer. How many pages is that in all? ________________ 4.By the end of the summer, all of Dennis’s freckles came out. He started with 702 freckles. Then his mom counted 589 more freckles. How many freckles did Dennis have at the end of the summer? ________________ 23 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 18 Subtracting Whole Numbers/ Word Problems Name Date Family Time Solve each word problem. Show your work in the tank. 1.The Ortiz family were driving from their house to their friends’ house 1,398 miles away. After 199 miles, they took a break for lunch. How many more miles did they have to drive to get to their friends? THINK TANK ___________________ 2.Carolina and her dad wanted to make the world’s largest chocolate-chip cookie with 72,390 chips in it. But they ran out of chips after they had used 55,431. How many more chocolate chips did they need to buy? THINK TANK ___________________ 24 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 19 Adding and Subtracting Decimals Name Date Decimal Derby Find each sum or difference. 1. 7 + 8.56 = __________________ 2. 0.852 + 0.45 + 0.2613 = __________________ 3. 2.08 + 0.707 = __________________ 4. 9.3 + 0.4637 + 0.5441 = __________________ 5. 8 – 2.0476 = __________________ 6. 0.91 – 0.745 = __________________ 7. 4.3 + 2.5 = __________________ 8. 7.65 – 4.3 = __________________ 9. 6.8 + 3.65 = __________________ 10. 8.25 – 1.4 = __________________ 11. 49.38 + 16.01 = __________________ 12. 67.39 – 4.934 = __________________ 25 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 20 Adding Decimals/ Word Problems Name Date Clubhouse Fill in words and numbers as directed. Then solve the problem. M and y friends (first name of a boy or girl) and I are building a (first name of a boy or girl) clubhouse in my yard for our club, the . We named our clubhouse Fort (plural noun) We are building it out of It has a room just for where we can (adjective) (type of substance) (verb ending in -ing) and (noun) (decimal number) (decimal number) meters long. Our flag and (color) (color) on it. That’s our club mascot. I can’t wait for our next meeting. We are going to ve Sol s! Thi . and a space on the roof we made out of two sticks we joined together. One was has a beautiful (type of substance) . . We put up a flagpole, too, which (present-tense verb) meters long and the other was (last name of a famous person) (present-tense verb) marshmallows! How long is the flagpole? Answer with a decimal. 26 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 21 Adding Decimals/Word Problems Name Date Decimal Jumps Solve each word problem. Show your work in the tank. 1. In the frog-jumping contest, Hannah’s frog jumped 48.7 cm on his first try and 35.9 cm on his second try. How far did Hannah’s frog jump in all? THINK TANK ___________________ 2. Francisco jumped 180.5 cm on his first standing long jump. On his second jump, he jumped 200.2 cm. On his third jump, he jumped 191.35 cm. How far did he jump in all? THINK TANK ___________________ 27 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 22 Subtracting Decimals/ Word Problem Name Date Gigantic Snacks Fill in words and numbers as directed. Then solve the problem. A new restaurant called Gigantic Snacks just opened up in . Everything (name of a town) on the menu here is enormous, and nothing cost more than (amount of money) ! The first time I went, I had an amazingly hamburger that weighed (adjective) pounds. It came with a special (number greater than 1) milkshake that was so (flavor) and creamy. I also got one French fry that was meters long! I dipped it in only ate (decimal less than 0.55) (type of condiment) -ounce (adjective) (decimal greater than 0.55) . It was delicious, but I meters of it. I was so full, I sadly did not have room for their famous chocolate-covered ve l o S s! Thi (number greater than 1) (plural noun) . How much of the French fry was left? Answer with a decimal. 28 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 23 Subtracting Decimals/ Word Problems Name Date Decimal Deli P eople order strange amounts of food at the Decimal Deli. Solve the problems to find out the final amounts. 1.Paula orders 3.75 pounds of macaroni salad and 2.25 pounds of coleslaw. How many more pounds of macaroni salad does she have than coleslaw? ________________ 2.Robby orders 1.33 pounds of turkey, then asks the clerk to put 0.425 pounds of it back. How much turkey did Robby end up with? ________________ 3.Anne-Marie orders 0.75 pounds of mozzarella cheese and 2.478 pounds of salami. How many more pounds of salami does she have than cheese? ________________ 4.Gabriella orders 27.152 pounds of olive loaf. Right after that, Christopher orders 35.08 pounds of it! How much more olive loaf did Christopher order? ________________ 29 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 24 Adding and Subtracting Decimals/Word Problems Name Date What did the buffalo mom say on Monday morning! Add or subtract. Solve the riddle using your answers. Jorge bought a new notebook for $3.99. How much change did he get from $10.00? I Ruby bought a set of watercolor paints and a sketchpad. The paints cost $8.75. The sketchpad cost $4.95. How much did she spend? O Marc bought a special gift pack of stickers and crayons for his little sister. The pack cost $3.75. How much change did he get from $5.00? E Amanda bought a new ring binder, 3-hole notebook paper, and a set of marking pens. Each cost $0.99. How much did she spend? S Jeri picked art paper and pastel markers. The art paper cost $7.99. The markers cost $4.69. How much did Jeri spend? N Five friends shared a pizza after shopping. The pizza cost $12.75. How much change did they get from $20.00? B Solve the Riddle! “ $7.25 Write the letter that goes with each answer. $6.01 – $2.97 30 $13.70 $12.68 !” 100 Math Practice Page, Grade 6 © 2015 • Scholastic Teaching Resources Multiplying With Mental Math and Estimation 25 Name Date Mental Multiplication Complete each set of problems below. 1. Use mental math to find each product. 4 × 90 = _______________ 50 × 600 = _______________ 7 × 40,000 = _______________ 7 × 7,000 = _______________ 100 × 80 = _______________ 20 × 9,000 = _______________ 60 × 800 = _______________ 30 × 2,000 = _______________ _______________ 500 × 1,000 = _______________ _______________ 300 × 400 = _______________ 70 × 40,000 = 50 × 50 = 2.Estimate the product by rounding each factor to its greatest place. 31 × 209 = ___________________ ___________________ 7 × 768 = 46 × 542 = ___________________ 84 × 6,441 = ___________________ 57 × 3,299 = ___________________ ___________________ 610 × 980 = 31 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 26 Multiplying 3-Digit by 3-Digit Numbers Name Date The Great Multiplier Solve each multiplication problem. 1. 388 x 222 5. 357 x 246 2. 407 x 123 6. 298 x 197 3. 250 x 150 7. 648 x 324 4. 966 x 509 8. 999 x 999 32 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 27 Multiplying 4-Digit by 2-Digit Numbers/Word Problems Name Date Superstar Math Solve each word problem. Show your work in the tank. 1. The Fuzzi Wuzzies’ new album has sold 1,562 copies. Each album cost $18. What’s the total amount collected for all of those albums? ___________________ THINK TANK 2.There were 6,257 teens at The Stinky Cheese concert. If each teen screamed 83 times during the concert, how many screams were there in all? ___________________ THINK TANK 33 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 28 Multiplying Decimals Name Date Why are Saturday and Sunday the strongest days? Multiply. Round the answers to the nearest hundredth. Solve the riddle using your answers. 3.1 x 0.04 4.9 x 5.6 T S 5.85 x 5.80 Y Solve the Riddle! 11.99 7.13 6.4 x 4.6 D 3.9 x 8.3 H 0.12 E 2.18 x 5.5 14.8 x 1.48 A 1.15 x 6.2 W N 0.92 x 0.41 6.05 x 0.40 K 2.2 x 2.7 O 5.31 x 0.05 R Write the letter that goes with each answer. 33.93 0.12 11.99 7.13 0.27 27.44 . 21.90 0.27 7.13 0.38 7.13 21.90 34 2.42 29.44 21.90 32.37 27.44 100 Math Practice Page, Grade 6 © 2015 • Scholastic Teaching Resources 29 Multiplying Decimals/ Word Problems Name Date Class Poster Fill in words and numbers as directed. Then solve the problem. I n Mr. ’s (last name of a boy) class, we are studying . (plural noun) My group has to make a poster. We bought some posterboard from (last name of a famous person) Store. It cost $ (noun) inch. We bought (number greater than 10) (decimal less than 0.99) (adjective) make it bright. We made a border out of glow-in-the-dark “ ve Sol s! Thi (plural noun) paint to and stuck across the bottom. Everyone said, (plural noun) (exclamation) per square square inches. We drew with and used (plural noun) ’s Art Supply and !” when they saw it. How much did the posterboard cost? Answer with a decimal. 35 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 30 Multiplying Decimals/ Word Problems Name Date It’s Time(s) for Decimals! Y ou’re just in time to solve three decimal multiplication problems! Read each problem carefully. 1.Speedy Sabrina runs a mile in 6.4 minutes. If she continues at this pace, how long will it take her to run 9.7 miles? ________________ 2.Fast Fred runs a mile in 6.04 minutes. If he continues at this pace, how long will it take him to run 11.1 miles? ________________ 3.Vincenzo ordered 9 veggie burgers to share with his victorious volleyball teammates. Each one costs $6.98. What’s the total price of the burgers? ________________ 4.Annabelle and 15 of her friends went to the movies. Each ticket cost $9.50, and everyone paid $2.95 for their own bag of popcorn. What was the total cost for the movie tickets and popcorn? ________________ 36 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 31 Dividing With Mental Math and Estimation Name Date Division Detective Use mental math and compatible numbers to estimate each quotient. 1. 2,157 ÷ 5 = __________________________ 2. 4,851 ÷ 7 = __________________________ 3. 80,026 ÷ 90 = __________________________ 4. 3,579 ÷ 68 = __________________________ 5. 5,513 ÷ 66 = __________________________ 6. 630,792 ÷ 79 = __________________________ 7. 621,004 ÷ 7 = __________________________ 8. 3,507 ÷ 313 = __________________________ 9. 395,122 ÷ 42 = __________________________ 10.31,512 ÷ 50 = __________________________ 11.16,123 ÷ 801 = __________________________ 12.420,045 ÷ 21 = __________________________ 37 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 32 Dividing Multi-Digit Whole Numbers Name Date Name That Quotient! Solve each division problem. 1. _____ 34 ) 5,777 2. _____ 15 ) 1,634 3. _____ 759 ) 2,710 4. _______ 72 ) 72,072 38 5. _______ 82 ) 36,389 6. _______ 57 ) 28,671 7. _______ 514 ) 88,408 8. _______ 45 ) 45,145 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 33 Dividing Multi-Digit Whole Numbers/Word Problems Name Date Dive Into Division! Solve each word problem. Show your work in the tank. 1. Juan is training to run a marathon. He is supposed to run 336 miles in 14 weeks. If he runs the same number of miles each week, how many miles will he run each week? THINK TANK ___________________ 2.Luigi’s Pizzeria puts 18 slices of pepperoni on each pepperoni pizza that is ordered. They used up all 1,746 slices of pepperoni they had one week. How many pepperoni pizzas did they make that week? THINK TANK ___________________ 39 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 34 Dividing Decimals by Whole Numbers Name Date Pointy Decimal Points! Watch out for the pointy porcupine! See how sharp your decimal division skills are by solving three problems in a row to get Tic-Tac-Math! 306.324 2216.72 14 114.8 50 1.515 60 96.66 25 201.5 37 9.287 41 82.82 86 137.6 40 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 35 Dividing by Whole Numbers/ Word Problems Name Date Snazzy Skis Fill in words and numbers as directed. Then solve the problem. I love skiing, especially on Mount (name of a place) . To get ready for my ski trip there next week, I packed long and warm . I asked my friend (type of clothing) (first name of a girl) I wanted them to be and (color) to help me get my skis ready by painting them! , (color) so ve Sol s! Thi meters all over. Believe me, these skis look (plural noun) (adjective) (decimal consisting of even digits) to finish it because we painted a (amount of time) cool pattern of , (color) . I did one ski by myself, and then we split the painting on the other ski evenly. The ski is long. It took us (type of clothing) , everyone will want to know where I got them! How much of the ski did each person paint? Answer with a decimal. 41 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 36 Dividing Decimals by Decimals Name Date What is a giraffe after it is three days old? Divide. Solve the riddle using your answers. 6.8 40.12 0.9 8.73 8.3 39.01 7.4 64.38 S 1.2 3.36 O D 5.4 18.09 A 9.3 73.47 8.7 4.1 84.87 U 3.1 7.13 T 5.2 30.42 F 2.9 20.30 Solve the Riddle! 3.35 Y 2.2 76.23 E R I L Write the letter that goes with each answer. 3.35 5.9 7 9.7 2.3 20.7 . 4.7 7.9 2.8 5.9 42 9.7 34.65 4.7 100 Math Practice Page, Grade 6 © 2015 • Scholastic Teaching Resources 37 Dividing Decimals by Decimals/ Word Problems Name Date Dare to Divide Decimals! D on’t try this stunt at home! Instead, divide decimals to solve these word problems! 3.9 ÷ 0.15 1.Franny gave out 26.4 pounds of delicious lemon squares to her family and friends. She gave each person a 0.4-pound portion. How many portions did Franny give out in all? ________________ 2.Hortence has 12.75 yards of ribbon, which she plans to cut into even strips of 0.75-yards. How many strips will she have? ________________ 3.Andy had 6.48 pounds of jelly beans, which he divided evenly into 0.06-pound bags. How many bags did he need? ________________ 4.Gina made 8.5 pounds of fudge, which she was putting into .75-pound bags to sell at the school bake sale. How many bags of fudge can she fill? How much fudge will she have left over? ________________ 43 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 38 Adding Mixed Numbers Name Date Home Sweet Home Scientists estimate that Earth may be home to up to 30 million different kinds of plants and animals. What word describes this amazing variety of life on our planet? Answer: ____________________________________________________________ 7 7 4 1 7 2 5 3 1 7 9 1 ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ 9 ___ 24 10 18 7 15 14 4 10 18 12 9 7 6 12 10 9 3 10 18 9 14 11 20 To answer the question, add the mixed numbers below. Be sure your answers are simplified. Write the letter of the problem in the space above its answer. Hint: One letter will be used more than once. Some letters will not be used. E. 1 5 5 4 –— 7 –— 2 –— 3 V. 9 I. 9 1 2 5 + 3 –— + 4 –— + 7 –— 2 3 6 _____________________ S. 1 2 3 3 –— 6 –— 4 –— 2 B. 3 O. 5 5 5 2 + 5 –— + 2 –— + 2 –— 6 8 3 _____________________ Y. 3 5 1 1 –— 5 –— 4 –— 4 J. 6 R. 2 3 1 4 + 9 –— + 2 –— + 7 –— 10 3 5 _____________________ T. 3 5 7 3 –— 7 –— 4 –— 7 M. 8 D. 12 3 1 2 + 6 –— + 3 –— + 9 –— 14 2 3 _____________________ 44 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 39 Adding Mixed Numbers/ Word Problems Name Date Frida’s Fractions Solve each word problem. Write all answers in simplest form. Show your work in the tank. 3 1. Frida was 48 ___ 4 inches tall on her birthday last year. This year 6 she grew 1 ___ 8 inches more. How tall is she now? ___________________ THINK TANK 2. O n Monday morning, 1 Frida walked 5 ___ 3 miles. On Wednesday morning 3 she walked 6 ___ 4 miles, and on Friday morning 7 she walked 5 ___ 8 miles. How many miles did she walk altogether? THINK TANK ___________________ 45 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 40 Subtracting Fractions and Mixed Numbers Name Date Fraction Leftovers What’s left over when you subtract these fractions and mixed numbers? Solve three problems in a row to get Tic-Tac-Math! Write all answers in simplest form. 3 ___ 4 – 7 1 ___ 4 1 3 1 ___ 7 ___ 5 – 3 5 = 2 ___ 9 ___ 4 – 3 2 = ___ 6 ___ 10 – 3 5 = 7 3 = 5 ___ 10 ___ 8 – 5 8 = 3 5 – 1 ___ 5 = 46 7 ___ – 8 3 ___ 16 5 = 5 ___ 6 ___ 12 – 5 12 = 2 17 ___ 3 – 6 ___ 15 = 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 41 Subtracting Mixed Numbers Name Date Ancient Doctor This man studied diseases and the human body nearly 2,500 years ago. He is often called the “father of medicine.” Who was this man? Answer: _______________________________________________________ 5 5 1 1 1 3 1 7 3 7 7 ___ ___ ___ ___ ___ ___ ___ __ ___ ___ 5 ___ 12 5 6 4 3 4 3 4 24 3 4 3 10 4 8 5 10 5 8 4 9 To answer the question, add the mixed numbers below. Be sure your answers are simplified. Write the letter of the problem in the space above its answer. Hint: One letter will be used more than once. Some letters will not be used. R. 4 5 1 9 –— 9 –— 8 –— 5 E. 8 H. 6 7 3 3 – 6 –— – 3 –— – 2 –— 10 4 4 _____________________ C. 5 1 6 –— 11 –— 12 P. 5 2 O.12 –— 3 2 13 5 – 2 –— – 6 –— – 8 –— 3 15 8 _____________________ D. 1 1 8 –— 7 S. 7 –— 2 N. 3 5 3 5 – 3 –— – 4 –— – 2 –— 6 4 9 _____________________ 1 3 1 T. 14 –— 7 –— 11 –— 2 A. 8 I. 10 1 1 4 – 9 –— – 2 –— – 5 –— 5 2 15 _____________________ 47 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 42 Subtracting Fractions and Mixed Numbers/Word Problems Name Date Weekend Math Solve each word problem. Write all answers in simplest form. Show your work in the tank. 1.Derek was building a tree house. He intended to cut a piece of wood 5 5 ___ 8 inches long. By mistake, he cut a piece 1 4 ___ 4 inches long. How much shorter was the piece than it was supposed to be? THINK TANK ___________________ 2.Maxine was planning 1 to run 10 ___ 4 miles on Saturday. She ran 4 3 ___ 5 miles before twisting her ankle. How many miles was Maxine short of her goal? THINK TANK ___________________ 48 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 43 Adding and Subtracting Mixed Numbers/Word Problems Name Date Taryn’s Fractions F ractions play an important part in Taryn’s life. Solve the following problems. Simplify your answers. 1 1.Last week Taryn biked 2 2 miles on Monday, 1 3 3 4 miles on Wednesday, 2 8 miles on Saturday. How far did she bike in all last week? ________________ 1 2.Aunt Inez’s recipe for punch called for 4 2 quarts of apple cider. When Taryn decided to make her 2 aunt’s punch, she had only 3 3 quarts of cider. How much more did she need? ________________ 3.Taryn tries to volunteer 6 hours each week at the 1 animal shelter. Last week she worked 1 2 hours 3 at the shelter on Tuesday and 3 4 hours on Thursday. By how much did he fall short of her goal last week? ________________ 4.Sal and Taryn grew bean plants for a science experiment. At the beginning of the month, Sal’s 1 1 plant was 3 4 inches tall and Taryn’s was 2 4 inches 1 tall. Two weeks later, Sal’s plant was 4 2 inches tall 7 and Taryn’s was 3 8 inches tall. Whose plant grew more during that two-week period? ________________ By how much? ________________ 49 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 44 Multiplying Whole and Mixed Numbers Name Date What should you do if a lion takes your pen? Multiply. Rename the answers in lowest terms. Solve the riddle using your answers. 3 4 1 2 1 3 8 x 2 = 3 9 x 4 = 11 12 x 3 = 5 8 x 5 = 4 6 x 4 = P 12 14 2 x 5 C 3 x 2 A 5 x 2 E 3 x 3 I Solve the Riddle! 3 8 3 x 4 13 1 8 1 8 = 4 10 = 6 12 = 4 5 = 2 7 = U L N S R Write the letter that goes with each answer. 5 3 4 6 3 4 50 13 1 8 7 1 2 17 1 3 6 2 3 10 4 5 . 100 Math Practice Page, Grade 6 © 2015 • Scholastic Teaching Resources 45 Multiplying Fractions and Mixed Numbers Name Date Recipe for Multipli-Fractions G et cooking on solving these fraction multiplication problems. Simplify your answers. 3 8 x 31 = 6. 2 1 x 33 = 4 5 x 1 = 7. 11 12 6 11 x 5 = 8. 2 2 x 36 = 4 2 x 82 = 1. 3 2. 3 3. 6 2 5 x 34 = 9. 5. 31 x 61 = 10. 4. 7 2 5 2 51 2 8 x 3 15 = 3 10 7 12 12 x 2 5 = 9 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 46 Multiplying Mixed Numbers Name Date A Traffic Stopper! In response to growing traffic problems, this African American invented the automatic traffic signal in 1923. What was this man’s name? Answer: ______________________________ _____ . 1 1 1 1 1 4 1 ___ ___ ___ ___ ___ ___ ___ 6 2 10 2 8 3 8 3 5 4 8 5 10 2 ______________________________ 1 1 1 1 1 8 ___ ___ ___ ___ ___ ___ 3 2 2 4 8 3 6 2 10 2 3 9 To answer the question, multiply the mixed numbers below. Be sure each answer is simplified. Write the letter of the problem in the space above its answer. Hint: Some letters will be used more than once. Some will not be used. 2 N. 1 2 ___ 3 2 x 1 ___ 3 = T. 2 ___ 3 3 x 3 ___ 10 = R. 3 3 ___ 4 2 x 2 ___ 9 = S. 2 4 ___ 5 3 x 3 ___ 4 = L. 1 1 ___ 4 2 x 1 ___ 5 = A. 1 2 ___ 3 1 x 4 ___ 2 = G. 2 ___ 10 1 x 2 ___ 2 = H. 1 1 ___ 3 1 x 1 ___ 2 = M. 1 1 ___ 2 1 x 2 ___ 3 = O. 1 1 ___ 2 1 x 1 ___ 2 = J. 1 3 ___ 3 3 x 1 ___ 4 = E. 3 4 ___ 8 1 x 1 ___ 5 = 6 52 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 47 Multiplying Mixed Numbers/ Word Problems Name Date Morning Math Solve each word problem. Write all answers in simplest form. Show your work in the tank. 1.A pancake recipe calls 3 for 2 ___ 4 cups of flour. If James triples the recipe, how much flour will he use? ___________________ THINK TANK 2.Patrice usually walks 1 1 ___ 2 miles each morning. But yesterday, she 1 walked only ___ 3 as far. How far did Patrice walk yesterday? ___________________ THINK TANK 53 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 48 Dividing Fractions by Fractions Name Date How is 2 + 2 = 5 like your left hand? Divide. Rename the answers in lowest terms. Solve the riddle using your answers. 1 2 ÷ 5 3 ÷ 7 12 ÷ 3 10 ÷ 2 3 ÷ 3 8 ÷ 6 9 = 2 3 = 3 4 = 1 8 = 4 5 = 1 3 = R L S H N G Solve the Riddle! 9 10 1 3 4 ‘ 7 9 3 5 ÷ 5 9 ÷ 1 6 ÷ 1 5 ÷ 1 4 ÷ 3 7 ÷ 4 6 = 5 8 = 1 4 = 2 5 = 1 7 = 1 2 = I W O C T B Write the letter that goes with each answer. 5 6 2 3 1 3 4 54 3 4 9 10 1 1 8 2 2 5 1 3 4 . 100 Math Practice Page, Grade 6 © 2015 • Scholastic Teaching Resources 49 Dividing Fractions by Fractions Name Date I Will Divide This Fraction in Half! Y ou don’t have to be a magician to divide fractions. Simply solve these problems! Express answers in simplest form. 1. 1 2 ÷ 1 = 7. 1 2 ÷ 1 = 2. 2 5 ÷ 1 = 8. 2 5 ÷ 1 = 3. 3 9 ÷ 2 = 9. 6 8 ÷ 3 = 4. 1 2 ÷ 1 = 10. 9 10 ÷ 6 = 5. 1 3 ÷ 2 = 11. 1 8 ÷ 1 = 6. 5 8 ÷ 5 = 12. 1 11 ÷ 1 = 2 8 5 8 3 8 55 4 10 8 7 5 6 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 50 Dividing Fractions by Whole Numbers/Word Problems Name Date Summer Camp Fill in words and numbers as directed. Then solve the problem. I went with my friend (first name of a boy) to a summer camp called Camp (adjective) . The camp leader, (noun) at the entrance to welcome us. We got to do like in (present-tense verb) and We were assigned to the stuff (adjective) (present-tense verb) and hike across (body of water) , was (name of a famous person) (type of animal) . We could swim (name of a place) . Patrol Tent. By the time we checked in, the tent was mostly full with other campers. There was only of the space left for us to sleep in. We split it up (choose a number: 1 — 2 , 1 — 3 , or 1 — 4 ) evenly though. I had plenty of room for my sleeping bag and my favorite (noun) ve Sol s! Thi , as well as my bag of (plural noun) . What fraction of the remaining tent space did each boy get for sleeping? 56 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 51 Dividing Mixed by Whole Numbers Name Date How is a teacher like an eye doctor? Divide. Rename the answers in lowest terms. Solve the riddle using your answers. 9 7 2 3 5 1 1 2 ÷ 3 = 1 7 ÷ 5 = 6 9 ÷ 4 = 1 3 ÷ 2 = 1 4 ÷ 7 = 1 2 ÷ 5 = 8 O 1 M 3 I 6 E 5 L 2 B Solve the Riddle! 3 10 3 1 1 6 1 4 3 4 ÷ 2 = 6 9 ÷ 5 = 4 5 ÷ 2 = 1 4 ÷ 5 = 2 3 ÷ 4 = 4 7 ÷ 3 = S H A P T U Write the letter that goes with each answer. 1 5 12 6 7 1 3 1 1 1 4 2 3 57 5 12 1 3 4 2 3 4 4 3 8 3 8 . 1 5 12 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 52 Dividing Mixed Numbers Name Date A Famous Toy In 1945, this man invented the Slinky. In 2000, the Slinky was placed in the National Toy Hall of Fame in Salem, Oregon. Who invented this famous toy? Answer: ___________________________________ _________________________ 1 3 4 5 3 1 3 3 3 3 1 2 ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 1 4 4 4 2 9 2 7 2 4 1 4 1 4 2 20 2 4 1 7 2 2 4 3 1 6 ___ 2 To answer the question, divide the mixed numbers below. Be sure your answers are simplified. Write the letter of the problem in the space above its answer. Hint: Some letters will be used more than once. Some will not be used. H. 1 1 ___ 9 ___ 2 ÷ 3 2 = M. 1 3 ___ 2 ___ 2 ÷ 1 4 = S. 1 3 ___ 17 ___ 2 ÷ 3 4 = T. 1 2 ___ 7 ___ ÷ 2 3 5 = D. 5 1 ___ 5 ___ ÷ 3 6 3 = E. 1 1 ___ 6 ___ ÷ 2 4 2 = Y. 1 4 ___ 11 ___ ÷ 1 4 5 = I. 1 1 ___ 6 ___ ÷ 1 3 3 = J. 3 1 ___ 5 ___ ÷ 2 8 2 = C. 1 1 ___ 5 ___ 2 ÷ 2 4 = A. 2 1 ___ 3 ___ 3 ÷ 1 3 = R. 2 1 ___ 6 ___ 3 ÷ 5 3 = 58 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 53 Converting Fractions to Decimals Name Date When should you bring your dad to school? Rename each fraction as a decimal. Solve the riddle using your answers. 2 4 3 717 1000 = 3 10 = 833 1000 = 70 100 = 95 100 = 7 100 = 1 Q P F R 7 Y 0.833 7.2 = 47 100 = 1 1000 = 5 100 = U T Z I 31 1 1000 = A Solve the Riddle! 3 100 2 10 D = O Write the letter that goes with each answer. 4.7 0.717 3.95 1.03 0.05 59 2.3 7.2 2.3 0.001 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 54 Converting Decimals to Percents Name Date Peanuts This African-American agricultural researcher discovered over 300 uses for the peanut. What was his name? Answer: _____ _____ _____ _____ _____ _____ 12.5% 375% 50% 3% 12.5% 375% _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ 110% 75% 10% 37.5% 20% 8% 12.5%245% 50% 8% ______________________________ 60% 75% 3% 120% 375% 3% To answer the question, convert each decimal to its equivalent percent. Write the letter of the each problem in the space above its answer. Hint: Some letters will be used more than once. Some will not be used. S. 0.10 = _______ B. 1.0 = _______ N. 0.08 = _______ L. 0.92 = _______ I. 0.2 = _______ H. 0.375 = _______ O. 0.500 = _______ C. 0.6 = _______ M. 0.64 = _______ R. 0.030 = _______ V. 1.2 = _______ W. 1.1 = _______ A. 0.75 = _______ G. 0.125 = _______ T. 2.45 = _______ E. 3.75 = _______ 60 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 55 Converting Fractions to Percents Name Date What did the doctor tell the little monster? Name the fraction that is shaded. Then rename the fraction as a percent. Solve the riddle using your answers. Solve the Riddle! 50% 1 10 30% Fraction Percent T Y S U E R O A N M G D Write the letter that goes with each answer. 9 10 70% 30% 61 7 10 – 3 10 1 10 60% 7 10 ! 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 56 Mixed Practice Name Date We’re All Equal! Fractions, decimals, and percents all express parts of a whole. Solve three problems in a row to get Tic-Tac-Math! What is the decimal 1 ___ equivalent of 4 ? 5 ___ 8 What is the percent equivalent equivalent of 0.6 of (in simplest form)? Which is greatest? Circle. 40% What is the fraction 0.6 Which is least? Circle. 1 ___ 5 15% 7 ___ 10 ? Which is greatest? Circle. 0.1 8 ___ 35% 25 2 ___ 5 0.39 Order the set from least to Order the set from greatest Order the set from least to greatest: to least: greatest: 7 ___ 0.38 24% 0.74 47.5% 0.48 0.55 1 ___ 45% 1 ___ 9.8% 3 ___ 0.52 1 ___ 3 ___ 0.6 1 ___ 0.35 0.05 25% 20 8 2 10 62 5 10 3 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 57 Calculating Percents Name Date Quilt Math This quilt is made of 25 square sections sewn together. The quilt represents one whole. Use the quilt to answer the questions. What percent is represented by 1. the dotted sections? ___________ 2. the starred sections? ___________ 3. t he dotted, starred, and circle sections? ___________ 4. all the sections? ___________ 5. all but the sections with crossed lines? ___________ 6. 1 quilt plus all the dotted and circle sections? ___________ 63 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 58 Calculating Percents Name Date Elementary, My Dear Watson “Elementary, my dear Watson” was the way the famous fictional detective Sherlock Holmes would begin his explanation of how a crime was committed. Who was the author of the Sherlock Holmes mysteries? Answer: _____ _____ _____ _____ _____ _____ 195 381.9 184 16.8 46 381.9 _____ _____ _____ _____ _____ 195 57.6 83.6 20.16 57.6 _________________________ 84.24 20.16 111 70.68 25.9 To answer the question, find the percent of each number. Write the letter of each problem in the space above its answer. Hint: Some letters will be used more than once. Some will not be used. H. 20% of 84 = _____________ N. 12% of 480 = _____________ L. 76% of 93 = _____________ K. 36% of 140 = _____________ E. 35% of 74 = _____________ Y. 50% of 222 = _____________ S. 75% of 150 = _____________ C. 110% of 76 = _____________ U. 46% of 100 = _____________ R. 95% of 402 = _____________ T. 92% of 200 = _____________ A. 125% of 156 = _____________ I. 25% of 112 = _____________ D. 27% of 312 = _____________ O. 6% of 336 = _____________ 64 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 59 Calculating Percents/ Word Problems Name Date Percent Power! Solve each word problem. Show your work in the tank. 1.Elizabeth collected baseball caps. She had 360 of them altogether. 18 of them had no writing on them. What percent of her caps had no writing on them? THINK TANK ___________________ 2.Antoine read 243 of the 675 pages of Invasion of the Smelly Jelly Rolls before his mom told him to turn off the lights and go to sleep. What percent of the book did he read? THINK TANK ___________________ 65 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 60 Calculating Percents/ Word Problems Name Date The Class Picnic L uis volunteered to work with his class Picnic Committee. Solve the following percent problems related to the picnic. 1.Based on the attendance at past picnics, Luis expects 95% of the students in his class to attend this year’s picnic. If 120 students are in the class, how many students are likely to attend the picnic? ________________ 2.When polled to find out if they preferred hamburgers or hot dogs, all 120 students in the class responded. Sixty-five percent said they preferred hamburgers, while the rest preferred hot dogs. The Picnic Committee decided to order 2 hamburgers or 2 hot dogs for each student, based on the students’ choices. How many hamburgers were ordered? ________________ How many hot dogs w ere ordered? ________________ 3.When asked if they preferred fruit juice or spring water, all 120 students answered. Fifty-five percent preferred juice, and 45% preferred spring water. The committee decided to order the equivalent of 3 cups of juice for each student who preferred juice. How many gallons of juice should the committee order? (16 cups equal 1 gallon. Round up when necessary.) ________________ The committee decided to order 2 bottles of spring water for each student who preferred water. How many bottles should they order? 66 ________________ 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 61 Calculating Percents/ Word Problems Name Date Which paddle should I use in my kayak? Solve the problems. Solve the riddle using your answers. $10 20% off $10 40% off $40 20% off $20 30% off $15 50% off $6 10% off Solve the Riddle! $14.00 $6.00 $7.50 The $10 headphones are 20% off. Now how much is each pair of headphones? R The $10 picture frames are 40% off. Now how much is each frame? I The $40 bike helmets are 20% off. Now how much is each helmet? H The $20 DVDs are 30% off. Now how much is each DVD? E The $15 mugs are 50% off. Now how much is each mug? T The $6 paint sets are 10% off. Now how much is each paint set? O Write the letter that goes with each answer. $32.00 $14.00 67 $8.00 $5.40 $8.00 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 62 Identifying Decimal Patterns Name Date Going Up? Although primitive elevators operated by human or animal power were in use over 2,000 years ago, the modern elevator can trace its roots to the invention of the elevator brake in 1853. Who was the inventor of the elevator brake? Answer: _____ _____ _____ _____ _____ _____ 12.5 2.250.1251.75 0.5 0.3 _____ _____ _____ _____ _____ __________ _____ _____ _____ 0.025 21.50.6 12.5 1.750.16 2.4 0.125 1.75 To answer the question, complete each pattern by writing the missing decimal. Then write the letter of the missing decimal in the space provided for that decimal above. Hint: Some letters will be used more than once. One letter will not be used. 1 0, 0.2, 0.4, 2 0.9, 1.4, 1.9, 3 4.0, 3.25, 2.5, 4 1.5, 1.75, 2, 5 0, 0.25, 0.75, 6 5.0, 4.5, 3.5, 7 0.1, 0.5, 2.5, , 2.9 8 1.6, 0.4, 0.1, ,1 9 0.125, 0.25, 0.5, , 2.5 10 0.125, 0.25, 0.375, , 2.5 11 0.01, 0.04, 0.09, ,0 12 1.0, 0.5, 0.25, , 0.8 V T S L A R 68 , 62.5 E , 0.00625 G ,2 P H O I , 0.0625 , 0.25 , 0.0625 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 63 Identifying Decimal Patterns Name Date Three Cheers for Decimal Patterns! Hip-hip-hooray! These girls are rooting for you to solve three pattern problems in a row and get Tic-Tac-Math! Find the next three numbers Find the next three numbers Find the next three numbers in in the pattern below. Then in the pattern below. Then the pattern below. Then explain explain the pattern in words. explain the pattern in words. the pattern in words. 5.1, 5.2, 5.3 10.75, 10.65, 10.55 9.1, 8.8, 8.5, 8.2 ____, ____, ____ ____, ____, ____ ____, ____, ____ Find the next three numbers Find the next three numbers Find the next three numbers in the pattern below. Then in the pattern below. Then in the pattern below. Then explain the pattern in words. explain the pattern in words. explain the pattern in words. 0.2, 7.9, 15.6, 23.3 0.2, 0.22, 0.24, 0.26 0.07, 0.08, 0.09 ____, ____, ____ ____, ____, ____ ____, ____, ____ Find the next three numbers Find the next three numbers Find the next three numbers in in the pattern below. Then in the pattern below. Then the pattern below. Then explain explain the pattern in words. explain the pattern in words. the pattern in words. 0.5, 0.05, 0.005 0.2, 0.6, 1.8 8.25, 7.65, 7.05 ____, ____, ____ ____, ____, ____ ____, ____, ____ 69 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 64 Identifying Fraction Patterns Name Date A Very Short River At just 201 feet in length, the shortest river in the world is located in this western state. What is the name of the river and in what state is it located? Answer: _____ _____ _____ 1 ___ 11 16 ___ 20 River, 4 ___ 8 _____ _____ _____ _____ _____ _____ _____ 2 ___ 5 16 ___ 20 1 ___ 81 1 ___ 16 3 1 ___ 81 3 To answer the question, complete each pattern by writing the missing fraction. Then write the letter of the missing fraction in the space above the fraction. Hint: Some letters will be used more than once. Some will not be used. 1 1 ___ 2 ___ 3 ___ 2 , 4 , 6 , 2 1 1 ___ ___ 2 , 1, 1 2 , 3 1 ___ 1 ___ 1 ___ 5 , 7 , 9 , 4 1 ___ 3 ___ 5 ___ 2 , 4 , 6 , 5 4, 3 3 , 3 3 , 2 ___ 5 ___ E 6 3 1 3 ___ ___ ___ 4 ,2 4 ,1 4 , ,2 2 7 1 ___ 1 ___ 1 ___ 3 , 9 , 27 , , 13 1 ___ 8 1 ___ 1 ___ 3 ___ 10 , 5 , 10 , 9 ___ 9 1 ___ 1 ___ 1 ___ 1 , 4 , 9 , 10 1 ___ 4 ___ 9 ___ 5 , 10 , 15 , , 10 1 ___ I R B 1 ___ , 10 2 ___ A ,2 3 , 70 3 ___ D ,2 4 1 ___ N , 243 1 ___ M , 2 1 ___ T O , 25 ,1 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 65 Identifying Fraction Patterns Name Date I Detect a Pattern Look for clues to help you uncover the next numbers in each pattern. Solve three pattern problems in a row to get Tic-Tac-Math! Find the next three numbers Find the next three numbers Find the next three numbers in the pattern below. Then in the pattern below. Then in the pattern below. Then explain the pattern in words. explain the pattern in words. explain the pattern in words. 1 ___ 8 , 3 ___ 8 , 5 ___ 8 , 7 ___ 4 ___ 8 3 ____, ____, ____ , 7 ___ 3 , 1 ___ 10 ___ 3 2 ____, ____, ____ , 1 ___ 4 1 ___ , 8 , 1 ___ 16 , 1 ___ 32 ____, ____, ____ Find the next three numbers Find the next three numbers Find the next three numbers in the pattern below. Then in the pattern below. Then in the pattern below. Then explain the pattern in words. explain the pattern in words. explain the pattern in words. 3 ___ 7 , 3 ___ 14 , 3 ___ 28 , 3 ___ 1 1 ___ 3 ___ 2 ___ 4 , 2, 1 4 56 ____, ____, ____ 5 ____, ____, ____ , 4 ___ 5 , 2 ___ 5 , 1, 3 ___ 5 1 ___ ,15 ____, ____, ____ Find the next three numbers Find the next three numbers Find the next three numbers in the pattern below. Then in the pattern below. Then in the pattern below. Then explain the pattern in words. explain the pattern in words. explain the pattern in words. 3 1 2 1 ___ ___ ___ 2 ___ 5 , 2 5 , 2 5 , 2, 2 5 3 5 1 3 ___ ___ ___ 3 ___ 8 , 3 8 , 3 2 , 3 4 , 5 ____, ____, ____ 7 1 ___ 3 , 2 ___ 3 1 ___ 2 ___ 1 ___ ,13,23,53 3 ___ ___ 3 ___ 8 , 3 8 , 3 4 , 4 ____, ____, ____ ____, ____, ____ 71 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 66 Factors, Primes, and Greatest Common Factor Name Date The Factor Factory T here’s a lot happening in the Factor Factory! It’s time to get to work solving these problems! 1. List all of the factors of 8 from least to greatest. ____________________ 2.List all of the factors of 14 from least to greatest. ____________________ 3.List all of the factors of 30 from least to greatest. ____________________ 4.Circle the prime numbers. 7 5.Circle the prime numbers. 39 9 15 53 21 47 35 29 37 33 41 6.List all of the prime numbers between 70 and 99. ____________________ 7.What is the greatest common factor of 8 and 12? ____________________ 8.What is the greatest common factor of 27 and 9? ____________________ 9.What is the greatest common factor of 45 and 60? ____________________ 10.What is the greatest common factor of 39, 78, and 104? ____________________ 72 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 67 Multiples and Least Common Multiple Name Date Mad About Multiples! Do you find multiples mesmerizing? Solve three problems in a row to get Tic-Tac-Math! Which of the following are Which of the following are Which of the following are multiples of 5? multiples of 6? multiples of 3? 20 52 23 35 30 18 30 25 16 29 24 78 31 52 102 What is the least common What is the least common What is the least common multiple of 7 and 4? multiple of 24 and 12? multiple of 15 and 21? Two dogs are sitting next to Barney and Julia are both Glenda and Penny are doing each other. Starting now, one very tired. Starting now, a sack race. Glenda jumps dog will bark every 3 seconds Barney will yawn every 8 forward 18 inches each time and the other dog will bark seconds and Julia will yawn she jumps. Each of Penny’s every 5 seconds. When is the every 4 seconds. When is the hops is 15 inches. How far from next time both dogs will bark next time both of them will the starting line will it be when at the same time? yawn at the same time? Glenda and Penny have both traveled the same distance? 73 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 68 Exponents Name Date The Power of Exponents Complete each set of problems below. 1. Write each power of 10 in standard form. 103 = ________________________________100 = ________________________________ 107 = ________________________________108 = ________________________________ 10 4 = ________________________________101 = ________________________________ 102 = ________________________________106 = ________________________________ 2. Write each as a power of 10. 100 = _______________________________ 1 = __________________________________ 10,000 = ____________________________ 1,000,000 = _________________________ 1,000 = _____________________________ 10,000,000 = ________________________ 3. Write each in standard form. (9 × 104) + (6 × 102) ___________________________________________________________ (3 × 105) + (2 × 104) + (7 × 102) ________________________________________________ 4. Write each number in expanded form using exponents. 1,005 _____________________________________________ 216 _______________________________________________ 42,906 ____________________________________________ 74 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 69 Exponents Name Date Underwater Exponents The largest freshwater fish in the world is found in Asia. It can grow to be 10 feet long and weigh as much as 1,600 pounds. What is the name of this fish? Answer: _____ _____ _____ _____ _____ _____ _____ 32 1610081343144343 _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ 64 0 243243125343 36 100144 16 To answer the question, find the value of each expression. Write the letter of the problem in the space above its answer. Hint: Some letters will be used more than once. Some will not be used. H. 24 = _____________ P. 43 = _____________ N. 92 = _____________ I. 102 = _____________ E. 73 = _____________ F. 62 = _____________ G. 33 = _____________ C. 25 = _____________ L. 53 = _____________ S. 122 = _____________ M. 28 = _____________ A. 05 = _____________ Y. 23 = _____________ O. 36 = _____________ D. 35 = _____________ 75 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 70 Identifying Properties Name Date Property Hunt Name the property shown. Write commutative, associative, identity, or distributive. 1. 4 + 7 = 7 + 4 ______________________________________ 2. (3 + 8) + 6 = 3 + (8 + 6) ______________________________________ 3. 8 × 1 = 8 ______________________________________ 4. –17 + 0 = –17 ______________________________________ 5. 3 × (8 + 7) = (3 × 8) + (3 × 7) ______________________________________ 6. 315 × 1 = 315 ______________________________________ 7. 1 + (2 + 9) = 2 + (1 + 9) ______________________________________ 8. –24 + 0 = –24 ______________________________________ 9. 52 + 70 = 70 + 52 ______________________________________ 10. 2 × (9 + 4) = (2 × 9) + (2 × 4) ______________________________________ 76 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 71 Order of Operations Name Date Time for Fun The oldest amusement park in the United States dates back to 1846 in Bristol, Connecticut. What is the name of this amusement park? Answer: _____ _____ _____ _____ 20351511 _____ _____ _____ _____ _____ _____ _____ _____ _____ 040216401033011 To answer the question, solve the following equations. Write the letter of each equation in the space above its answer. Hint: Some letters will be used more than once. Some will not be used. E.3(4 + 1) – 4 = ____________ A.5(6 – 3) + 2(2 + 8) ÷ (6 – 5) = ____________ M.6(3 + 4) ÷ 2 = ____________ O.3(2 + 6) + 4(7 – 3) = ____________ N.3 + 6(2 + 3) = ____________ R.(14 ÷ 2) – (6 – 2) = ____________ K.2(12 ÷ 3) + 7 = ____________ U.4(2 + 3) ÷ (4 – 2) = ____________ C.2(12 ÷ 3) – 8 = ____________ S.8(4 + 2) ÷ (2 × 6) = ____________ L.9 – (3 – 2) + (3 × 4) = ____________ P.2 + 7 – (8 ÷ 4) – 1 = ____________ 77 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 72 Order of Operations C Name Date What’s Your Order? omplete each equation by filling in the missing number. Remember to use the order of operations. 1. (2 + ______) x (3 – 1) = 16 2. ______ (5 – 2) = 15 3.(32 ÷ 4) – (2 x ______) = 0 4.______ (6 + 2) ÷ (6 – 3) = 8 5. 9 + (______ x 2) – 6 = 17 6.3(25 ÷ 5) + (8 ÷ ______) = 19 7. ______ – (4 x 2) x (6 – 2) = 6 8.32 ÷ ______ + 3(7 + 2) = 31 9. (27 – 11) ÷ 2(______ – 10) = 4 10. 4( ______ – 5) x 2(5 – 4) = 48 11. 4(3 – 1) + 5(______ – 7) = 38 12. 3(14 – 6) + 8(6 – ______) ÷ (16 ÷ 2) = 8 78 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 73 Writing Expressions Name Date Express Yourself Write each expression as an algebraic expression. Use n as the variable. 1. a number increased by 7 ________________________________________ 2. a number decreased by 2.8 ________________________________________ 3. eight more than a number squared ________________________________________ 4. the product of a number and 12 ________________________________________ 5. 3 more than twice a number ________________________________________ 6. three times a number decreased by 42 ________________________________________ 7. 5 less than twice a number ________________________________________ 8. the sum of 8.5 and 2.5 times a number ________________________________________ 9. a squared number multiplied by 45 ________________________________________ 10. 10 more than a number ________________________________________ 11. a number decreased by 6 ________________________________________ 12. a number divided by 4 ________________________________________ 79 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 74 Writing Expressions/ Word Problems Name Date Onion Cooking Contest Fill in words and numbers as directed. Then solve the problem. C hef just held her (first and last name of a girl) First Annual Onion Cooking Contest. She had onions, and there were three contestants: (first and last name of a boy or girl) , and (triple-digit number) (first and last name of a boy or girl) (name of a famous person) contestant had to create a delicious and , . Each (adjective) onion dish using onions, of course, along with other ingredients like and (plural noun) used for (single-digit number greater than 1) (type of substance) . Each contestant onions per hour. The contestants cooked hours. The chef sampled each dish and (single-digit number greater than 1) finally awarded the prize to the contestant who prepared Baked Onions With Sauce. The prize was an all-expenses-paid trip (noun) to (name of a place) ve Sol s! Thi . Write an expression that describes how to find the number of onions left. 80 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Writing Expressions/ Word Problems 75 Name Date A Very Cold Day The lowest temperature ever recorded on Earth occurred at a Russian station in Antarctica. On July 21, 1983, the temperature fell to -128.6°F. What was the name of this Russian station? Answer: _____ _____ _____ _____ _____ _____ 123456 Answer Box To answer the question, write an algebraic expression for each word problem. Find your answers in the Answer Box, then write the letter of each answer in the space above its problem number. Hint: Some letters will not be used. 1 J. 150 + n O.50n K. 2n + 3 V. 150 ÷ n O. n + 25 U. n ÷ 150 T. 150 – n H.2n – 3 R.25n S.3n 4 Keri divided her collection of 150 stamps equally into n categories. Write an expression to show the number of stamps in each category. Juan and his two sisters are saving money for a new stereo, which costs $150. If n stands for the total amount they have saved so far, write an expression to show how much more money they need. ______________________________________ ______________________________________ 2 Robb earned $25 more than his brother Mike doing chores for the neighbors last week. Mike earned n dollars. Write an expression to show Robb’s earnings. The speed limit on the highway is 50 miles per hour. Write an expression to show the distance traveled at the speed limit in n hours. ______________________________________ ______________________________________ 5 3 6 Carl has three times as many baseball cards as his cousin Nick. Nick has n cards. Write an expression to show the number of cards in Carl’s collection. Let n be any number. Write an expression that is three more than twice that number. ______________________________________ ______________________________________ 81 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 76 Simplifying Expressions Name Date It Is Simple! Simplify each expression. 1.7n – 2n ___________________________ 2. n + 2n ___________________________ 3.5n – 2n + 4n ___________________________ 4.5n + 2n – 3s ___________________________ 5.6y + (3y + 2) ___________________________ 6.3(2t + 2t) ___________________________ 7.10w – 8w ___________________________ 8.3p + 11p – 4p ___________________________ 9.7b + (5b – 7) ___________________________ 10. 10 (4x + 12x)___________________________ 82 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 77 Evaluating Expressions Name Date Watch Your Step With a drop of 3,212 feet, this waterfall is the highest in the world. What is the name of this waterfall, and in which country is it located? To answer the question, evaluate each expression for n = 3, t = 5, and y = 7. Then write the letter of the expression in the space above its answer. The first one has been done for you. Hint: Some letters will be used more than once. Some will not be used. 18 ____ ____ ____ ____ ________ ____ ____ ____ ____ 41203026 8 42 4 8 8 56 U ____ ____ ____ ____ ____ ____ ____ ____ ____ 132612026121826 8 4 U.6 x n ____________ R. t + y + 4 ____________ B.(n + t) ÷ 4 ____________ A. 14 – (n + y) ____________ L. 24 ÷ n ____________ T. t x 4 – n ____________ W. (18 ÷ n) ÷ 2 ____________ F.2 x (n x y) ____________ N.10 x (y + t) ____________ S.8 x y ____________ H. 75 ÷ (n x t) ____________ V. (70 ÷ y) + n ____________ E.(t x n) + (y + 4) ____________ G. 45 – (n x t) ____________ J.(y + 8) – (t – 4) ____________ Z. 24 ÷ (y – t) ____________ 83 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 78 Evaluating Expressions Name Date X Marks the Spot! You’ve found it—the secret to evaluating variable expressions. Solve three problems in a row to get Tic-Tac-Math! x + 7, 3x, x ÷ 5, where x = 8 where x = 4 where x = 30 2x – 3, 1 + 4x, 13x – 28, where x = 7 where x = 2 where x = 5 9x + 6 – 5x, where x = –1 A hot dog costs $1.27 more A super sundae costs $.88 than twice the price of a less than 3 times the price soda. Write an expression of a single cone. Write an that shows the price of a hot expression that shows the dog in relation to the price price of a super sundae in of a soda. Then evaluate relation to the price of a single where a soda costs $.99. cone. Then evaluate where a single cone costs $1.39. 84 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 79 Evaluating Expressions Name Date Expressions Everywhere Complete each set of problems below. 1. Evaluate each expression for n = 4. 3 + n ______________________5.5n ______________________ 7 − n ______________________2n + 6 ______________________ n ___ 4 ______________________ n2 − 5 ______________________ n2 + n + 7.5 ______________________3n – 8 ______________________ 15 – 2.5n ______________________ n(3 x 0) ______________________ 2. Evaluate each expression for a = 0.75 and b = 2.06. a + b + 8 ______________________2(a + b) ______________________ a + b – 2.2 ______________________3a + 2b ______________________ a + 4.55 – b ______________________(2a + b) ÷ 4 ______________________ 85 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 80 Writing Equations Name Date A Famous Author C. S. Lewis is well known as the author of the series Chronicles of Narnia. Less well known is his full name. What do the initials C. S. stand for? Answer: ________________________________________ 5n – 6 = 9 n÷8=9 n(2 + 1) = 9 n+4=9 3(n + 1) = 9 ________________________________________________________ (3n + 3) ÷ 3 =9 n–4=9 3n – 3 = 9 n÷2+5=9 n÷8=9 3(n + 1) = 9 (3n + 3) ÷ 3 =9 To answer the question, write an algebraic equation for each sentence. Write the letter of each problem in the space above its equation. Hint: Some letters will be used more than once. Some will not be used. V. 4 more than n is 9. ______________________________________________ T. 4 less than n is 9. ______________________________________________ L. n divided by 8 is 9. ______________________________________________ R. 3 times n is 9. ______________________________________________ P. 5 more than n divided by 2 is 9. ____________________________________________ C. 6 less than 5 times n is 9. ______________________________________________ N. n times 3 divided by 4 is 9. ______________________________________________ A. 3 times n minus 3 is 9. ______________________________________________ H. the sum of n and 4 divided by 2 is 9. ________________________________________ E. 3 times the sum of n and 1 is 9. ____________________________________________ S. the sum of 3 times n plus 3 divided by 3 is 9. ______________________________ I. n times the sum of 2 and 1 is 9. ___________________________________________ 86 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 81 Writing Equations Name Date Balancing Act Write an equation for each statement. 1. A number w increased by 2.5 is equal to 3.8. ____________________________ 2. The difference between a number y and 82 is 47. ____________________________ 3. A number n divided by 0.5 is equal to 2. ____________________________ 3 7 ___ 4. The product of a number k and ___ 8 is 1 8 . ____________________________ 5. The quotient of a number z and 175 is 25. ____________________________ 6. The sum of 1,231 and a number b is equal to 2,342. ____________________________ 7. A number d multiplied by 64 is 960. ____________________________ 8. A number 4,050 divided by a number x equals 81. ____________________________ 9. Fifteen is equal to a number m divided by 75. ____________________________ 10. A number v increased 160 times is equal to 1,760. ____________________________ 87 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 82 Writing Equations/ Word Problems Name Date Give Y a Try! Write an algebraic equation to represent and solve each problem. Solve three problems in a row to get Tic-Tac-Math! A rectangle’s length is y cm. A rectangle’s length is y Harold’s dad is 3 times his age. Its width is 5 cm. Its perimeter cm. Its width is 2 cm. The The sum of Harold’s age and his is 34 cm. Find the length of perimeter is 10 cm. Find the father’s age is 60 years. How old the rectangle. rectangle’s width. is Harold? How old is his dad? Oriana is 5 years older than Ella is twice Bella’s age, Harlan’s dad is 3 years more her brother Francisco. The sum and Stella is three times than 4 times Harlan’s age. The of their ages is 27. How old is Bella’s age. The difference difference in their ages is 30 each child? between Stella’s and Bella’s years. How old is Harlan? How ages is 8 years. How old is old is his dad? each girl? Sally has twice as many hair Janet bought 3 dozen Ty, Malcolm, and Fred were ribbons as Natasha. Bethany donuts from Delectable playing basketball. Malcolm has 3 less than Sally. The sum Donuts. She bought 3 times made 2 more baskets than Ty, of all three girls’ ribbons is 32. as many honey-dipped as and Fred made 4 more than How many hair ribbons does plain. She bought 6 fewer twice the number that Ty made. each girl have? chocolate-frosted than Together, the boys made 42 honey-dipped. How many of baskets. How many baskets did each did she buy? each boy make? 88 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 83 Writing Equations/ Word Problems Name Date A Sticky Situation In 1955, George D. Mestral invented a product that most Americans since then have used at one time or another. What is this product? Answer: ________________________________________________ 3 x 12 = n 12 + 3 = n 16 –12 = n 12 ÷ 3 = n 36 ÷ 3 = n 12 – 4 = n To answer the question, write an equation for each problem. Then write the letter of the problem in the space above its equation. Let n stand for the missing numbers. E.Tyrell can run a mile in 12 minutes. It takes his friend Ryan 3 minutes longer to run a mile. How long does it take Ryan to run a mile? L.Joe had to complete 12 algebra problems for homework. He copied his assignment incorrectly and completed 16 problems. How many extra problems did he do? ____________________________________ ____________________________________ C.Danielle is selling wrapping paper to raise money for her class. The class will reach its goal if everyone sells 12 rolls. Danielle plans to reach this goal if she sells 3 rolls of paper per day. How many days will it take her to sell the wrapping paper? O.Mike lost some of the pieces of his checkers set. He now has only 12 pieces, including 4 four red ones. How many black pieces does he have? ____________________________________ ____________________________________ R.Marie and her two cousins are planning refreshments for a family gathering. They need 3 dozen cupcakes. How many cupcakes should each girl bake if they are to bake the same amount? ____________________________________ V.Marina is helping her teacher by cutting out circles for a class activity. There are three groups of students and each group needs a dozen circles. How many circles does Marina need to make? ____________________________________ 89 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 84 Solving Equations Name Date Equation Expert Solve the equations. 1.n + 119 = 254 7.n ÷ 100 = 0.021 n = ____________________ n = ____________________ 2.m + 11 + 17 = 44 8.n ÷ 10 = 0.35 m = ____________________ 3. 23 + 76 = b b = ____________________ n = ____________________ 9.n ÷ 1,000 = 0.024 n = ____________________ 4. 0 + y = 13 10.n ÷ 1,000 = 2.004 y = ____________________ n = ____________________ 5. 56 − t = 42 11.n ÷ 10 = 0.09 t = ____________________ n = ____________________ 6. 316 + n = 401 + 226 12.n ÷ 100 = 0.012 n = ____________________ 90 n = ____________________ 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 85 Solving Equations Name Date Uncle Sam Most people are familiar with the image of “Uncle Sam.” With his white hair and top hat, he is a symbol of the United States. The artist who drew the picture used himself as a model. Who was this artist? Answer: ____________________ 168 6 1212584 ________________________________________ 1233243714433121253147 L ____________________ 526 144 144 To answer the question, solve the equations. Write the letter of the problem in the space above its answer. The first one has been done for you. Hint: Some letters will be used more than once. Some will not be used. L.7 2 n = 14 M. n 2 6 = 72 Y. n 3 7 = 21 n = ________ . n = ________ . n = ________ . T. n 2 9 = 63 N. n 3 3 = 81 A.64 2 n = 384 n = ________ . n = ________ . n = ________ . R.14 2 n = 42 H. n 3 5 = 73 O. n 2 11 = 363 n = ________ . n = ________ . n = ________ . U. n 3 8 = 9 F.84 2 n = 420 G. n 3 12 = 12 n = ________ . n = ________ . n = ________ . E. n 3 25 = 5 S. n 3 7 = 12 J. n 3 2 = 84 n = ________ . n = ________ . n = ________ . 2 91 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 86 Writing and Solving Inequalities Name Date What’s the Inequality? Complete each set of problems. 1. What inequality is shown? Use n as the variable. – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 __________________ – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 __________________ – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 __________________ – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 __________________ 2. Circle each number that will make the inequality true. 3 + n > 14 4 12 10 3n > 26 13 10 8 12 n ÷ 4 > 6 28 24 20 7 3 9 2n ÷ 4 > 3 n – 6 < 3 9 8 10 6 2 8 4(n + 5) < 33 32 92 4 5 3 6 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 87 Writing Rules for T-Tables Name Date Let’s Go Biking In 1871, an Englishman built what many historians consider to be the first true bicycle. What was his name? Answer: ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ 4 3 2 9 1 1637895 To answer the question, write the rule above each problem. Find each rule in the Rule Box, then write the letter of each rule in the space above its problem number. Hint: Some letters will be used more than once. 1 2 _______________ _______________ x y x 1 2 3 3 4 5 – _______________ x 1 0 1 – 3 4 1 0 1 5 x 2 0 2 1 2 3 _______________ x y 3 4 9 12 5 15 6 1 0 1 – Rule Box x y T. y = x – 4 3 2 – 1 4 2 0 2 1 0 – – 8 x y 2 – 4 – 6 1 2 3 1 3 5 9 x y 5 4 – 3 1 2 3 5 3 7 – 93 Y. y = –2x 1 R. y = ___ 2 x L. y = 2x – 1 E. y = 2x + 1 A. y = 3x J. y = x – 2 _______________ y – S. y = x + 2 M. y = 2x _______________ y – _______________ x _______________ y _______________ y – 7 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 88 Identifying Ratios Name Date Ready, Set, Ratio! Complete each set of problems. 1. Write each ratio in simplest form. 4 to 12 8 : 20 21 63 12 to 18 50 : 30 _________ _________ _________ _________ _________ 24 to 12 14 : 3.5 12 84 1.2 to 2.0 5 : 2.5 _________ _________ _________ _________ _________ 2. Circle each ratio equivalent to the first ratio. 3:2 30 to 2 9 to 6 15 9 10 7 20 : 14 25 to 14 1 to 0.7 1 7 45 to 25 50 : 30 9 to 5 5 to 9 40 20 36 : 24 3. Which ratios are equivalent? Write = or = . 7 5 ____ 15 : 36 12 10 : 4 ____ 10 2 36 ____ 3 : 4 48 1.5 : 0.5 ____ 1 8 ____ 16 to 14 5 ____ 10 to 4 94 25 3 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 89 Solving Proportions Name Date Founder of the Girl Scouts The Girl Scouts was founded in Savannah, Georgia. Who was the founder of the Girl Scouts? Answer: ____ ____ ____ ____ ____ ____ ____ ____ 4128 7 536365 ____ ____ ____ ____ ____ ____ 2124 9 3 2418 ____ ____ ____ 8 2415 To answer the question, solve each proportion. Write the letter of the problem in the space above its answer. Hint: Some letters will be used more than once. Some will not be used. 18 R. ___ = ___ 12 24 15 5 M. ___ = ___ 18 36 J. ___ = ___ 45 5 5 10 N. ___ = ___ 9 1 E. ___ = ___ 3 15 8 C. ___ = ___ 9 54 4 2 I. ___ = ___ 14 6 2 D. ___ = ___ 9 8 24 G. ___ = ___ 7 3 U. ___ = ___ 4 16 5 W. ___ = ___ 8 24 9 27 T. ___ = ___ 12 12 24 L. ___ = ___ 4 12 4 S. ___ = ___ 30 3 O. ___ = ___ 11 88 To find the year the Girl Scouts was founded, circle the correct proportion below. The correct date follows it. 6 10 ___ = ___ 1915 9 18 8 20 ___ = ___ 1919 12 36 15 9 ___ = ___ 1912 40 24 95 10 3 ___ = ___ 1921 15 5 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 90 Calculating Rate Name Date What’s the Rate? Find the unit rate or unit price. 1.28 miles in 4 hours _____________________ 2. 7 DVDs for $42 _____________________ 3. 96 feet in 12 seconds _____________________ 4. 6 cards for $21 _____________________ 5. 24 pages read in 16 minutes _____________________ 6. 1 dozen cans for $7.20 _____________________ Think Tank ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ Henry rode his bike 5 miles in 25 minutes. What was his average speed in miles per hour? _____________________ At that rate, how far does Henry ride in half an hour? THINK TANK _____________________ Show your work in the tank. 96 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 91 Graphing a Coordinate Plane Name Date Canine Coordinates T he map of Canine County is graphed on a coordinate plane. Use the information on the grid to answer the questions. y II I 8 7 Terrier 6 5 Shepherd Beagle 4 3 2 Dalmation Hound 1 0 -8 -7-6-5-4-3-2-112345678 -1 -2 Collie -3 Golden Doodle x -4 -5 -6 -7 III Boxer -8 IV 1. In which quadrant will you find each town? Beagle __________ Terrier __________ Golden Doodle __________ 2. What are the coordinates for each town? Shepherd __________ Collie __________ Hound __________ 3. Which town is located at (4, –7)? ____________________________________ In which quadrant is that town? __________ 97 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 92 Graphing a Coordinate Plane Name Date Going Solo In 1933, a U.S. pilot made the first solo round-the-world flight. What was this pilot’s name? Answer: ____ ____ ____ ____ ____ ____ ____ ____ ____ 12345 6789 To answer the question, find each ordered pair on the diagram. Write the letter of each point in the space above its problem number. Hint: Some letters will not be used. S I W M E L O P Y A T 98 1 (2, 3) 2 (–1, 4) 3 (0, 0) 4 (–4, 1) 5 (–2, –3) 6 (–3, –2) 7 (5, 0) 8 (0, 5) 9 (3, –4) 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 93 Graphing a Coordinate Plane Name Date Ship Math The map of the sea floor is graphed on a coordinate grid. Each letter on the grid marks the location of a sunken ship. Each small square on the grid has an area of 1 mi2. N 9 8 7 6 y B 5 4 3 E W 2 D 1 x 0 -9-8-7 -6-5 -4-3-2 -1 -1 F -2 1 2 3 4 5 67 8 9 E A -3 -4 C -5 -6 -7 -8 -9 S Use the grid to answer the questions. 1. Which ship is 6 miles west of ship A? _______________ 2. Which ship is 5 miles east of ship E? _______________ 3. Which one is 7 miles west, 11 miles south of ship B? _______________ 4. Which one is 6 miles east, 4 miles north of ship E? _______________ 5. Which ship is directly northeast of ship F? _______________ 99 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 94 Calculating Area Name Date Figure It Out Use the figure and the formulas to calculate the area for each problem. H A I G Formulas 5 ft 5 ft E B Area of a square = s2 F Area of a rectangle = l x w 6 ft 15 ft 9 ft C K J D 1. Area of square ABDC = __________ sq ft 2. Area of rectangle EGKC = __________ sq ft 3. Area of square HBFI = __________ sq ft 4. Area of rectangle EFDC = __________ sq ft 5. Area of square EIJC = __________ sq ft 6. Area of rectangle GIJK = __________ sq ft 7. Area of rectangle HBDJ = __________ sq ft 8. Area of rectangle IFDJ = __________ sq ft 100 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 95 Calculating Area Name Date The Biggest Sleepyhead Averaging about 22 hours of sleep each day, this animal is considered to be the sleepiest of all animals. What is this sleepy animal? Answer: ____ ____ ____ ____ ____ 881608814448 To answer the question, find the area of each triangle. Write the letter of the triangle in the space above its area. When you are done reverse the letters. Hint: One letter will be used more than once. Some letters will not be used. 1 Use this formula to find the area of a triangle: A = ___ bh. 2 S. R. K. b = 10 ft b = 2 ft b = 16 ft h = 12 ft h = 12 ft h = 6 ft A = ________ sq ft A = ________ sq ft O. b = 16 ft h = 18 ft A = ________ sq ft A = ________ sq ft L. b = 20 ft A. h = 16 ft b = 8 ft A = ________ sq ft h = 22 ft A = ________ sq ft J. T. E. b = 24 ft b = 14 ft b = 16 ft h = 6 ft h = 9 ft h = 7 ft A = ________ sq ft A = ________ sq ft A = ________ sq ft 101 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 96 Calculating Averages, Means, Median, and Mode Name Date Mean and Median à la Mode Yum! Look at the tasty mean, median, and mode problems. Solve three in a row to get Tic-Tac-Math! Find the median of the Find the median, mode, Find the mean, median, following data: and range of the following mode, and range of the lengths of pieces of wood following numbers: 7, 12, 15, 12, 5, 6, 4, 1 (all the measurements are 6, 1, 3, 1, 5 in inches): 4, 3, 8, 3, 5, 2, 3 What whole number must the What whole number must What must the missing piece missing piece of data be to the missing piece of data be of data be to have a mean have a range of 15? to have a mode of 3? of 8? 14, ____, 9, 12, 5, 2, 3, 3, 2, 4, ____ 7, 12, ____, 3, 11 2, 2, 8, 2, 1 What must the missing piece What must the missing piece What must the missing piece of data be to have a mean of data be to have a mean of data be to have a mean of 30? of 20? of 33? 20, 30, 50, 40, ____ 18, 11, 7, 15, 51, 52, ____, 23, 32, 27, ____ 21, 17, 37, 45 102 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 97 Data Analysis Name Date Pop Quiz T he students in Ms. Bunsen’s science class took a pop quiz today. The line plot shows their scores. Use the data to answer the questions. Quiz Scores x x x x x x x x x x x x x 556065707580859095100 Score 1. How many students took the quiz? ________________________ 2. Which score is an outlier? ______________________________ How do you know? ____________________________________________________ 3.Around which score do the data cluster? ___________________________ 4.What are the range, mean, median, and mode of the scores? _____________________________________________________________________________ 5.What are the range, mean, median, and mode of the scores without the outlier? _____________________________________________________________________________ 103 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 98 Data Analysis Name Date Sizing Up the Data The line plot shows the shoe sizes of all the members of the school baseball team. Shoe Sizes x x x x x x x x x x x x x x x x x x x x x x x x x 5 6 7 8 9 1011121314 Score The team’s equipment manager made the line plot from data she collected and recorded in a frequency table. Show what that table would look like. Then summarize what the data shows. Shoe Size Tally Frequency ___________________________________________________________________________________ ___________________________________________________________________________________ ___________________________________________________________________________________ 104 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 99 Data Analysis Name Date Baxter’s Budget Baxter has a part-time job. The double line graph shows his monthly income and expenses for 6 months. Use the data to answer the questions. BAXTER’s Income and Expenses $400 income Money 350 300 250 expenses 200 150 0 Jan Feb Mar Apr May Jun Month 1.What was the difference between Baxter’s income and expenses in May? __________________________________________________ 2.In which month did Baxter save the most money? _______________________________ 3.To the nearest dollar, was the mean monthly difference between Baxter’s income and his expenses? ___________________________ 4.In which month were Baxter’s expenses the greatest percent of his income? ______________________________________________ 5.Write a question that can be answered using the graph. __________________________ _________________________________________________________________________________ 105 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 100 Data Analysis Name Date Message Math T he histogram shows the number of text messages sixth graders sent one Saturday. Use the data to answer the questions. Number of Kids Text Messages Sent 5 4 3 2 1 0 21–2526–3031–3536–4041–4546–50 Number of Messages 1. How many kids sent between 46 and 50 messages? ____________________ 2.How many kids sent fewer than 36 messages? ____________________ 3.How many more kids sent between 36 and 40 messages than sent between 21 and 25 messages? ____________________ 4.What is the mode of the data? ________________________ How can you tell? _________________________________________________________________________ Bonus! Draw a line to match the type of graph to the data it would best describe. 1. You want to compare the first month’s book sales of two biographies of a famous actor. a. histogram 2. You want to show how your cat spends a typical 24-hour day. b. line 3. A rock group just released a new CD. You want to show monthly sales over a 6-month time period. c. bar 4. You want to show what music people like in their teens, twenties, thirties, and forties. d. circle 106 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Answer Key 6 Comparing Fractions Name Date Fractions Beyond Compare These fractions are simply gorgeous! Solve three problems in a row to get Tic-Tac-Math! Practice Page 1: 1. 300,000,000,010 2. 59,000,000,130 3. 606,000,000,000 4. 32,000,000,000,104 5. 7,000,000,000,400 6. 5,024,020 7. 24,016,000,000 8. 152,002,000,000,005 9. 97,014,011 10. 48,900,001,027 Practice Page 2: 1. < 2. > 3. > 4. > 5. < 6. = 7. > 8. > 9. > 10. > Practice Page 3: Pittsburgh I. 4 R. 6 C. 7 S. 3 H. 8 Practice Page 6: Circle the fractions that are Circle the fractions that are greater than 2 . less than 2 . 1 ___ 1 ___ 105 , 3 10 , 14615 , 34 9 12 18 18 4 28 16 ___ ___ ___ ___ 15 ___ 9 ___ 4 ___ 21 ___ 28 16 10 60 10 , 22 , 36 20 44 72 ___ 6 ___ 18 14 ___ Hortence is really hungry. Which amount of pizza should she eat if she wants to eat 2 of a pizza 3 2 ___ ___ 56 ___ 50 2 ___ more: 4 of a pizza or 3 of Marco studied for 16 of an hour, and Melissa studied for 3 ___ 4 of an hour. Who studied Marco 4 ___ 7 ___ Bekah ran 5 of a mile and Paula Sue completed 8 Jeff ran 3 of a mile. Who ran more? of her homework, and 2 ___ Bekah 1 ___ Frangelica swam 2 2 laps at They both swam an equal distance. the pool, while her sister Bailey 2 ___ swam 2 4 laps. Who swam more? longer? a pizza? 1 ___ equivalent to 2 using the 1 3, 615 7 6 29 7 18 1 ___ Write three fractions that are denominators 20, 44, and 72. 3 ___ Roberto skied 4 5 miles on the cross-country trails, while his 15 ___ 9 ___ brother Pascal skied 4 10 miles. Who skied a greater distance? Janet Lynn completed 20 of her homework. Who did Pascal Paula Sue a greater portion of her homework? Practice Page 7: The Great Train Robbery 1. T, 1001; H, 1.010 E, 1.101 2. G, 4.205; R, 4.245; E, 4.25 3. A, 0.853 T, 0.8539; T, 0.854 4. 8 R, 0.00802; A, 0.0082; I, 0.0820 5. N, 17.013; R,Round 17.1002; ’emO, Up17.1020; B, 17.120 6. B, 2.00325; E, 2.03254; R, 2.325; Y, 2.3253 12 Rounding U. 2 B. 1 G. 0 P. 9 T. 5 1. 1 2. 9 3. 0 4. 5 Practice Page 4: 1. 0.8 2. 0.06 3. 0.63 4. 0.016 5. 0.0009 6. 1.02 7. 0.00012 8. 60.09 9. 0.0047 10. 7,000.022 Practice Page 5: West Quoddy Head 1. U, 0.5 8. Y, 12.54 2. S, 0.37 9. W, 4.781 3. A, 2.99 10. Q, 19.03 4. D, 15.40 11. E, equal 5. T, 0.075 12. D, 0.0530 6. O, 0.81 13. D, 11.75 7. E, equal 14. H, 23.64112 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Name Date Complete each set of problems below. Practice Page 8: 1. Round each number to the nearest 1,000 and 100,000. 1. Number Nearest 1,000 Nearest 100,000 389,900 1,844,938 24,061,562 390,000 390,000 1,845,000 1,845,000 24,062,000 24,062,000 400,000 400,000 1,800,000 1,800,000 24,100,000 24,100,000 of the underlined digit. 2.2.(Round Leftto thetoplace right) 30,900,000; 92,807.05; 30,948,007 _____________________ 92,807.045 _____________________ 1,286,000.4; 4,000,041,000; 8,726,739.03; 1,286,000.372 __________________ 4,000,040,706 ___________________ 5,528,910,000 _________________ 5,528,908,282 ___________________ 3. (8,726,739.0283 Left to right) 0.05; 10; 0.009; 40; 7,000; 0.005 3. Round to the greatest nonzero place. Practice Page 9: 0.00872 ________________________ 44.4123 ________________________ 1. 0.06 6. 297.04 6,727.39 _______________________ 0.00526 ________________________ 2. 6.04 7. 12.4080 3. 4.750 8. 27 4. 30 9. 6.3872 5. 0.07048 10. 63.302 0.047 __________________________ Practice Page 12: wandering albatross 1. <, T 10. >, R 2. <, O 11. <, R 3. >, D 12. <, I 4. <, N 13. <, G 5. >, S 14. <, W 6. >, A 15. >, A 7. <, A 16. >, B 8. >, N 17. <, S 9. >, L 18. >, E Practice Page 13: (Left to right) 326; 15; 18; 4.5; 2⁄5; 0.6; 22; 0; 87; 5 ⁄8 ; 2⁄3; 75 1. T 2. F 3. T 4. F Practice Page 14: Jacob Ludwig Karl, Wilhelm Karl D. 6 S. 16 E. 8 R. 23 I. 17 U. 15 C. 3 O. 7 P. 14 K. 2 M. 12 G. 62 15 B. 0 W. 53 A. 5 L. 24Positive! Absolutely H. 9 J. 54 Mixed Practice Name Being negative isn’t so bad. Negative numbers are actually pretty cool. Solve three integer problems in a row to get Tic-Tac-Math! Practice Page 15: What is the absolute value What is the absolute value of –8? of –13? 8 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Practice Page 10: John Gorrie 1. -6, J 6. 0, O 2. 0, O 7. 1, R 3. 3, H 8. 1, R 4. -3, N 9. -1, I 5. 6, G 10. -2, E Practice Page 11: 1. -9, -6, -5, -2; -40, -4, 4, 40 2. 19, 9, -9, -91; 17, 7, -17, -77 3. -5; +400; -75; +6 107 Fill in the box with <, >, or =. –3 13 Fill in the box with <, >, or =. Imagine a number line with < 2 What is the sum of –3 and +7? negative numbers to the left 6 > –5 9.807 __________________________ 14 Date of zero and positive numbers to its right. If you start on +7 +10 and move three spaces to the right, on what number +4 will you land? Find the sum: –4 + –3 + –11 –18 Talia added –4 + –5 + 8 and What number should you add got –17. She made an error. to –8 to get +12? She added –8 instead of +8. made? What is the correct answer? Her answer should have been –1. What error do you think she Practice Page 16: 1. 10,801 2. 767 3. 22,416 4. 1,157 5. 76,120 6. 28,962 7. 155,181 8. 762,184 9. 2,110,889 10. 4,608,022 21 +20 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Answer Key Practice Page 17: 1. 46,561 waves 2. 160,318 visitors 3. 2,108 pages 4. 1,291 freckles Practice Page 18: 1. 1,199 miles 2. 16,959 more chocolate chips Practice Page 19: 1. 15.56 2. 1.5633 3. 2.787 4. 10.3078 5. 5.9524 6. 0.165 7. 6.8 8. 3.35 9. 10.45 10. 6.85 11. 65.39 12. 62.456 Practice Page 20: Answers will vary. Check students’ work. Practice Page 21: 1. 84.6 cm 2. 572.05 cm Practice Page 22: Answers will vary. Check students’ work. Practice Page 23: 1. 1.5 pounds 2. 0.905 pounds 3. 1.728 pounds 4. 7.928 pounds more Practice Page 24: “Bi-son!” I-$6.01, O-$13.70, E-$1.25, S-$2.97, N-$12.68, B-$7.25 Practice Page 25: 1. (Left to right) 360; 30,000; 280,000; 49,000; 8,000; 180,000; 48,000; 60,000; 2,800,000; 500,000; 2,500; 120,000 2. 6,000; 8,000; 25,000; 480,000; 180,000; 600,000 Practice Page 26: 1. 86,136 2. 50,061 3. 37,500 4. 491,694 5. 87,822 6. 58,706 7. 209,952 8. 998,001 Practice Page 27: 1. $28,116 2. 519,331 Practice Page 35: Answers will vary. Check students’ work. Practice Page 36: It is four days old. S-5.9, Y-2.8, E-5.85, O-9.7, F-7, R-20.7, D-4.7, U-2.3, I-3.35, T-8.7, A-7.9, L-34.65 Practice Page 28: The others are weak days. T-0.12, S-27.44, K-2.42, O-33.93, N-5.94, A-21.90, W-0.38, E-7.13, D-29.44, H-11.99, Y-32.37, R-0.27 Practice Page 37: 1. 66 portions 2. 17 strips 3. 108 bags 4. 11 bags with 0.25 pounds left over Practice Page 29: Answers will vary. Check students’ work. Practice Page 30: 1. 62.08 minutes 2. 67.044 minutes 3. $62.82 4. $199.20 Practice Page 38: biodiversity E. 7 5⁄6 S. 9 1⁄3 Y. 11 1⁄20 T. 9 9⁄14 V. 12 2⁄9 B. 9 7⁄24 Practice Page 31: Answers may vary; sample answers: 1. 400 2. 700 3. 900 4. 50 5. 80 6. 8,000 7. 90,000 8. 12 9. 10,000 10. 6,000 11. 20 12. 20,000 40 Mixed Numbers Practice Page 39: 1. 50 ⁄2 inchesFraction Leftovers 2. 17 23⁄24 miles Subtracting Fractions and Dividing Decimals by Whole Numbers Practice Page 40: 3 ___ 4 6.324 50 1.515 0.0303 37 9.287 0.251 1 ___ 4 3 1 2 3 10 7 5 1 5 4 22 16.72 14 0.76 60 96.66 25 1.611 41 82.82 40 114.8 8.2 86 1 1 5 5 1 2 5 – 1___ 5 = 17 ___ 3 – 2 3 5 46 = 11 16 16 ___ 6 ___ 12 – 5 12 = 6 4 3 3 ___ 6 ___ 4 = 17 15 15 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources N. 21⁄4 A. 47⁄8 H. 5 5⁄12 O. 41⁄24 S. 4 7⁄9 I. 5 5⁄6 Practice Page 42: 1. 13⁄8 inches 2. 6 9⁄20 miles 201.5 8.06 2.02 3 – 8 ___ 9 ___ 4 – 3 2 = Practice Page 41: Hippocrates R. 31⁄10 C. 33⁄4 D. 4 2⁄3 T. 5 3⁄10 E. 5 7⁄8 P. 41⁄3 Date 7 ___ 2 4 5 3 2 1 ___ 7 ___ 5 – 3 5 = = ___ 10 ___ 8 – 5 8 = Practice Page 34: 30 – 7 Watch out for the pointy porcupine! See how sharp your decimal division skills are by solving three problems in a row to get Tic-Tac-Math! 0.2108 Date What’s left over when you subtract these fractions and mixed numbers? Solve three problems in a row to get Tic-Tac-Math! Write all answers in simplest form. ___ 6 ___ 10 – 3 5 = Name Name 1 Practice Page 32: 1. 169 R31 2. 108 R14 3. 3 R433 4. 1,001 5. 443 R63 6. 503 7. 172 8. 1,003 R10 34 Practice Page 33: 1. 24 miles Pointy Decimal Points! 2. 97 pepperoni pizzas J. 8 1⁄6 M. 11 1⁄8 I. 10 7⁄18 O. 7 4⁄15 R. 12 3⁄10 D. 14 1⁄4 Practice Page 43: 1. 8 1⁄8 miles 2. 5⁄6 quart 3. 3⁄4 hour (45 minutes) 4. Taryn’s; 3⁄8 inch 137.6 1.6 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 108 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Answer Key Practice Page 44: Use a pencil. P-6 3⁄4, U-123⁄8, C-17 1⁄3, L-10 4⁄5, A-5 3⁄4, N-7 1⁄2, E-131⁄8, S-14, I-6 2⁄3, R-9 6⁄7 Practice Page 45: 1. 11⁄4 2. 4⁄15 3. 5⁄11 4. 28 3⁄25 5. 22 3⁄4 6. 8 7⁄16 7. 11⁄60 8. 10 2⁄7 9. 34 3⁄10 10. 30 2⁄3 Practice Page 46: Garret A. Morgan N. 38⁄9 S. 16 1⁄2 G. 6 1⁄2 O. 2 1⁄4 T. 8 4⁄5 L. 13⁄4 Practice Page 52: Richard James H. 2 5⁄7 M. 13⁄7 S. 4 2⁄3 T. 3 1⁄18 D. 2 7⁄12 E. 11⁄4 Practice Page 58: Arthur Conan Doyle H. 16.8 N. 57.6 L. 70.68 K. 50.4 E. 25.9 Y. 111 S. 112.5 C. 83.6 U. 46 R. 381.9 T. 184 A. 195 I. 28 D. 84.24 O. 20.16 Y. 61⁄4 I. 4 3⁄4 J. 2 3⁄20 C. 24⁄9 A. 2 3⁄4 R. 11⁄4 Practice Page 53: for a pop quiz Q-0.717, U-1.03, P-2.3, T-0.47, F-0.833, Z-0.001, R-4.7, I-0.05, A-3.95, D-1.031, Y-0.07, O-7.2 H. 2 J. 5 5⁄6 R. 8 1⁄3 A. 10 1⁄2 M. 31⁄2 E. 5 1⁄4 Practice Page 47: 1. 8 1⁄4 cups 2. 1⁄2 mile Practice Page 48: It’s not right. R-3⁄4, I-9⁄10, L-21⁄2, W-8⁄9, S-7⁄9, O-2⁄3, H-22⁄5, C-1⁄2, N-5⁄6, T-13⁄4, G-11⁄8, B-6⁄ 7 Practice Page 49: 1. 1 2. 3 2⁄5 3. 5⁄6 4. 4 5. 1⁄2 6. 1 7. 2 8. 4 9. 2 10. 11⁄20 11. 5⁄8 12. 6⁄11 Practice Page 50: Answers will vary. Check students’ work. Practice Page 51: Both test pupils. O-3 1⁄6, S-4 3⁄8, M-13⁄ 7, H-1⁄3, I-2⁄3 , A-19⁄10, E-12⁄3, P-11⁄4, L-3⁄4, T-15⁄12, B-3⁄10, U-6⁄ 7 Practice Page 54: George Washington Carver S. 10% B. 100% N. 8% L. 92% I. 20% H. 37.5% O. 50% C. 60% M. 64% R. 3% V. 120% W. 110% A. 75% G. 12.5% T. 245% E. 375% Date T- ⁄10, Y-50%, S⁄10, U-30%, We’re All Equal!E- ⁄10, R-70%, O-1⁄10, A-10%, N-6⁄10, M-60%, G-9⁄10, D-90% 5 3 7 Fractions, decimals, and percents all express parts of a whole. Solve three problems in a row to get Tic-Tac-Math! Practice Page 56: What is the decimal equivalent of 1 ___ 4 ? What is the fraction What is the percent equivalent equivalent of 0.6 of (in simplest form)? Which is greatest? Circle. 40% 5 ___ 58 8 7 ___ 10 ? 3 5 0.25 0.6 70% Which is least? Circle. 1 ___ 15% 5 0.1 Which is greatest? Circle. 0.1 35% 8 ___ 25 2 5 2 ___ 5 0.05, 1 , 1 , 10 5 1 1 0.55 ___ 1 45% ___ 25%, 10 , 0.35,3 3 1 ___ 0.35 0.05 25% 5 45%, 0.55 Order the set from least to to least: greatest: 20 70.38, 3 24% 20 8 3 ___ 8 0.52 0.38, 0.52 9.8% Practice Page 57: 1. 20% 2. 28% 3. 68% 4. 100% 5. 76% 6. 140% 62 Name Date Hip-hip-hooray! These girls are rooting for you to solve three pattern problems in a row and get Tic-Tac-Math! Practice Page 63: Find the next three numbers Find the next three numbers Find the next three numbers in in the pattern below. Then in the pattern below. Then the pattern below. Then explain explain the pattern in words. explain the pattern in words. Find the next three numbers Find the next three numbers 7.9, 7.6, 7.3 in words. 10.45, 10.35, the pattern 5.4, 5.5, 5.6 (subtract 0.3 10.25 (subtract 5.1, 5.2, 5.3 10.75, 10.65, 10.55 9.1, 8.8, 8.5, 8.2 (add 0.1 to the from the previous 0.1 from the previous number) ____, ____, ____ ____, ____, ____ ____, ____, ____ number) previous number) Find the next three numbers the pattern below. Then in the pattern below. Then 31, 38.7, 46.4 inexplain the pattern in words. explain the pattern in words. 0.28, 0.3, 0.32 0.1, 0.11, 0.12 (add 7.7 to (add 0.02 to the (add 0.01 to the 0.2, 7.9, 15.6, 23.3 0.2, 0.22, 0.24, 0.26 0.07, 0.08, 0.09 the previous previous number) previous number) number) ____, ____, ____ ____, ____, ____ ____, ____, ____ explain the pattern in words. Order the set from greatest 7 ___ Identifying Decimal Patterns in the pattern below. Then greatest: 0.74, 0.6, 1 , 0.48,0.48 0.74 47.5% 2 1 3 ___ ___ 3 0.6 247.5%, 10 10 Practice Page 62: Elisha Graves Otis 1. V, 0.6 7. E, 12.5 2. T, 2.4 8. G, 0.025 3. S, 1.75 9. P, 1 63 4. L, 2.25 10. H, 0.5 Three Cheers for 5. A, 1.5 11.Decimal O, 0.16 Patterns! 6. R, 2 12. I, 0.125 0.39 Order the set from least to 9.8%, 24% Practice Page 60: 1. 114 2. 156; 84 3. 13; 108 Practice Page 61: Either or R-$8.00, I-$6.00, H-$32.00, E-$14.00, T-$7.50, O-$5.40 Practice Page 55: 56 Mixed Practice Name You grue-some! Practice Page 59: 1. 5% 2. 36% 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Find the next three numbers 0.0005, in the pattern below. Then 5.4, 16.2, 48.6 0.00005, explain the pattern in words. (multiply the 0.000005 (divide 0.5, 0.05, 0.005 0.2, 0.6, 1.8 previous number the previous ____, ____, ____ ____,by 3) ____, ____ number by 10 or multiply it by 0.1) Find the next three numbers Find the next three numbers in in the pattern below. Then the pattern below. Then explain explain the pattern in words. the pattern in words. 6.45, 5.85, 5.25 (subtract 0.6 8.25, 7.65, 7.05 from the previous ____, ____, ____ number) Practice Page 64: Roe River, Montana 1. E, 4⁄8 6. D, 21⁄4 2. I, 2 7. N, 1⁄81 1 3. R, ⁄11 8. M, 2⁄5 4. B, 7⁄8 9. T, 1⁄16 5. A, 3 10. O, 16⁄20 69 109 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 65 Identifying Fraction Patterns Name Date Answer Key I Detect a Pattern Look for clues to help you uncover the next numbers in each pattern. Solve three pattern problems in a row to get Tic-Tac-Math! Practice Page 65: 9 , 11 , 13 in the pattern below. Then explain words. 8 the pattern 8 in 8 Find the next three numbers 5 1 ___ 1 ___ 3 ___ 13 , 16 , 19 in the pattern below. Then explain 3 the pattern 3 in words. 3 Find the next three numbers 2 7 ___ 4 ___ 3 7 ___ 10 ___ 3 , 3 , 3 to (add 1 or 3 the previous ____, ____, ____ number) 8 , 8 , or 8 , 8 (add 4 8 to the previous ____, ____, ____ number) 1 , 1 , 1 the in pattern below. Then explain pattern in 256 words. 64 the128 1 (divide the 1 ___ 1 ___ 1 ___ 1 ___ ___ 2 , 4 , 8 , 16 , 32 previous number by 2 or multiply it ____, ____, ____ by 12 ) Find the next three numbers 1numbers 4 next three 2 numbers Find next three numbers Find the1 next three Find the 3thepattern in the , 3below., Then3 1pattern 1 ,1below. in the below. in the 5 pattern Then 2 ,1 4 , Then 5 , 1 explain pattern in words. in words. 112 the224 448 explain the pattern in words. explain the pattern 3 (add to the (divide the 1 3 1 1 3 ___ 3 ___ 3 ___ 3 1 ___ 4 ___ 25 3 ___ ___ ___ 2 4 , 2 , 1 from 1 1 4 7 , 14 , 28 , 56 5 , 5 , 5 , , 5 , 5 (subject previous number; 4 previous number 2 the previous by 2 or multiply it then subtract ____, ____, ____ ____, ____, ____ ____, ____, ____5 by 12 ) number) from that number) ___ 4 3 ___ 7 ___ 1 Find the next three numbers Find the next three numbers in the pattern below. Then in the pattern below. Then explain the pattern in words. explain the pattern in words. 1 5 , 2, 1 5 2 3 8 , 4 8 , 4 10 23 , 21 13 , 42 23 Find the next three numbers in the pattern below. Then 1 explain the pattern in words. 3 5 to the 1 3 (add (subtract 3 1 2 from 1 1 2 1 1 ___ 2 ___ 3 8 , 3 84, 3 2 , 3 4 , 2 5 , 2 5 , 2 55, 2, 2 5 , 3,13,23,53 3(multiply the previous number; the previous 5 7 3 3 8 , 3 8 , 3 4 , 41 previous number then subtract 8 number; then add ____, ____, ____ ____, ____, ____ 1 by 2) ____, ____, ____ 5 to that number) from that number) ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 71 ___ 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Practice Page 66: 1. 1, 2, 4, 8 2. 1, 2, 7, 14 3. 1, 2, 3, 5, 6, 10, 15, 30 4. 7, 29 5. 37, 41, 47, 53 6. 71, 73, 79, 83, 89, 97 7. 4 67 8. 9 Mad About Multiples! 9. 15 10. 13 Multiples and Least Common Multiple ___ ___ Name Date Do you find multiples mesmerizing? Solve three problems in a row to get Tic-Tac-Math! Practice Page 67: Which of the following are Which of the following are Which of the following are multiples of 5? multiples of 6? multiples of 3? 20 52 35 20, 30, 35 23 30 18 30 16 18, 24, 30 25 24 29 31 52 78, 102 78 102 What is the least common What is the least common What is the least common multiple of 7 and 4? multiple of 24 and 12? multiple of 15 and 21? 28 24 105 Two dogs are sitting next to Barney and Julia are both Glenda and Penny are doing each other. Starting now, one very tired. Starting now, a sack race. Glenda jumps dog will bark every 3 seconds Barney will yawn every 8 forward 18 inches each time seconds and Julia will yawn she jumps. Each of Penny’s every 4 seconds. When is the hops is 15 inches. How far from next time both of them will the starting line will it be when yawn at the same time? Glenda and Penny have both In 15 seconds and the other dog will bark every 5 seconds. When is the next time both dogs will bark at the same time? In 8 seconds 90 inches from the starting line traveled at the same distance? Practice Page 68: 1. (Left to right) 1,000; 1; 10,000,000; 100,000,000; 10,000; 10; 100; 1,000,000 2. (Left to right) 102; 10 0; 104; 106; 103; 107 3. 90,600; 320,700 4. (1 × 103) + (5 × 10 0); (2 × 102) + (1 × 101) + (6 × 10 0); (4 × 104) + (2 × 103) + (9 × 102) + (6 × 10 0) 73 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Practice Page 69: Chinese paddlefish H. 16 P. 64 N. 81 I. 100 E. 343 F. 36 G. 27 C. 32 L. 125 S. 144 M. 256 A. 0 Y. 8 O. 729 D. 243 Practice Page 70: 1. commutative 2. associative 3. identity 4. identity 5. distributive 6. identity 7. associative 8. identity 9. commutative 10. distributive Practice Page 71: Lake Compounce E. 11 M. 21 N. 33 K. 15 C. 0 L. 20 A. 35 O. 40 R. 3 U. 10 S. 4 P. 6 Practice Page 75: Vostok 1. 150 ÷ n 2. n + 25 3. 3n 4. 150 – n 5. 50n 6. 2n + 3 Practice Page 76: 1. 5n 2. 3n 3. 7n 4. 7n – 3s 5. 9y + 2 6. 12t 7. 2w 8. 10p 9. 12b – 7 10. 160x Practice Page 77: Angel Falls, Venezuela U. 18 R. 16 B. 2 A. 4 L. 8 T. 17 W. 3 F. 42 N. 120 S. 56 78 H. 5 V. 13 X Marks E. 26 G.the 30 Spot! J. 14 Z. 12 Evaluating Expression Name Date You’ve found it—the secret to evaluating variable expressions. Solve three problems in a row to get Tic-Tac-Math! Practice Page 78: Practice Page 72: 1. 6 2. 5 3. 4 4. 3 5. 7 6. 2 7. 38 8. 8 9. 12 10. 11 11. 13 12. 1 x + 7, 3x, x ÷ 5, where x = 8 where x = 4 where x = 30 15 12 2x – 3, 1 + 4x, 13x – 28, where x = 7 where x = 2 where x = 5 9 37 11 9x + 6 – 5x, where x = –1 2 Practice Page 73: 1. n + 7 2. n – 2.8 3. n2 + 8 4. 12n 5. 2n + 3 6. 3n – 42 7. 2n – 5 4. 2.5n + 8.5 9. 45n2 10. n + 10 11. n – 6 12. n⁄4 6 A hot dog costs $1.27 more A super sundae costs $.88 than twice the price of a less than 3 times the price soda. Write an expression of a single cone. Write an that shows the price of a hot expression that shows the dog in relation to the price price of a super sundae in of a soda. Then evaluate relation to the price of a single where a soda costs $.99. cone. Then evaluate where a h = 2s + $1.27; $3.25 s = 3c – $.88; $3.29 single cone costs $1.39. Practice Page 79: 1. (Left to right) 7; 22; 3; 14; 1; 11; 27.5; 4; 5; 0 2. (Left to right) 10.81; 5.62; 0.61; 6.37; 3.24; 0.89 84 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Practice Page 74: Answers will vary. Check students’ work. 110 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Answer Key Practice Page 80: Clive Staples V. n + 4 = 9 T. n – 4 = 9 L. n ÷ 8 = 9 R. 3n = 9 P. (n ÷ 2) + 5 = 9 C. 5n – 6 = 9 N. 3n ÷ 4 = 9 A. 3n – 3 = 9 H. (n + 4) ÷ 2 = 9 E. 3(n + 1) = 9 S. (3n + 3) ÷ 3 = 9 I. n(2 + 1) = 9 Practice Page 81: 1. w + 2.5 = 3.8 2. y – 82 = 47 3. n⁄0.5 = 2 4. 3⁄8 k = 1 7⁄8 5. z⁄175 = 25 6. b + 1,231 = 2,342 7. 64d = 960 82 8. 4,050⁄x = 81 9. m⁄75 = 15 Give Y a Try! 10. 160v = 1,760 Writing Equations/ Word Problems Name Date Practice Page 82: A rectangle’s length is y cm. A rectangle’s length is y Harold’s dad is 3 times his age. Its width is 5 cm. Its perimeter cm. Its width is 2 cm. The The sum of Harold’s age and his y + y + the rectangle. 5 + 5 = 34 cm; y = 12 cm perimeter is 10 cm. Find the Oriana is 5 years older than Ella is twice Bella’s age, her brother Francisco. The sum and Stella is three times F + F + 5 = 27; Francisco is 11 and Oriana is 16 y + y + 2 + 2 = 10; y = 3 cm rectangle’s width. 3B – B = 8; difference in their ages is 30 4H + 3 – H = 30; How old is Harlan? How Bella is 4, Ella is years. old is his dad? ages is 8 years. How old is Harlan is 9 and his each girl? 8, and Stella dad is 39 is 12 than 4 times Harlan’s age. The Bella’s age. The difference each child? between Stella’s and Bella’s Sally has twice as many hair H + 3H = 60; is Harold? How old is his dad? Harold is 15 years old and his father is 45 father’s age is 60 years. How old Harlan’s dad is 3 years more of their ages is 27. How old is Janet bought 3 dozen Ty, Malcolm, and Fred were playing basketball. Malcolm from Delectable N + 2N + 2N – 3 donuts P + 3P + 3P – 6 T + T + 2 + 2T + 4 made 2 more baskets than Ty, Donuts. She bought 3 times = 32; Natasha = 36; 6 plain, 18 = 42; Ty made 9 and Fred made 4 more than as many honey-dipped as of all three girls’ ribbons is 32. twice the number that Ty made. She bought 6 fewer How many hair ribbons does has 7 ribbons, plain. honey-dipped, baskets, Malcolm Together, the boys made 42 chocolate-frosted than each girl have? baskets. How many baskets did honey-dipped. How many of Sally has 14, and and 12 chocolate made 11, and Fred each boy make? she buy? Bethany has 11 each didfrosted made 22 ribbons as Natasha. Bethany has 3 less than Sally. The sum Practice Page 83: Velcro L. 16 – 12 = n O. 12 – 4 = n R. 36 ÷ 3 = n E. 12 + 3 = n C. 12 ÷ 3 = n V. 3 × 12 = n 88 Practice Page 92: Wiley Post 1. W 2. I 3. L 4. E 5. Y Practice Page 85: James Montgomery Flagg L. 11 F. 5 T. 7 S. 84 R. 3 Y. 147 U. 72 A. 6 E. 125 O. 33 M. 12 G. 144 N. 243 J. 168 H. 365 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Practice Page 87: James Starley 1. y = x + 2 2. y = 2x 3. y = 3x 4. y = x – 2 5. y = -2 x Practice Page 94: 1. 400 sq ft 2. 90 sq ft 3. 25 sq ft 4. 300 sq ft 5. 225 sq ft 6. 135 sq ft 7. 100 sq ft 8. 75 sq ft Practice Page 95: koala S. 60 sq ft T. 63 sq ft O. 144 sq ft K. 48 sq ft 96 J. 72 sq ft A. 88 sq ft R. 12 sqMean ft and Median E. 56 sq ft Mode à la L. 160 sq ft Calculating Averages, Means, Median, and Mode 6. y = x – 4 7. y = 1⁄2 x 8. y = 2x – 1 9. y = 2x + 1 Name Date Yum! Look at the tasty mean, median, and mode problems. Solve three in a row to get Tic-Tac-Math! Practice Page 96: Practice Page 88: 1. ( Left to right) 1 to 3; 2 : 5; 1⁄3; 2 to 3; 5 : 3; 2 to 1; 4 : 1; 1⁄7; 3 to 5; 2 : 1 2. ( Top to bottom) 9 to 6, 36 : 24; 20 : 14, 1 to 0.7; 9 to 5 3. (Left to right) ; =; =; ; =; = Practice Page 89: Juliette Gordon Low R. 9 W. 15 N. 18 S. 10 I. 7 J. 4 U. 12 C. 48 L. 8 G. 21 M. 6 T. 36 E. 5 O. 24 D. 3 1912 Find the median of the Find the median, mode, Find the mean, median, following data: and range of the following mode, and range of the lengths of pieces of wood following numbers: 7, 12, 15, 12, 5, 6, 4, 1 1 2 6.5 or 6 median: 3; mode: 3; 4, 3, 8, 3, 5, 2, 3 range: 6 (all the measurements are in inches): mean: 3.2; median: 3; 6, 1, 3, 1, 5 mode: 1; range: 5 What whole number must the What whole number must What must the missing piece missing piece of data be to the missing piece of data be of data be to have a mean have a range of 15? to have a mode of 3? of 8? 16 14, ____, 9, 12, 3 7 5, 2, 3, 3, 2, 4, ____ 7, 12, ____, 3, 11 2, 2, 8, 2, 1 What must the missing piece What must the missing piece What must the missing piece of data be to have a mean of data be to have a mean of data be to have a mean of 30? of 20? of 33? 10 20, 30, 50, 40, ____ 30 18 18, 11, 7, 15, 51, 52, ____, 23, 32, 27, ____ 21, 17, 37, 45 Practice Page 97: 1. 13 2. 55; Answers may vary, but should express that 55 is the score that is not within range of the others. 3. 95 4. 45, about 89, 95, 95 5. 20, about 92, 95, 95 102 Practice Page 90: 1. 7 mph 2. 1 for $6 3. 8 ft/sec 4. 1 for $3.50 5. 1.5 pages/min 6. 1 can for $.60 Think Tank: 12 mph; 6 mi 111 6. P 7. O 8. S 9. T Practice Page 93: 1. F 2. D 3. C 4. B 5. D Practice Page 86: 1. n > 3; n ≥ -2; n ≤ 0; n < -4 2. (Top to bottom) 12, 13; 8; 28, 32; 9; 10, 8; 3 Write an algebraic equation to represent and solve each problem. Solve three problems in a row to get Tic-Tac-Math! is 34 cm. Find the length of Practice Page 91: 1. I, II, III 2. (1, 6), (5, –2), (6, 2) 3. Boxer, IV Practice Page 84: 1. n = 135 2. m = 16 3. b = 99 4. y = 13 5. t = 14 6. n = 311 7. 2.1 8. 3.5 9. 24 10. 2,004 11. 0.9 12. 1.2 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Shoe Sizes x 5 6 x x x x x x x x x x x x x x x x x x x x x x x 7 8 9 10 11 12 Answer Key x 13 14 Score e team’s equipment manager made the line plot from data she collected d recorded in a frequency table. Practice Page 98: ow what that table would look like. Then summarize what the data shows. Shoe Size 6 Tally Frequency 1 1 5 6 4 4 3 1 7 8 9 10 11 12 14 Summaries will vary. _________________________________________________________________________________ _________________________________________________________________________________ Practice Page 99: 1. $75 2. January 3. $79 4. March 5. Questions will vary. _________________________________________________________________________________ 104 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources Practice Page 100: 1. 1 2. 8 3. 2 4. 36–40; it is the tallest bar. Bonus — 1. c 2. d 3. b 4. a 112 100 Math Practice Pages, Grade 6 © 2015 • Scholastic Teaching Resources
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