Grateful acknowledgment is given for the contributions of Student Book Rosemary Theresa Barry Karen R. Boyle Barbara Brozman Gary S. Bush John E. Cassidy Dorothy Kirk Teacher Book Contributing Writers Dr. Judy Curran Buck Assistant Professor of Mathematics Plymouth State College Plymouth, New Hampshire Dr. Richard Evans Professor of Mathematics Plymouth State College Plymouth, New Hampshire Dr. Mary K. Porter Professor of Mathematics St. Mary's College Notre Dame, Indiana Sharon Ann Kovalcik Bernice Kubek Donna Marie Kvasnok Ann Cherney Markunas Joanne Marie Mascha Kathleen Mary Ogrin Dr. Anne M. Raymond Assistant Professor of Mathematics Keene State College Keene, New Hampshire Stuart P. Robertson, Jr. Education Consultant Pelham, New Hampshire Dr. David Rock Associate Professor, Mathematics Education University of Mississippi Oxford, Mississippi Copyright © 2000 by Houghton Mifflin Company. All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system without the prior written permission of the copyright owner, unless such copying is expressly permitted by federal copyright law. Address requests for permission to make copies of Houghton Mifflin materials to School Permissions, Houghton Mifflin Company,222 Berkeley Street, Boston, MA 02116. Printed in the U.S.A. ISBN-13: 978-0-395-98535-9 ISBN-10: 0-395-98535-8 17 18 0928 17 16 15 14 13 12 11 4500311334 Judith Ostrowski Jeanette Mishic Polomsky Patricia Stenger Annabelle L. Higgins Svete Michelle Lynn Rock Elementary Teacher Oxford School District Oxford, Mississippi Dr. Jean M. Shaw Professor of Elementary Education University of Mississippi Oxford, Mississippi c: B ..c: C"> ::J o :r: © Unit 1 Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Unit 2 Addition and Subtraction of Whole Numbers . . . . . . . . . . . . . 19 Unit 3 Multiplication of Whole Numbers . . . . . . . . . . . . . . . . . . . . .45 Unit 4 Division with 1-Digit Divisors . . . . . . . . . . . . . . . . . . . . . . . . 73 Unit 5 Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . 109 Unit 6 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Unit 7 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 173 Unit 8 Decimals . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Unit 9 Division with 2-Digit Divisors . . . . . . . . . . . . . . . . . . . . . . . 233 Unit 10 Data, Statistics, and Probability . . . . . . . . . . . . . . . . . . . . . 259 Unit 11 Algebra: Variables and Coordinate Graphing . . . . . . . . . . . . 283 Tables of Measures ................... . ............. ' .. 309 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 iii > c '" 0.. E o u -� :t: � c .s � 0> ::::> o ::r: @ � � 0> .� 0.. o U I- i i ! I UNIT 1 • TABLE OF CONTENTS Place Value Lesson ' Page 1 Place Value: Hundred Thousands . . . . . . . . . . . . . . . 3 2 Comparing and Ordering Numbers . . . . . . . . . . . . . . 5 3 Rounding to the Nearest Ten, Hundred, or Thousand ' " 7 4 Problem Solving A.pplication: Use a Graph . . . . . . . . 9 5 Millions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 6 Rounding Greater Numbers . . . . . . . . . . . . . . . . . . 1 3 7 Problem Solving Strategy: Find a Pattern . . . . . . . . 1 5 • Unit 1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 • Cumulative Review * Test Prep . . . . . . . . . . . . . . . . 1 8 Unit 1 1 Dear Family, During the next few weeks, our math class will be learning and practicing place value. You can expect to see homework that provides practice with rounding. Here is a sa'mple you may want to keep handy to give help if needed. Rounding to the Nearest Hundred We will be using this vocabulary: place value the value given to the place, or position, of a digit in a number round to replace an exact number by another number that is easier to use compare to decide which number of a group of numbers is greatest or least order to arrange a group of numbers in a certai n way, such as from least to greatest or from g reatest to least To round a number such as 4,175 to the nearest hundred, first find the digit in the hundreds place. Hundreds Place � 4,175 t greater than 5 Next, look at the digit in the place to the right (7). If the digit in the place to the right is less than 5, round down. If it is greater than or equal to 5, round up. Since the digit to the right of the hundreds place is greater than 5, round 4,175 up to 4,200, the nearest hundred. During this unit, students will need to continue practicing rounding and other skills related to place value, such as comparing numbers. Sincerely, Name _________________________ ____ __ ---� � --�Place Value: -- .;Thousands I Period Ones Period Hundred Thousands The standard form of the number written in this place-value chart is VI "0 C co VI VI � "0 0 C ..c: co VI of-' VI "0 "0 � C OJ 0 co � ..c: VI "0 of-' � C 0 � C � ..c: I I-- 1 0 5 VI "0 Q) � "0 C VI � C � I 0 4 VI OJ C 0 3 105,043 t When writing numbers in standard form, remember to use a comma to separate the periods. The number 105,043 is read as: one hundred five thousand, forty-three. Each group of 3 digits, separated by a comma, is called a period. Place a comma in each number. Then write each number in the place-value chart above. 1. 1 0 0 0 0 4 2 5 1 0 0 8 0 2 6 0 1 4 0 4 2 _ e_ " '� ' � ___ '''- ____ .. _. . . __ � ____ __ . _________ _ _ Read each number. Then write it in words. 2. 70,051 ____ ____________________ ______________ �--------- 3. 9,940 __________ ______________________________________ __ 4. 800,306�-----------�------------ --.,-.-� -�.--�- . _- -- Write each number in standard form. 5. seven thousand, five hundred nine 6. six hundred three thousand, twenty 7. fifteen thousand, three hundred --.�.-.---�.---�- · _. _____ . ___ ___ ___ ,_ .� Study the number 780,425. Write the digit that is in the 8. hundreds place __ _ 9. ones place __ __ 10. tens place thousands place __ _ hundred thousands place __ _ ten thousands place __ __ _ Unit 1 Lesson 1 3 � ""- ---- ---'- ' . •• "�--.-.... ".--".-� ..•. �.,, .. --•. -• • � , •. . -.. ,.=., .. ·· ··· ·,,_· · . ___ •• "·" ··_� _ _ Study the number 407,653. Write the place value of each digit. 11. 5 12. 7 13. 3 _____ place _____ place _____ place 14. 6 15. 0 16. 4 place place _____ place -. -. -= . - -- ._ . _ _ . ---- .- =".-.. -�-,-, .. �.-'". -- �.-.... = ,,- . � =-��---.. ,," ... . � . - .. -- - -.. �. Count by 100,000'5, as shown in the example below. 1 5,407, 1 1 5,407, 215,407, 31 5,407 17. 18,527, ___ ____________ _ 18. 5,728, _____ _____ . �---- 19. 208,752, ____ , _____ ____ _ 20. 743,101, ____ , __ ___ ____ _ rmng"i1J'Mi.i" Solve:Use the follo ify _. _ Reasonmg _ mystery number. 21. i am a 5-digit number. My tens digit is the sum of my hu'ndreds digit and thousands digit. My tens digit is twice my ones digit. My hundreds digit is 1 more than zero . . My thousands digit is seven times my hundreds digit. My ten thousands digit is the same as my ones digit. What is the mystery number? . Test Prep * Mixed Review � Which number sentence belongs to the same family of facts as 4 + 7 = II? A 1 1 + 4 = 15 B 7 - 4= 3 C 1 1- 7 = 4 D 18 - 7 = 1 1 4 Unit 1 Lesson 1 @) Samuel had 4 pieces of colored paper. He cut 3 paper birds from each piece . of paper. How many birds did he cut out in all? F 8 G 9 H 12 J 16 Name __________________________ __ Comparbig and. Ordering Numbers Follow these steps to compare 27,409 and 27,490: 1. Line up the numbers using place value. 2. Begin at the greatest place value. Find the first place value where the digits are different. 3. Compare those digits. Write >, <, or =. 27,409 27,490 ! 27,409 27,490 t Because 9 > 0, you can say that 27,490 G 27,409. > is greater than < is less than is equal to Because 0 < 9, you can also say that 27,409 @ 27,490. Write <, >, or = in each circle. 1. 43 0 73 58 0 50 + 8 36 0 26 2. 807 0 809 1,713 0 1,723 8,529 0 8,629 3. 28,916 0 27,916 35,499 0 35,500 67,999 0 68,000 4. 806,000 0 860,000 397,426 0 397,419 605,200 0 602,500 M�:l'''''I\_._': __ .. 'N_,>It,�_' .... _ " _··_. � w .. .. __ . ___ ." . ___ _ _ Compare to write the numbers in the column in order from greatest to least. 5. 1 51,51 5 6. 950,564 7,207. 407,704 245,039 1,275 898,090 713,280 96,371 60,000 Unit 1 Lesson 2 5 - - Writethe num least to greatest. 7. 50,020 52,000 52,020 50,200 52,002 8. 400,600 406,000 460,000 400,006 400,060 Write < or > in each circle. 9. 4,343 0 4,334 10. 53,742 0 53,821 11. 207,390 0 203,790 703 0 730 69,385 0 60,381 763,510 0 763,780 16,303 0 16,330 42,500 0 45,200 593,000 0 539,000 Solve. 12. What is the greatest 3-digit number you can write using each of the digits 4, 1, and 5 once? What is the least three-digit number? 13. What is the greatest 4-digit number you can write using each of the digits 2, 6, 3, and 9 once? What is the least four�digit number? Test * Mixed Beview � Which number sentence belongs to the � At the playground, 32 students divided same family of facts as 17 - 8 = 9? into teams with 8 children on each A 9 + 8 = 17 team. How many teams were there? B 17 + 9 = 26 C 9 - 8= 1 D 17 + 8 = 25 6 Unit 1 Lesson 2 F 16 G 8 H 6 J 4 Name __________________________ __ Bounding to the Nearest Ten, Hundred, or Thousand You can use a number line to round numbers. Round 1 32 to the nearest ten. 1. 132 is between 130 and 140. 7 .. I I I • 2. Since 132 is closer to 130 than to 140, 132 rounds down to 130. 130 140 Round 857 to the nearest hundred. 1. 857 is between 800 and 900. 2. Since 857 is closer to 900 than to 800, 857 rounds up to 900. � .. I I I I I I I I I I I I I I I I I I I I I I II I I I I I I I I II I • 600 700 800 900 Here's how to round without using a number line. 1 . Find the digit i n the place to the right of the place you are rounding to. 2. If that digit is less than 5, round the number down to the place you are rounding to. If that digit is 5 or greater, round the number up to the place you are rounding to. Other Examples· Round to tens. � 132 L Less than 5 So, 1 32 rounds down to 1 30. Round to hundreds. � L 5 or greater So, 857 rounds up to 900. Rounded to the nearest thousand, 1,462 rounds down to 1,000 because the digit in the place to the right of the thousands place is less than 5. Rounded to the nearest thousand, 7,503 rounds up to 8,000 because the digit in the place to the right of the thousands place is 5 or greater. _ _ .• �._,��. '''>�_,�._,_''''�_._, . .,., .• ,�,.= __ ., .... � .•... ,., .. _�,�,_.·.,_- ·· '' _·· •• .,, _. __ c_, _ · .. __ • _. __ _ Use the number line above to round each number to the nearest ten. 1. 1 31 ____ _ 136 ___ _ 2. 137 __ __ 133 ___ __ 139 __ _ 1 34 ___ _ 135 __ __ 138 __ _ -----".-.. ,-"----, . . ��-.... .- --' ,-- ---�,,-,-.- .. -.-.---, Use the number line above to round each number to the nearest hundred. 3. 612 __ _ 850 __ _ 4. 820 __ � 688 __ _ 760 ___ _ 706 __ _ 675 __ _ 815 __ _ Unit 1 Lesson 3 7 ''.'' '''' . . �"" .. -,,, .. ,,,'-. ..•. '�-'-�',.".��--. ,.-,""-'-�-.'�-'-'- Round to the nearest ten. 5. 25 _ _ _ 16 __ _ 9 __ _ 631 __ _ 6. 35 __ _ 55 __ _ 24 _ _ _ 358 __ _ Round to the nearest hundred. 7. 348 __ _ 420 _ _ _ 3,283 _ _ _ 8. 580 _-- 940 __ _ 5,775 _ _ _ '.n""""'.�,.,' or <. 17. 9,327 0 9,486 18. 27,087 0 27,807 19. 140,265 0 1 04,265 Round each number to the nearest thousand. 20. 4,509 8 Unit 1 lesson 3 21. 7,353 22. 8,099 Work Space. "" c: ro c E o u .!: t:= � c: B ..c Cl ::J o ::r:: @ - ..c Cl ·c > c o U Name ____ __ __ __ __ ______ __ __ __ __ __ __ How deep is the ocean? This bar graph shows the estimated depth of four oceans. In this lesson, you will use graphs to compare, make estimates, and draw conclusions about the data. Tips to Remember: 1. Understand 2. Decide 3. Solve 4. Look back . r • Ask yourself: Have I solved a problem like this one before? How did I solve it? • Compare the labels on the graph with the words and numbers in the problem. Find the facts you need from the graph. • When you can, make a prediction about the answer. Then compare your answer with your prediction. 1. What is the estimated depth of the Arctic Ocean to the nearest thousand feet? Think: How do you estimate a number using the graph? Ansvver __ __ __ ______ __ __ __ __ __ 3. Lake Baikal, the deepest lake in the world, is about 1,800 feet deeper than the Arctic Ocean. Estimate the depth of Lake Baikal. Problem Solving Application: Use a Graph Estimated Depth of Oceans 13,000 12,000 1 1,000 10,000 9,000 .... . Tuvalu '- +" c:: � 0 u Palau San Marino Liechtenstein 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 Population .=· ·· -�.��_� _" '<" '''''''_'"''.''_'_'�''·._'·��·-''·'''·'. _.=''W'''''- .•. , .. = ... " .... , ........ , . ·c,·,·.� .. , ._ ... ��.= �,�,,�""�_ . _, ..• �., . _ .•. · .,'" .... ". _. _ _ _ _ _ _ Solve. Use the bar graph above. 5. Which country shown in the graph has the greatest population? What is the population to the nearest thousand? 6. Which country has a population about three times the population of Tuvalu? ................................................................................................................................. ! ........................................................................................................................... . 7. Which two countries on the graph have about the same population? Extend Your Thinking 9. Can you use the graph to find which country in the world has the greatest population in the world? Explain. 10 Unit 1 Lesson 4 8. Wichita, Kansas has a population of 304,01 1 . Does this city have more or fewer people than the countries shown in the graph? Explain. 10. Explain the method you used to solve problem 6. c .8 ..c: 0> :::J o I @ - ..c: Ol .� o U Name ______ __ __ __ ______________ __ lVIillions The period after the thousands period is called the millions period. Millions f Thousands I'· ' Ones',' The standard form for the numbers written in this chart is 5,054,782. To read a number, say the number in each period, beginning with the greatest period, then say the name of each period, except for the ones period. The number 5,054,782 is read as: five million, fifty-four thousand, seven hundred eighty-two. ·27,001,909 Read: twenty-seven million, one thousand, nine hundred nine 300,518,040 Read: three hundred million, five hundred eighteen thousand, forty VI C 0 .---.- E "'0 (1) 10- "'0 C ::J I Period VI "'0 C ctJ VI ::J 0 VI c ....c 0 +' .- "'0 - VI - (1) .- c E 10- 0 "'0 .- C - c -.- ::J � � I 5 0 �erio : .' :Period' ,.;: VI "'0 c ctJ VI VI "'0 VI ::J C "'0 0 (1) ctJ ....c VI 10- +' ::J "'0 VI VI 0 c (1) c C ::J C � ....c � l- I 0 5 4 7 8 2 ··':""'I""tI/." ... ��'."wr."�'·'"."·,,."·w,,:.·_,,::.·;.".·."".".":.".".':;:,-,�: ···-··;;·-'-·'·-7·'·.";,""'�,''":;:¥�'>''''''''''''''=''<'�,;'�":'-·;.","c"".%'., ... �:" '" ;·�'*",:;:"":_"."."':.<.,.,,'."",".-:,',':o:';:,·�':,· . .,.,"'��:".,'.",.""":'''.,'O:I«',''''",'',<;:.'J,! ... '.''''.'::,....,.;.':.":<.,.;.'."t·_�-,K.·�:.·x:,,;-; -;m,·:,,-.·,-,-,,.·,,,,,,,;::,"'''''�''':;J!O._',.,'_1I'_�·,�,''''-;''',',,�� Place commas in each number. Then write each number in the place-value chart. 1. 1 2 0 0 0 1 7 2. 1 8 4 2 8 0 0 0 3. 4. 3,782,410 80,050,520 9 0 5 0 4 6 1 1 0 3 6 0 0 3 0 1 1 7 0 0 5 6 0 5 4 9 0 2 1 7 0 5 0 te ea erinstandard iorm '· ·'·�"��--�"�-=·�·�'=· ,�-- .. � ... ,,�--. -- . , ... "., ..... commas to separate the periods .. 5. eight million, two hundred fifty-one thousand, six hundred ninety-seven 6. three million, one hundred thousand, fifteen When a number is written using digits, it is written in standard form. For example, 24,035,600 is written in standard form. Unit 1 Lesson 5 1 1

Math Steps Level 4 (Grade 4)

Similar Math Steps Level 4 (Grade 4)