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Glenview, Illinois • Boston, Massachusetts Chandler, Arizona • Shoreview, Minnesota Upper Saddle River, New Jersey Copyright © by Pearson Education, Inc., or its affiliates. All rights reserved. Printed in the United States of America. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. The publisher hereby grants permission to reproduce Practice Pages and Tests, in part or in whole, the number not to exceed the number of students in each class. For information regarding permissions, write to Pearson School Rights and Permissions Department, One Lake Street, Upper Saddle River, New Jersey 07458. Pearson © is a trademark, in the U.S. and/or other countries, of Pearson plc or its affiliates. Grade 3: Step Up to Grade 4 Teacher’s Guide • Teacher Notes and Answers for Step-Up Lessons • Practice • Answers for Practice • Test • Answers for Test Scott Foresman and enVisionMATH™ are trademarks, in the U.S. and/or other countries, of Pearson Education, Inc., or its affiliates. ® 45095_SLPSHEET_FSD 1 6/6/08 3:57:25 PM F8 45095_SLPSHEET_FSD 2 Rounding Numbers Through Thousands F9 Comparing and Ordering Numbers Through Thousands F10 Place Value Through Millions F11 Rounding Numbers Through Millions F29 Patterns and Equations G7 Estimating Sums G42 Dividing with Objects G59 Factoring Numbers G66 Mental Math: Multiplying by Multiples of 10 G67 Estimating Products H1 Equal Parts of a Whole H2 Parts of a Region H3 Parts of a Set H14 Equivalent Fractions H18 Mixed Numbers I8 Congruent Figures and Motions I10 Solids and Nets I11 Views of Solid Figures I13 Congruent Figures I45 More Perimeter 6/6/08 3:57:30 PM Math Diagnosis and Intervention System Rounding Numbers Through Thousands Math Diagnosis and Intervention System Intervention Lesson Name Intervention Lesson F8 Teacher Notes F8 Rounding Numbers Through Thousands To round 34,853 to the nearest ten thousand, answer 1 to 6. Ongoing Assessment Materials 8 inches of yarn per pair Ask: What does 99,249 round to when rounded to the nearest hundred thousand? 100,000 1. Plot 34,853 on the number line below. 2. Use the yarn to help you decide whether 34,853 is closer to 30,000 or 40,000. Which is it closer to? Error Intervention 30,000 3. So, what is 34,853 rounded to the nearest If students have trouble remembering place value, 30,000 ten thousand? then have the students make a table across the top of their page that looks like the following: 4. Plot 37,421 on the number line above. 5. Use the yarn to help you decide whether 37,421 is closer to 30,000 or 40,000. Which is it closer to? less than 5 If the digit to the right of the number is 5 or more, the number rounds up. If the digit is less than 5, the number rounds down. 11. Keep the 7 and change the other digits to 0s. So, 739,218 rounds to If You Have More Time down 10. Do you need to round up or down? Ones © Pearson Education, Inc. 9. Is that digit less than 5, or is it 5 or greater? Tens 3 8. What digit is to the right of the 7? Hundreds 7 7. Which digit is in the hundred thousands place? Thousands 40,000 ten thousand? Round 739,218 to the nearest hundred thousand without using a number line. Answer 7 to 11. Ten Thousands Hundred Thousands 40,000 6. So, what is 37,421 rounded to the nearest 700,000 . Intervention Lesson F8 71 Math Diagnosis and Intervention System Intervention Lesson Name F8 Have students list all the four-digit numbers that stay the same when rounded to the nearest thousand (the multiples of 1,000), the five-digit numbers that stay the same when rounded to the nearest ten thousand (the multiples of 10,000), and the six-digit numbers that stay the same when rounded to the nearest hundred thousand (the multiples of 100,000). Rounding Numbers Through Thousands (continued) Round each number to the nearest ten. 12. 94,519 94,520 537,680 13. 537,681 Round each number to the nearest hundred. 14. 968,458 968,500 58,300 15. 58,326 Round each number to the nearest thousand. 16. 318,512 319,000 21,000 17. 21,236 Round each number to the nearest ten thousand. 18. 285,431 290,000 180,000 19. 184,032 Round each number to the nearest hundred thousand. 20. 735,901 700,000 500,000 21. 472,992 Use the information in the table for Exercises 22–23. 22. What is the price of the house rounded to the nearest hundred thousand? 200,000 Real Estate Amount Sale in Dollars Price of House 169,256 Advertising Fee 7,177 Repairs 5,873 23. What is the cost of repairs rounded to the nearest thousand? 6,000 rounded to the nearest thousand. Any numbers between 43,500 and 44,499 25. Reasoning Explain how to round 496,275 to the nearest ten thousand. Sample answer: The digit in the ten thousands place is 9. The digit to the right of 9 is 6, which is 5 or greater. So, round up. Think of adding 1 to 49 to make 50. To the nearest ten thousand, 496,275 rounds to 500,000. © Pearson Education, Inc. © Pearson Education, Inc. 3 24. Reasoning Write three numbers that would round to 44,000 when 72 Intervention Lesson F8 Intervention Lesson F8 Comparing and Ordering Numbers Through Thousands Math Diagnosis and Intervention System Intervention Lesson Name Math Diagnosis and Intervention System Intervention Lesson F9 Teacher Notes F9 Comparing and Ordering Numbers Through Thousands Ongoing Assessment In a recent county election, Henderson received 168,356 votes. Juarez received 168,297 votes. Determine who received more votes by answering 1 to 7. 1. Write 168,356 and 168,297 in the place-value chart. hundred thousands ten thousands thousands hundreds tens ones 1 1 6 6 8 8 3 2 5 9 6 7 Error Intervention For Exercises 2–5, write ⬍, ⬎, or ⫽. 2. Start with the left column in the chart. 100,000 ⴝ 100,000 60,000 ⴝ 60,000 8,000 ⴝ 8,000 300 ⬎ 200 3. Since the hundred thousands are equal, compare the ten thousands. 4. Since the ten thousands are equal, compare the thousands. 5. Since the thousands are equal, compare the hundreds. 6. Since 300 ⬎ 200, compare 168,356 and 168,297. 168,356 If students have trouble ordering numbers that are written horizontally, then encourage them to write one number above the other, making sure they line up corresponding place values. Then compare the numbers in each column. 168,297 ⬎ Henderson 7. So, which candidate received more votes? © Pearson Education, Inc. Ask: Why do you work from left to right instead of right to left when comparing or ordering numbers? Sample answer: The digits on the left have a higher value than the digits on the right. If You Have More Time Have students write ordering problems for a partner to solve. Order 346,217; 319,304; and 348,862 from least to greatest by answering 8 to 12. 8. Write 346,217; 319,304; and 348,862 in the place-value chart on the next page. Intervention Lesson F9 73 Math Diagnosis and Intervention System Intervention Lesson Name F9 Comparing and Ordering Numbers Through Thousands (continued) hundred thousands ten thousands thousands hundreds tens ones 3 3 3 4 1 4 6 9 8 2 3 8 1 0 6 7 4 2 9. Start on the left. Write ⬍, ⬎, or ⫽. 300,000 ⴝ ⴝ 300,000 300,000 10. Since the hundred thousands are all equal, compare the ten thousands. Since 10,000 ⬍ 40,000, what is the least number? 319,304 < 8,000, compare the thousands place 11. Since 6,000 _____ of the other two numbers. 346,217 ⬍ 348,862 12. The numbers in order from least to greatest are: 319,304 346,217 348,862 Use ⬍ or ⬎ to compare each pair of numbers. 13. 8,112 < 8,221 14. 418,412 15. 321,159 > 312,147 16. 20,657 17. 118,111 < 118,147 18. 914,146 < < > 481,930 21,687 904,168 Order the numbers from least to greatest. 20. 12,984; 12,875; 11,987 21. 200; 12,945; 2,309 11,987; 12,875; 12,984 22. 321,984; 345,879; 323,490 200; 2,309; 12,945 321,984; 323,490; 345,879 23. Reasoning When comparing 17,834 and 17,934, can you start by comparing hundreds? Explain. No; Always compare the left-most digit first. 74 Intervention Lesson F9 Intervention Lesson F9 © Pearson Education, Inc. 820; 7,980; 8,200 © Pearson Education, Inc. 3 19. 8,200; 820; 7,980 Math Diagnosis and Intervention System Intervention Lesson Place Value Through Millions Math Diagnosis and Intervention System Intervention Lesson Name F10 Teacher Notes F10 Place Value Through Millions 1. Write 462,397,158 in the place-value chart below. Ongoing Assessment Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones Ones Ten Millions Thousands Hundred Millions Millions 4 6 2 3 9 7 1 5 8 Ask: How does the number of zeros in the place value chart change as you move each place to the left? One zero is added to each place as you move left away from the ones. 2. Complete the table to find the value of each digit in 462,397,158. Digit Place Error Intervention Value 4 hundred millions 400,000,000 6 60,000,000 2,000,000 millions 300,000 hundred thousands 90,000 ten thousands 7,000 thousands 100 hundreds 50 tens 8 ones If students are having trouble remembering the number of zeros each value has, ten millions 2 3 9 7 1 5 8 then encourage students to write #00,000,000 above the heading hundred millions, #0,000,000 above the heading ten millions, #,000,000 above the heading millions, and so on. That way they know to place the number (#) and then the appropriate number of zeros. © Pearson Education, Inc. 3. Use the table above to help you write 462,397,158 in expanded form. 400,000,000 ⫹ 90,000 ⫹ 60,000,000 7,000 2,000,000 ⫹ ⫹ 100 ⫹ 50 8 ⫹ 300,000 ⫹ ⫹ . If You Have More Time 4. Write the short word form of 462,397,158. 462 million, 397 Have students look up the population of the United States and write the number in standard form, expanded form, and word form. thousand, 158 Four hundred sixty-two million, three hundred ninety-seven thousand, one hundred fifty-eight 5. Write 462,397,158 in word form. Intervention Lesson F10 75 Math Diagnosis and Intervention System Intervention Lesson Name F10 Place Value Through Millions (continued) Write the value of the underlined digit. 6. 4,562,398 7. 15,347,025 60,000 8. 37,814,956 5,000,000 9. 526,878,953 10. 782,354,065 500,000,000 4,000 11. 918,403,760 60 10,000,000 Write each number in word form and in short word form. 12. 2,160,500 Two million, one hundred sixty thousand, five hundred; 2 million, 160 thousand, 5 hundred 13. 91,207,040 14. 510,200,450 Ninety-one million, two hundred seven thousand, forty; 91 million, 207 thousand, 40 Five hundred ten million, two hundred thousand, four hundred fifty; 510 million, 200 thousand, 4 hundred, 50 15. An underground rail system in Osaka, Japan carries 988,600,000 passengers per year. Write this number in expanded form. 16. Reasoning What number would make the number sentence below true? 3,589,000 ⫽ 3,000,000 ⫹ ■ ⫹ 80,000 ⫹ 9,000 17. Reasoning What number can be added to 999,990 to make 1,000,000? 500,000 © Pearson Education, Inc. © Pearson Education, Inc. 3 900,000,000 ⴙ 80,000,000 ⴙ 8,000,000 ⴙ 600,000 10 76 Intervention Lesson F10 Intervention Lesson F10 Math Diagnosis and Intervention System Rounding Numbers Through Millions Math Diagnosis and Intervention System Intervention Lesson Name Intervention Lesson F11 Teacher Notes F11 Rounding Numbers Through Millions Round 4,307,891 to the nearest million by answering 1 to 5. 1. What digit is in the millions place? 4 Ongoing Assessment 2. What digit is to the right of the 4? 3 Ask: What is the smallest number that will round to 1,000,000 when rounded to the nearest million? 950,000 3. Is the digit to the right of 4 less than 5, less than 5 or is it 5 or greater? If the digit to the right of the number is 5 or more, the number rounds up. If the digit is less than 5, the number rounds down. Down 4. Do you need to round up or down? 5. Keep the 4 and change the other digits to 0s. What is 4,307,891 rounded to the nearest million? Error Intervention 4,000,000 then have the students make a place value chart across the top of their page. Round 6,570,928 to the nearest hundred thousand by answering 6 to 11. 6. Which digit is in the hundred thousands place? 5 7. What digit is to the right of the 5? 7 8. Is the digit to the right of 5 less than 5, If students do not know the place values, 5 or greater or is it 5 or greater? then use F10: Place Value Through Millions. Up 9. Do you need to round up or down? 10. Change the 5 to the next highest digit and change © Pearson Education, Inc. If students are having trouble identifying the place values for rounding, the other digits to 0s. What is 6,570,928 rounded to the nearest hundred thousand? 6,600,000 11. What is 6,570,928 rounded to the nearest thousand? 6,571,000 Intervention Lesson F11 If You Have More Time Have students round 5,830,957 to the nearest ten, hundred, thousand, ten thousand, hundred thousand, and million. Repeat with 9,999,999. 77 Math Diagnosis and Intervention System Intervention Lesson Name F11 Rounding Numbers Through Millions (continued) Round 1,581,267 to each place. 12. ten 1,581,270 14. thousand 1,581,000 16. hundred thousand 1,600,000 13. hundred 1,581,300 1,580,000 15. ten thousand 17. million 2,000,000 Round each number to the nearest ten. 18. 3,194,764 3,194,760 19. 8,967,001 8,967,000 Round each number to the nearest hundred. 20. 1,265,906 1,265,900 21. 6,906,294 6,906,300 Round each number to the nearest thousand. 22. 8,070,126 8,070,000 23. 9,264,431 9,264,000 Round each number to the nearest ten thousand. 24. 7,514,637 7,510,000 25. 2,437,894 2,440,000 Round each number to the nearest hundred thousand. 26. 1,395,384 1,400,000 27. 3,992,460 4,000,000 5,000,000 29. 5,022,121 5,000,000 30. 2,439,019 2,000,000 31. 8,888,888 9,000,000 32. Reasoning A number rounded to the nearest million is 4,000,000. One less than the same number rounds to 3,000,000 when rounded to the nearest million. What is the number? 3,500,000 78 Intervention Lesson F11 Intervention Lesson F11 © Pearson Education, Inc. 28. 4,578,952 © Pearson Education, Inc. 3 Round each number to the nearest million. Math Diagnosis and Intervention System Intervention Lesson Patterns and Equations Math Diagnosis and Intervention System Intervention Lesson Name F29 Teacher Notes F29 Patterns and Equations 1. Complete the table at the right. 2. What expression describes the cost with delivery for a food order costing c dollars? Cost of Food Order c Cost with Delivery d $8.50 $10.50 $9.25 $11.25 $10.47 $12.47 c2 3. Set d equal to the expression to get an equation representing the relationship between the cost of the food order c and the cost with delivery d. $10.98 $12.98 $12.06 $14.06 $16.52 4. Use the equation to find d, when c ⫽ $14.52. 5. Complete the table at the right. 6. Write an equation representing the relationship between the number of pretzels p and the total cost c. If students have trouble writing an expression for the pattern in the table, Number of Pretzels p Total Cost c 2 $11.00 c 5.5p 7. Use the equation to find c, when p ⫽ 4. $22.00 then use F26: Expressions with Addition and Subtraction or F27: Expressions with Multiplication and Division. 3 $16.50 5 $27.50 6 $33.00 7 $38.50 to show the relationship between the number of field goals f and the number of points p. Sample answers are shown in the table. Field Goals (f) 1 Points (p) 3 2 6 3 9 4 12 If You Have More Time Have students think of a real-world situation which can be represented by an equation, write the equation, and create a table. 8. A field goal in football is worth 3 points. Complete the table below © Pearson Education, Inc. Ask: If a rule for a table is x 7, what equation represents the relationship between the inputs x and the outputs y? y ⫽ x ⫹ 7 Error Intervention c2 d⫽ Ongoing Assessment 5 18 9. Write an equation to represent the relationship between p 3f the number of field goals f and points p. Intervention Lesson F29 113 Math Diagnosis and Intervention System Intervention Lesson Name F29 Patterns and Equations (continued) Write an equation to represent the relationship between x and y in each table. Then use the equation to complete the table. 10. 11. y x y x y 2 8 12 2 4 32 3 9 18 3 5 40 8 14 24 4 7 56 14 20 30 64 27 42 5 7 8 21 10 80 yx6 13. yx6 14. 15. x y x y x y 1 2 4.8 50 10 14 5 3 7.2 40 8 22 13 4 9.6 35 7 26 17 6 14.4 25 5 30 21 7 16.8 15 3 y 2.4x yx5 x 2 2.5 3.2 3.8 4.7 y 9.8 10.3 11 11.6 12.5 © Pearson Education, Inc. © Pearson Education, Inc. 3 y 8x 10 yx9 16. 12. x y x 7.8 17. Reasoning If a rule is c ⫽ p ⫹ 5, what is c when p ⫽ 20? 25 114 Intervention Lesson F29 Intervention Lesson F29 Math Diagnosis and Intervention System Intervention Lesson Estimating Sums Math Diagnosis and Intervention System Intervention Lesson Name G7 Teacher Notes G7 Estimating Sums When Joseppi added 43 and 28, he got a sum of 71. To check that this answer is reasonable, use estimation. Ongoing Assessment 1. Round each addend to the nearest ten. 43 rounded to the nearest ten is 40 . 28 rounded to the nearest ten is 30 . 2. Add the rounded numbers. Error Intervention 70 40 30 If students are having trouble with rounding the addends correctly, Since 71 is close to 70, the answer is reasonable. When Ling added 187 and 242, she got a sum of 429. To check that this answer is reasonable, use estimation. then use F2: Rounding to Nearest Ten and Hundred. 3. Round each addend to the nearest hundred. 187 rounded to the nearest hundred is 200 If You Have More Time . © Pearson Education, Inc. Ask: When estimating 124 ⴙ 138, which would give a closer estimate, rounding to the nearest ten or to the nearest hundred? Rounding to the nearest ten. 242 rounded to the nearest hundred is 200 . Have students work with a partner to list ten different sums which are about 300 when estimated by rounding each addend to the nearest hundred. 4. Add the rounded numbers. 200 200 400 Since 429 is close to 400, the answer is reasonable. Intervention Lesson G7 91 Math Diagnosis and Intervention System Intervention Lesson Name G7 Estimating Sums (continued) Estimate by rounding to the nearest ten. 5. 71 36 6. 24 81 110 9. 68 27 7. 43 91 100 10. 19 93 100 8. 54 66 130 11. 89 75 110 120 12. 54 33 170 80 Estimate by rounding to the nearest hundred. 13. 367 14. 791 506 15. 141 _ 632 _ 249 _ 500 1,400 700 17. 940 190 1,100 20. 369 481 900 18. 675 460 16. 1,400 19. 531 776 1,200 21. 151 260 458 891 _ 1,300 22. 705 936 500 1,600 23. Reasoning Jaimee was a member of the school chorus 24. Luis sold 328 sport bottles and Jorge sold 411. About how many total sport bottles did the two boys sell? 130 700 to 46 so that the sum is 70 when both numbers are rounded to the nearest ten? Explain. 24; Since 46 rounds to 50, and 20 ⴙ 50 ⴝ 70, you need the largest number that rounds to 20, which is 24. 92 Intervention Lesson G7 Intervention Lesson G7 © Pearson Education, Inc. 25. Reasoning What is the largest number that can be added © Pearson Education, Inc. 3 for 3 years. Todd was a member of the school band for 2 years. The chorus has 43 members and the band has 85 members. About how many members do the two groups have together? Math Diagnosis and Intervention System Intervention Lesson Dividing with Objects Math Diagnosis and Intervention System Intervention Lesson Name G42 Teacher Notes G42 Dividing with Objects Materials 7 counters and 3 half sheets of paper for each student or pair Ongoing Assessment Andrew has 7 model cars to put on 3 shelves. He wants to put the same number of cars on each shelf. How many cars should Andrew put on each shelf? Answer 1 to 8. Ask: Why should the remainder always be less than the divisor? For example, when dividing 10 by 3, why can you not have a remainder of 4? If the remainder is equal to or greater than the divisor, then the quotient should be larger. For example, when dividing 10 counters into 3 equal groups, if 4 are left, there are enough to put another counter into each group. Find 7 3. 1. Show 7 counters and 3 sheets of paper. 2. Put 1 counter on each piece of paper. 3. Are there enough counters to put yes another counter on each sheet of paper? Error Intervention 4. Put another counter on each piece of paper. If students have trouble completing problems using counters or drawings, 5. Are there enough counters to put © Pearson Education, Inc. then encourage them to use repeated subtraction to solve the problem. Continue to subtract until it can no longer be done. What is left is the remainder. no another counter on each sheet of paper? 6. How many counters are on each sheet? 2 7. How many counters are remaining, or left over? 1 So, 7 3 is 2 remainder 1, or 7 3 2 R1. If You Have More Time 8. How many cars should Andrew put on each shelf? How many cars will be left over? Andrew can put 2 cars on each shelf with 1 car left over. Intervention Lesson G42 161 Have partners find all the division sentences that can be written if 8 is the dividend and the divisor is 1 to 8. Math Diagnosis and Intervention System Intervention Lesson Name G42 Dividing with Objects (continued) Use counters or draw a picture to find each quotient and remainder. 9. 8 3 10. 17 3 5 R2 11. 14 3 4 R2 2 R3 13. 22 4 5 R2 14. 34 4 8 R2 15. 13 5 2 R3 16. 27 5 5 R2 17. 46 5 9 R1 18. 14 6 2 R2 19. 26 6 4 R2 20. 38 6 6 R2 21. 17 7 2 R3 22. 27 7 3 R6 23. 45 7 6 R3 24. 18 8 2 R2 25. 28 8 3 R4 26. 37 8 4 R5 27. 14 9 1 R5 28. 28 9 3 R1 29. 39 9 4 R3 30. 12 8 1 R4 31. 68 7 9 R5 32. 59 8 7 R3 34. 26 5 5 R1 35. 34 6 5 R4 37. 21 6 3 R3 38. 3 2 2 R1 36. 14 5 2 R4 1 R1 39. Reasoning Grace is reading a book for school. The book has 26 pages and she is given 3 days to read it. How many pages should she read each day? Will she have to read more pages on some days than on others? Explain. © Pearson Education, Inc. 12. 11 4 33. 9 4 © Pearson Education, Inc. 3 2 R2 She should read 8–9 pages each day; she will read 9 pages on 2 days and 8 pages on 1 day. 162 Intervention Lesson G42 Intervention Lesson G42 Math Diagnosis and Intervention System Intervention Lesson Factoring Numbers Math Diagnosis and Intervention System Intervention Lesson Name G59 Teacher Notes G59 Factoring Numbers Materials color tiles or counters, 24 for each student Ongoing Assessment The arrays below show all of the factors of 12. Ask: What is the only even prime number? 2 1 ⫻ 12 Error Intervention If students do not find all of the factors of a number, 2⫻6 3⫻4 The order factors are listed may vary. 1. What are all the factors of 12? 1 , 2 , 3 4 , 4⫻3 6 , , 6⫻2 12 2. Create all the possible arrays you can with 17 color tiles. 1 3. What are the factors of 17? , 12 ⫻ 1 17 Numbers which have only 2 possible arrays and exactly 2 factors are prime numbers. 4. Is 17 a prime number? 5. Is 12 a prime number? If You Have More Time yes Have students write any number from 1 to 1,000 on a note card. Collect all of the cards and shuffle them. Have a student draw a card and explain why the number on the cards is either prime or composite. Repeat until all students have a turn. no © Pearson Education, Inc. Numbers which have more than 2 possible arrays and more than 2 factors are composite numbers. 6. Is 17 a composite number? no 7. Is 12 a composite number? yes The order factors are listed may vary. 8. What are all the factors of 24? then have them use manipulatives such as color tiles or counters to create arrays. Have them find all arrays methodically. Start with 1 row. See if the given number of counters can be put into 2 rows. Then see if they can be put into 3 rows and so on. 1, 2, 3, 6, 8, 12, 24 9. Is 24 a prime number or a composite number? composite Answers: Exercise 22 from page 196 Intervention Lesson G59 195 18 ⫻ 1 ⫽ 18 Math Diagnosis and Intervention System Intervention Lesson Name G59 Factoring Numbers (continued) Find all the factors of each number. Tell whether each is prime or composite. 10. 7 11. 8 12. 21 1, 7; 1, 2, 4, 8; 1, 3, 7, 21; prime composite composite 13. 48 14. 51 15. 9 1, 2, 3, 4, 6, 8, 1, 3, 17, 51; 1, 3, 9; 12, 16, 24, 48; composite composite composite 16. 13 17. 26 1, 13; 1, 2, 13, 26; prime composite 19. 55 20. 70 6 ⫻ 3 ⫽ 18 2 ⫻ 9 ⫽ 18 18. 40 3 ⫻ 6 ⫽ 18 1, 2, 4, 5, 8, 10, 20, 40; composite 1 ⫻ 18 ⫽ 18 21. 83 1, 5, 11, 55; 1, 2, 5, 7, 10, 1, 83; composite 14, 35, 70; composite prime 22. Mr. Lee has 18 desks in his room. He would like them arranged in a rectangular array. Draw all the different possible arrays and write a multiplication sentence for each. odd number. Is Lee’s reasoning correct? Give an example to prove your reasoning. No; 53 is a prime number not because it is an odd number, but because it only has 2 factors: 1 and 53. A counterexample is 15 is an odd number but it is not a prime number because 15 has more than 2 factors: 1, 3, 5, 15. 196 Intervention Lesson G59 Intervention Lesson G59 © Pearson Education, Inc. 23. Reasoning Lee says 53 is a prime number because it is an 9 ⫻ 2 ⫽ 18 © Pearson Education, Inc. 3 See answers on page 59. Mental Math: Multiplying by Multiples of 10 Math Diagnosis and Intervention System Intervention Lesson Name Math Diagnosis and Intervention System Intervention Lesson G66 Teacher Notes G66 Mental Math: Multiplying by Multiples of 10 A publishing company ships a particular book in boxes with 6 books each. How many books are in 20 boxes? How many in 2,000 boxes? Ongoing Assessment Find 20 ⫻ 6 and 2,000 ⫻ 6 by filling in the blanks. 1. 20 ⫻ 6 ⫽ (10 ⫻ 2) ⫻ 6 2 ⫽ 10 ⫻ ( 2. 2,000 ⫻ 6 ⫽ (1,000 ⫻ 2) ⫻ 6 ⫻ 6) ⫽ 1,000 ⫻ ( 12 ⫽ 10 ⫻ 120 ⫽ 2 12,000 ⫽ 120 books 12,000 books 3. How many books are in 20 boxes? 4. How many books are in 2,000 boxes? ⫻ 6) 12 ⫽ 1,000 ⫻ Error Intervention If students are making mistakes with multiplication facts, The same publishing company ships a smaller book in boxes with 40 books each. How many books are in 50 boxes? How many are in 500 boxes? then use some of the intervention lessons on basic multiplication facts, G25 to G32. Find 50 ⫻ 40 and 500 ⫻ 40 by filling in the blanks. 5. 50 ⫻ 40 ⫽ (5 ⫻ 10 )⫻ (4 ⫻ 10 ) 4 ⫽5⫻ © Pearson Education, Inc. ⫽ 20 ⫻ ⫽ 100 6. 500 ⫻ 40 ⫽ (5 ⫻ 10 (4 ⫻ ⫻ 10 ⫻ 10 ⫽5⫻ 100 4 ⫽ 20 ⫻ 2,000 8. How many books are in 500 boxes? ⫻ 100 ⫻ 10 1,000 2,000 books 20,000 books 7. How many books are in 50 boxes? )⫻ ) Intervention Lesson G66 If You Have More Time Have students write and solve a word problem that involves multiplying multiples of ten. 20,000 ⫽ Ask: Will the number of zeros in the product always be the same as the sum of the number of zeros in the factors? No Why not? Sometimes the leading numbers in the factors will multiply to make another zero such as 4 ⫻ 5 ⫽ 20. 209 Math Diagnosis and Intervention System Intervention Lesson Name G66 Mental Math: Multiplying by Multiples of 10 (continued) Notice the pattern when multiplying multiples of 10. 9. 7 ⫻ 80 ⫽ 560 10. 4 ⫻ 60 ⫽ 240 70 ⫻ 80 ⫽ 5,600 40 ⫻ 60 ⫽ 2,400 70 ⫻ 800 ⫽ 56,000 40 ⫻ 600 ⫽ 24,000 Multiply. 11. 30 ⫻ 40 ⫽ 1,200 14. 50 ⫻ 400 ⫽ 20,000 17. 600 ⫻ 30 ⫽ 18,000 20. 70 ⫻ 500 ⫽ 35,000 23. 800 ⫻ 80 ⫽ 64,000 12. 10 ⫻ 600 ⫽ 6,000 15. 700 ⫻ 30 ⫽ 21,000 18. 40 ⫻ 90 ⫽ 3,600 21. 30 ⫻ 800 ⫽ 24,000 24. 30 ⫻ 600 ⫽ 18,000 13. 70 ⫻ 20 ⫽ 1,400 16. 40 ⫻ 800 ⫽ 32,000 19. 90 ⫻ 500 ⫽ 45,000 22. 200 ⫻ 70 ⫽ 14,000 25. 40 ⫻ 300 ⫽ 12,000 a school fundraiser. If each of them collects 400 pennies, how many have they collected all together? 12,000 27. Reasoning Raul multiplied 60 ⫻ 500 and got 30,000. Since there are 4 zeros in the answer, he thought his answer was incorrect? Do you agree? Why or why not? pennies © Pearson Education, Inc. © Pearson Education, Inc. 3 26. A class of 30 students is collecting pennies for No, one of the zeros is from 6 ⴛ 5 which is 30. 210 Intervention Lesson G66 Intervention Lesson G66 Math Diagnosis and Intervention System Intervention Lesson Estimating Products Math Diagnosis and Intervention System Intervention Lesson Name G67 Teacher Notes G67 Estimating Products Mrs. Wilson’s class at Hoover Elementary School is collecting canned goods. Their goal is to collect 600 cans. There are 21 students in the class and each student agrees to bring in 33 cans. Answer 1 to 7 to find if the class will meet their goal. Ongoing Assessment Ask: Why is it preferable to round 591 to the nearest hundred rather than the nearest ten? It is easier to multiply 600 than 590. Estimate 21 ⫻ 33 and compare the answer to 600. Round each factor to get numbers you can multiply mentally. 20 1. What is 21 rounded to the nearest ten? 30 2. What is 33 rounded to the nearest ten? Error Intervention 600 20 ⫻ 30 ⫽ 3. Multiply the rounded numbers. If students have problems rounding numbers, The answer is the same as the number needed to meet the goal. 4. 21 was rounded to 20. Was it rounded up or down? down 5. 33 was rounded to 30. Was it rounded up or down? down 6. Is 21 ⫻ 33 more or less than 20 ⫻ 30? more yes 7. Will the goal be reached? then use F2: Rounding to Nearest Ten and Hundred and F4: Numbers Halfway Between and Rounding. If You Have More Time Hoover Elementary School had a goal to collect 12,000 canned goods. There are 18 classes and each class collects 590 cans. Answer 8 to 13 to find if the school will meet their goal. Have students name situations when an estimate if sufficient and situations when an exact answer is needed. Estimate 18 ⫻ 590 and compare the answer with 12,000. © Pearson Education, Inc. Round each factor to get numbers you can multiply mentally. 20 8. What is 18 rounded to the nearest ten? 600 9. What is 590 rounded to the nearest hundred? 10. Multiply the rounded numbers. 20 ⫻ 600 ⫽ 12,000 The answer is the same as the number needed to meet the goal. Intervention Lesson G67 211 Math Diagnosis and Intervention System Intervention Lesson Name G67 Estimating Products (continued) up 11. 18 was rounded to 20. Was it rounded up or down? up 590 was rounded to 600. Was it rounded up or down? less 12. Is 18 ⫻ 590 more or less than 20 ⫻ 600? no 13. Will the goal be reached? Round each factor so that you can estimate the product mentally. 14. 71 ⫻ 382 15. 27 ⫻ 62 70 ⴛ 400 30 ⴛ 60 28,000 1,800 17. 58 ⫻ 176 18. 831 ⫻ 42 60 ⴛ 200 800 ⴛ 40 12,000 32,000 20. 87 ⫻ 67 21. 373 ⫻ 95 16. 45 ⫻ 317 50 ⴛ 300 15,000 19. 16 ⫻ 768 20 ⴛ 800 16,000 22. 57 ⫻ 722 90 ⴛ 70 400 ⴛ 100 60 ⴛ 700 6,300 40,000 42,000 23. Debra spends 42 minutes each day driving to 1,200 minutes the estimate be an overestimate or an underestimate? Explain. It would be an underestimate because you are rounding both factors down. 212 Intervention Lesson G67 Intervention Lesson G67 © Pearson Education, Inc. 24. Reasoning If 64 ⫻ 82 is estimated to be 60 ⫻ 80, would © Pearson Education, Inc. 3 work. About how many minutes does she spend driving to work each month? Math Diagnosis and Intervention System Intervention Lesson Equal Parts of a Whole Math Diagnosis and Intervention System Intervention Lesson Name H1 Teacher Notes H1 Equal Parts of a Whole Materials rectangular sheets of paper, 3 for each student; Ongoing Assessment crayons or markers fold 1. Fold a sheet of paper so the two shorter edges Ask: Looking at the names for shapes divided into 4, 5, 6, 8, 10, and 12 equal parts, what might be the name of a shape divided into seven equal parts? sevenths are on top of each other, as shown at the right. 2. Open up the piece of paper. Draw a line down the fold. Color each part a different color. The table below shows special names for the equal parts. All parts must be equal before you can use these special names. 3. Are the parts you colored equal in size? 4. How many equal parts are there? yes Number of Name of Equal Parts Equal Parts 2 5. What is the name for the parts you colored? halves 6. Fold another sheet of paper like above. Then fold it again so that it makes a long slender rectangle as shown below. 7. Open up the piece of paper. Draw lines down the folds. Color each part a different color. 8. Are the parts you colored equal in size? © Pearson Education, Inc. 9. How many equal parts are there? yes 2 halves 3 thirds 4 fourths 5 fifths 6 sixths 8 eighths If You Have More Time tenths 12 twelfths New fold 10. What is the name for the parts you colored? If children have trouble understanding the concept of equal parts, then use A35: Equal parts. 10 4 Error Intervention Old fold Have students fold other rectangular sheets of paper and circular pieces of paper to find and name other equal parts. fourths 11. Fold another sheet of paper into 3 parts that are not equal. Open it and draw lines down the folds. In the space below, draw your rectangle and color each part a different color. Check that students draw unequal parts. Intervention Lesson H1 85 Math Diagnosis and Intervention System Intervention Lesson Name H1 Equal Parts of a Whole (continued) Tell if each shows parts that are equal or parts that are not equal. If the parts are equal, name them. equal 12. 13. not equal fourths 14. equal 15. thirds 16. equal equal eighths 17. not equal 19. equal twelfths 18. not equal fifths 20. equal 21. not equal 23. not equal halves equal sixths 24. Reasoning If 5 children want to equally share a large pizza and each gets 2 pieces, will they need to cut the pizza into fifths, eighths, or tenths? tenths © Pearson Education, Inc. © Pearson Education, Inc. 3 22. 86 Intervention Lesson H1 Intervention Lesson H1 Math Diagnosis and Intervention System Intervention Lesson Parts of a Region Math Diagnosis and Intervention System Intervention Lesson Name H2 Teacher Notes H2 Parts of a Region Materials crayons or markers Ongoing Assessment __ 1. In the circle at the right, color 2 of the equal Ask: Janet said she ate 4 of an orange. Explain parts blue and 4 of the equal parts red. 4 Write fractions to name the parts by answering 2 to 6. 2. How many total equal parts does the circle have? 3. How many of the equal parts of the circle are blue? 6 why Janet could have said she ate the whole 2 orange. Sample answer: The orange would be cut 4. What fraction of the circle is blue? in 4 pieces and she ate 4 pieces, so she ate the 2 ⫽ _____________________________ number of equal parts that are blue (numerator) ____ ⫽ ____________ (denominator) total number of equal parts 6 whole thing. Two sixths of the circle is blue. 4 5. How many of the equal parts of the circle are red? Error Intervention 6. What fraction of the circle is red? If children have trouble writing fractions for parts of a region, 4 ⫽ ____________________________ number of equal parts that are red (numerator) ____ ⫽ ____________ (denominator) total number of equal parts 6 Four sixths of the circle is red. then use A36: Understanding Fractions to Fourths and A38: Writing Fractions for Part of a Region. © Pearson Education, Inc. 3 by answering 7 to 9. Show the fraction __ 8 3 7. Color __ of the rectangle at the right. 8 8. How many equal parts does If You Have More Time 8 the rectangle have? 9. How many parts did you color? 3 Intervention Lesson H2 87 Have students design a rectangular flag (or rug, placemat, etc.) that is divided into equal parts. Have them color their flag and then on the back write the fractional parts of each color. Math Diagnosis and Intervention System Intervention Lesson Name H2 Parts of a Region (continued) Write the fraction for the shaded part of each region. 10. 11. 12. _2_ _1_ 3 13. 14. 5 15. _1_ _2_ 2 16. _4_ 4 _2_ 5 8 17. 18. _1_ _3_ _5_ 5 3 8 Color to show each fraction. 5 20. __ 6 7 21. ___ 10 each of the parts in half. What fraction of the parts does 1 the __ represent now? Check 3 students’ drawings. 23. Ben divided a pie into 8 equal pieces and ate 3 of them. How much of the pie remains? 88 Intervention Lesson H2 Intervention Lesson H2 _2_ 6 _5_ 8 © Pearson Education, Inc. 1 22. Math Reasoning Draw a picture to show __. Then divide 3 © Pearson Education, Inc. 3 3 19. __ 4 Math Diagnosis and Intervention System Intervention Lesson Parts of a Set Math Diagnosis and Intervention System Intervention Lesson Name H3 Teacher Notes H3 Parts of a Set Materials two-color counters, 20 for each pair; crayons or markers Ongoing Assessment 1. Show 4 red counters and 6 yellow counters. 2 2 2 2 9 9 9 9 9 3 of a group of Ask: What does it mean that ___ 9 12 marbles are green? There are 3 green marbles out Write a fraction for the part that is red and the part that is yellow by answering 2 to 6. 2. How many counters are there in all? 10 3. How many of the counters are red? 4 of a total of 12 marbles. 4. What fraction of the group of counters is red? Error Intervention 4 ⫽ __________________________ number of counters that are red (numerator) ____ ⫽ ____________ 10 total number of counters If children have difficulty describing parts of a set, (denominator) Four tenths of the group of counters is red 5. How many of the counters are yellow? then use A37: Fractions of a Set and A39: Writing Fractions for Part of a Set. 6 6. What fraction of the counters are yellow? 6 ⫽ _____________________________ number of counters that are yellow (numerator) ____ ⫽ ____________ 10 total number of counters If You Have More Time (denominator) Six tenths of the group of counters is yellow. Answer can vary on 7 and 8. Another correct set of answers is 12 and 10. Have students look around the classroom and © Pearson Education, Inc. 5 Show a group of counters with __ red by answering 7 to 9. 6 7. How many counters do you need in all? 6 name different fractions they see. For example: ___ 6 8. How many of the counters need to be red? 18 5 2 of the of the students have their math book out; __ Check that students color 5 circles red. 9. Show the counters and color below to match. 5 5 of the boys have on computers are turned off; __ 9 Intervention Lesson H3 89 shorts. Math Diagnosis and Intervention System Intervention Lesson Name H3 Parts of a Set (continued) Write the fraction for the shaded parts of each set. 10. 11. _2_ _1_ 3 12. 2 13. _3_ _4_ 5 4 14. 15. _2_ _4_ 5 6 Draw a set of shapes and shade them to show each fraction. 5 16. __ 9 6 17. ___ 10 18. Reasoning If Sally has 5 yellow marbles and 7 blue marbles. What fraction of her marbles are yellow? Draw a picture to justify your answer. __5 ; Students should draw 12 marbles with 5 blue. 12 © Pearson Education, Inc. © Pearson Education, Inc. 3 Check students’ drawings. 90 Intervention Lesson H3 Intervention Lesson H3 Math Diagnosis and Intervention System Intervention Lesson Equivalent Fractions Math Diagnosis and Intervention System Intervention Lesson Name H14 Teacher Notes H14 Equivalent Fractions Materials crayons or markers Ongoing Assessment 1 2 1 1. Show __ by coloring 2 of the __ strips. 3 3 1 __ 1 __ 3 1 2. Color as many __ strips as it takes 6 2 to cover the same region as the __ . 3 1 How many __ strips did you color? 6 1 __ 3 1 __ 1 __ 6 6 1 __ 3 1 __ 6 6 1 __ 6 1 __ 6 4 2 __ ____ 3 6 Error Intervention 2 You can use multiplication to find a fraction equivalent to __ . To do this, 3 multiply the numerator and the denominator by the same number. If students do not understand how two fractions can be equivalent, 2 4. What number is the denominator 2 of __ multiplied by to get 6? 3 4 2 __ ____ 3 6 2 2 then use H7: Using Models to Find Equivalent Fractions. 5. Since the denominator was multiplied by 2, the numerator must also be multiplied by 2. Put the product of 2 2 in the numerator of the second fraction above. Multiply the numerator and denominator of each fraction by the same number to find a fraction equivalent to each. 3 © Pearson Education, Inc. 3 If You Have More Time 4 7. 6 2 __ ____ 3 Have students create and number a cube 2, 2, 3, 3, 4 1 __ ____ 9 2 4 8 6 , ___ 6 , ___ 6 , ___ 6, 1 , __ 2 , __ 4 , ___ 6, and 6. Label 8 index cards: __ 9 1 8. Show ___ by coloring 9 of the ___ strips. 12 12 1 9. Color as many __ strips as it takes 4 9 to cover the same region as ___ . 12 1 strips did you color? How many __ 4 7 form. 3 and 7 have only 1 as a common factor. 4 2 1 3. So, __ is equivalent to four __ strips. 3 6 6. __ Ask: Explain how you can tell 3 is in simplest 2 3 6 18 24 10 12 1 1 __ 1 __ 4 4 1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 12 12 12 12 12 12 12 1 __ 1 __ 4 4 1 ___ 1 ___ 1 ___ 1 ___ 1 ___ 12 12 12 12 12 3 Intervention Lesson H14 111 3 . Shuffle the index cards. One student rolls the and __ 4 number cube and the other draws an index card. Both students find a fraction equivalent to the one on the index card by either multiplying or dividing Math Diagnosis and Intervention System Intervention Lesson Name by the number rolled. Have students check each H14 others’ work. Sometimes either operation can be Equivalent Fractions (continued) done, sometimes only one can be used. 3 9 9 1 10. So, ___ is equivalent to three __ strips. ___ ____ 4 4 12 12 9 You can use division to find a fraction equivalent to ___ . To do this, 12 divide the numerator and the denominator by the same number. 3 11. What number is the denominator of 9 ___ divided by to get 4? 3 12 3 9 ___ ____ 12 3 4 12. Since the denominator was divided by 3, the numerator must also be divided by 3. Put the quotient of 9 3 in the numerator of the second fraction above. Divide the numerator and denominator of each fraction by the same number to find a fraction equivalent to each. 2 13. 14. 10 2 5 2 10 ___ ____ 4 8 ___ ____ 15 5 5 3 If the numerator and denominator cannot be divided by anything else, then the fraction is in simplest form. yes 5 15. Is ___ in simplest form? 12 6 16. Is __ in simplest form? 8 no 4 8 ____ 18. ___ 5 10 1 19. _2_ ____ 4 8 14 7 ____ 20. ___ 20 10 3 6 ____ 21. ___ 7 14 16 8 ____ 22. ___ 22 11 Write each fraction in simplest form. 23. _6_ 8 _3_ 4 8 24. ___ 12 _2_ 3 7 25. ___ 35 _1_ 5 16 26. ___ 24 _2_ 3 4 27. Reasoning Explain why __ is not in simplest form. 6 Sample answer: 4 and 6 have a common factor of 2. 112 Intervention Lesson H14 Intervention Lesson H14 © Pearson Education, Inc. 3 17. _1_ ____ 15 5 © Pearson Education, Inc. 3 Find each equivalent fraction. Math Diagnosis and Intervention System Intervention Lesson Mixed Numbers Math Diagnosis and Intervention System Intervention Lesson Name H18 Teacher Notes H18 Mixed Numbers Materials fraction strips Ongoing Assessment A mixed number is a number written with a whole number and a fraction. An improper fraction is a fraction in which the numerator is greater than or equal to the denominator. ___ 1. Circle the number that is a mixed number. 3 1 4__ 3 8 __ 2. Circle the number that is an improper fraction. 3 __ 3 2__ 9 __ 4 3 Ask: What is 15 written as a mixed number? 3__ 5 Error Intervention 4 7 as a mixed number by answering 3 to 6. Write the improper fraction __ 3 1 3. Show seven __ fraction strips. 3 4. Use fraction strips. How many 1 strips can you make with 2 1 seven __ strips? 3 1 5. How many __ strips do you 3 21 __ 7 6. Write __ as a mixed 3 1 have left over? 3 number. 7 Write __ as a mixed number without fraction strips by answering 7 to 9. 3 7. Divide 7 by 3 at the right. © Pearson Education, Inc. Quotient 2 1 Remainder 3 Divisor 6 1 1 strips are left over. The remainder 1 tells how many __ 3 2_1_ 3 Intervention Lesson H18 119 Math Diagnosis and Intervention System Intervention Lesson Name Mixed Numbers (continued) __ 5 strips. How many _1_ strips does it 5 _? take to equal 2_1 5 fractions strips. 12. Use fraction H18 24 14 10. Since 14 5 2 R4, what is ___ as a mixed number? 5 1_ _ Write 2 5 as an improper fraction by answering 11 to 13. 1 11. Show 2__ with 5 then use G42: Dividing with Objects and H15: Fractions and Division. If students are changing a mixed number to an improper fraction and the students multiply the whole number and the numerator, If You Have More Time Notice, the quotient 2 tells how many one strips you can make. 7 9. Write __ as a mixed number. 3 If students have difficulty dividing when converting from an improper fraction to a mixed number, then, have the students write the word DoWN on their paper to remind them of the correct procedure: (D W) N. 2 R1 3 7 8. Fill in the missing numbers below. 4 4 5 Have students work in pairs. Have each student write 5 mixed numbers on index cards, one number per card. Then have students each write an improper fraction on an index card to match each mixed number written by the partner. Then the pair can play a memory game. Have the students shuffle the cards and lay them face down in an array. Have one student flip over two cards. If the cards are a match, then that player keeps the cards and can take another turn. If the cards are not a match, then the cards are turned back over and the other student has a chance to find a match. The game continues until all of the matches are found. The player with the most matches wins. __ 11 11 1 5 13. What improper fraction equals 2__? 5 1_ _ Write 2 5 as an improper fraction without using fraction strips by answering 14 to 16. 14. Fill in the missing numbers. Whole Number Denominator Numerator 2 5 1 10 1 1 16. What improper fraction equals 2__? 5 _ strips equal 2 wholes. The 1 tells Notice, 2 5 tells how many _1 5 1_ _ how many additional 5 strips there are. 3 17. Since 6 4 3 27, what is 6__ as an improper fraction? 4 Change each improper fraction to a mixed number or a whole number and change each mixed number to an improper fraction. 2 18. 3__ 7 23 __ 7 19. _7_ 3 __ 21 3 20. _7_ 2 __ 31 2 1 21. 1___ 10 11 __ __ 11 5 11 5 __ 27 4 © Pearson Education, Inc. © Pearson Education, Inc. 3 15. Write the 11 you found above over the denominator, 5. __ 11 10 120 Intervention Lesson H18 Intervention Lesson H18 Math Diagnosis and Intervention System Congruent Figures and Motions Math Diagnosis and Intervention System Intervention Lesson Name Intervention Lesson I8 Teacher Notes I8 Congruent Figures and Motions Materials construction paper, markers, and scissors Ongoing Assessment Follow 1–10. 1. Cut a scalene triangle out of construction paper. Slide 2. Place your cut-out triangle on the bottom left side of another piece of contruction paper. Trace the triangle with a marker. Ask: Why are all squares not congruent? Congruent figures must have the same size and shape. Squares can be different sizes. 3. Slide your cut-out triangle to the upper right of the same paper and trace the triangle again. Error Intervention 4. Look at the two triangles that you just traced. Are the yes two triangles the same size and shape? If students have trouble understanding congruency, When a figure is moved up, down, left, or right, the motion is called a slide, or translation. then use D54: Same Size, Same Shape. Figures that are the exact same size and shape are called congruent figures. 5. On a new sheet of paper, draw a straight dashed line as If students have trouble differentiating between slides, flips, and turns, Flip shown at the right. Place your cut-out triangle on the left side of the dashed line. Trace the triangle with a marker. then use D55: Ways to Move Shapes. 6. Pick up your triangle and flip it over the dashed line, like you were turning a page in a book. Trace the triangle again. 7. Look at the two triangles that you just traced. Are the © Pearson Education, Inc. If students understand congruency, but have trouble deciding if two figures are congruent, yes two triangles congruent? When a figure is picked up and flipped over, the motion is called a flip, or reflection. then have students trace one of the figures and place the tracing over the other figure to see if it has the same size and shape. Turn 8. On a new sheet of paper, draw a point in the middle of the paper. Place a vertex of your cut-out triangle on the point. Trace the triangle with a marker. 9. Keep the vertex of your triangle on the point and move the triangle around the point like the hands on a clock. Trace the triangle again. Intervention Lesson I8 105 Have students write their name using letters that have been flipped, turned, or slid. Exchange with a partner and have the partner identify what motion was used on each letter. Show the students that some letters can look like a slide and a flip. For example, the letter “I” looks the same when it is flipped and slid to the right. Math Diagnosis and Intervention System Intervention Lesson Name I8 Congruent Figures and Motions (continued) 10. Look at the two triangles you just traced. Are the two yes triangles congruent? If You Have More Time When a figure is turned around a point, the motion is a turn, or rotation. Write slide, flip, or turn for each diagram. 11. 12. slide 14. 13. flip turn 15. turn 16. flip slide For Exercises 17 and 18, use the figures to the right. by a slide, a flip, or a turn? 18. Are Figures 1 and 3 related by a slide, a flip, or a turn? slide flip © Pearson Education, Inc. If so, what motion could be used to show it? Yes; one is a turn of the other. Intervention Lesson I8 ;^\jgZ' ;^\jgZ( 19. Reasoning Are the polygons at the right congruent? 106 Intervention Lesson I8 ;^\jgZ& © Pearson Education, Inc. 3 17. Are Figures 1 and 2 related Math Diagnosis and Intervention System Intervention Lesson Solids and Nets Math Diagnosis and Intervention System Intervention Lesson Name I10 Teacher Notes I10 Solids and Nets Materials tape, scissors, copy of nets face: flat surface of a solid for all prisms, square and rectangular pyramids from Teaching Tool Masters Cut out and tape each net to help complete the tables. Each group should make 7 solids. Solid 1. Ongoing Assessment vertex: point where 3 or more edges meet (plural; vertices) Ask: What solid best represents a can of corn? cylinder edge: line segment where 2 faces meet Faces Edges Vertices Shapes of Faces Pyramid 1 square 5 8 Error Intervention If students have trouble identifying solids, 5 then use I1: Solid Figures. 4 triangles 2. Rectangular Pyramid 5 3. © Pearson Education, Inc. 4. 5. 8 5 1 rectangle, 4 triangles Cube 6 12 8 6 squares 6 12 8 6 rectangles 5 9 6 2 triangles, 3 rectangles Rectangular Prism Triangular Prism Intervention Lesson I10 If You Have More Time In pairs, have students play Guess My Solid. One student should select a solid made from the nets; make sure the other student cannot see which solid the partner picks. The second student asks yesor-no questions such as, Does it have more than 5 vertices? Does it have at least one square face? and then tries to guess what the solid is using the clues. 109 Math Diagnosis and Intervention System Intervention Lesson Name I10 Solids and Nets (continued) What solid will each net form? 6. 7. cylinder 8. cube 9. rectangular prism 10. 11. cone square pyramid 12. Reasoning Is the figure a net for a cube? Explain. © Pearson Education, Inc. © Pearson Education, Inc. 3 triangular prism No; the net only has five faces and a cube has six faces. 110 Intervention Lesson I10 Intervention Lesson I10 Math Diagnosis and Intervention System Intervention Lesson Views of Solid Figures Math Diagnosis and Intervention System Intervention Lesson Name I11 Teacher Notes I11 Views of Solid Figures Materials 6 blocks or small cubes from place-value blocks for Ongoing Assessment each pair or group, crayons or markers Top View Stack blocks to model the solid shown at the right. Assume that there are only 6 cubes in the solid so that none are hidden. Side View The top view of the solid is the image seen when looking straight down at the figure. Draw the top view of the solid at the right by answering 1 and 2. Front View 1. How many cubes can you see when you look straight 3 down at the solid? Error Intervention 2. Color in squares on the grid to indicate If students have trouble seeing the views using blocks or small cubes, the blocks seen from the top view. The front view is the image seen when looking straight at the cubes. then use larger boxes to illustrate the solids in front of the class. Draw the front view of the solid above by answering 3 and 4. 3. How many cubes can you see when you look straight 6 at the solid? If You Have More Time 4. Color in squares on the grid to indicate the blocks seen from the front view. Have student work in pairs. One student draws a top, side, or front view and the other student constructs a possible solid having the given view with blocks or small cubes. © Pearson Education, Inc. The side view is the image seen when looking at the side of the cubes. Draw the side view of the solid above by answering 5 and 6. 5. How many cubes can you see when you look at the solid from the side? Ask: Which views would change if a cube were added behind the far, back, left cube in a solid? The top view and the side view would change. The front view would not change. 3 6. Color in squares on the grid to indicate the blocks seen from the side view. Intervention Lesson I11 111 Math Diagnosis and Intervention System Intervention Lesson Name I11 Views of Solid Figures (continued) Draw the front, right, and top views of each solid figure. There are no hidden cubes. 7. 8. Side 9. Top 10. Front Side Top 11. Top Top Top Front Front Front Side Side Side Exercise 11, what views would change? What view would not change? The front and side views would change but the top view would not. 112 Intervention Lesson I11 Intervention Lesson I11 © Pearson Education, Inc. 12. Reasoning If a cube is added to the top of the solid in © Pearson Education, Inc. 3 Front Math Diagnosis and Intervention System Intervention Lesson Congruent Figures Math Diagnosis and Intervention System Intervention Lesson Name I13 Teacher Notes I13 Congruent Figures Materials tracing paper and scissors Ongoing Assessment Two figures that have exactly the same size and shape are congruent. Ask: Do figures have to be facing the same way in order to be considered congruent? No, they have to be the same size and the same shape but they can be turned in different directions and still be considered congruent. 1. Place a piece of paper over Figure A and trace the shape. Is the figure you drew congruent to Figure A? yes Cut out the figure you traced and use it to answer 2 to 10. Figure A Error Intervention Figure B Figure C 2. Place the cutout on top of Figure B. no Is Figure B the same size as Figure A? then have students trace one figure and move the tracing over the other figure. no 3. Is Figure B congruent to Figure A? 4. Place the cutout on top of Figure C. no Is Figure C the same shape as Figure A? no 5. Is Figure C congruent to Figure A? 6. Place the cutout on top of Figure D. © Pearson Education, Inc. If students have trouble identifying shapes that are the same size, Figure D If You Have More Time Is Figure D the same size as Figure A? yes 7. Is Figure D the same shape as Figure A? yes 8. Is Figure D congruent to Figure A? yes Have student work in pairs to find congruent objects in the classroom. 9. Circle the figure that is congruent to the figure at the right. Intervention Lesson I13 115 Math Diagnosis and Intervention System Intervention Lesson Name I13 Congruent Figures (continued) Tell if the two figures are congruent. Write Yes or No. 10. 11. yes 13. 12. no 14. yes 16. yes 15. no 17. yes no 18. no no 19. Divide the isosceles triangle shown at the right into 2 congruent right triangles. 20. Divide the hexagon shown at the right into 6 congruent equilateral triangles. 21. Divide the rectangle shown at the right © Pearson Education, Inc. 3 22. Reasoning Are the triangles at the right congruent? Why or why not? No; the triangles are the same shape, but they are not the same size. © Pearson Education, Inc. into 2 pairs of congruent triangles. 116 Intervention Lesson I13 Intervention Lesson I13 Math Diagnosis and Intervention System Intervention Lesson More Perimeter Teacher Notes Math Diagnosis and Intervention System Intervention Lesson Name I45 I45 More Perimeter Jonah’s pool is a rectangle. The pool is 15 feet long and 10 feet wide. What is the perimeter of the pool? Ongoing Assessment Find the perimeter of the pool by answering 1 to 3. 1. Write in the missing measurements on the pool 15 ft shown at the right. 10 10 ft ⫹ 15 ft ⫹ 15 ft ⫹ 10 10 ft 2. Add the lengths of the sides. 50 50 ft ft ⫽ 3. What is the perimeter of the pool? 15 ft ft ft Ask: Why is the formula for the perimeter of a square P ⴝ 4s? Because all of the sides of a square are equal, you can just multiply one side by 4 instead of adding each side. Find a formula for the perimeter of a rectangle by answering 4 to 10. 3 in. Rectangle A Rectangle B 8 in. Error Intervention 4 ft If students do not know the properties of rectangles, 5 ft 4. Write the side lengths of the rectangle. 8 8⫹3⫹ ⫹3⫽ 22 3 ⫽ )⫽ 22 6 ⫽ 22 in. © Pearson Education, Inc. 16 ⫹ 4 5⫹5⫹ in. 6. Rewrite the number sentence. 3 4 ⫹ ⫽ 18 ft ⫽ 18 ft 8. Rearrange the numbers. 22 2(8) ⫹ 2 ( 5 5⫹4⫹ 5. Rearrange the numbers. 8⫹8⫹3⫹ 7. Write the side lengths of the rectangle. in. 4 ⫹ 9. Rewrite the number sentence. in. 2(5) ⫹ 2( 4 )⫽ 18 10 ⫽ 18 ft 8⫹ ft Length Width A 8 2( B 5 3 4 Perimeter Any ᐉ w 2ᐉ ⫹ 2 8 ) ⫹ 2(3) 2(5) ⫹ 2(4) If You Have More Time w Intervention Lesson I45 179 Math Diagnosis and Intervention System Intervention Lesson Name I45 More Perimeter (continued) The formula for the perimeter of a rectangle is P ⫽ 2ᐉ ⫹ 2w 11. Reasoning Use the formula to find the perimeter of Jonah’s pool. P⫽ 2ᐉ ⫹ P⫽2( 15 ) ⫹ 2( 10 ) ⫽ 30 If students are having trouble remembering the formula for the perimeter of a square and the formula of the perimeter of a rectangle, then have students create formula cards on note cards including examples of how to use the formula correctly. 10. Complete the table. Rectangle then use I7: Quadrilaterals. Have students work in pairs to create a stack of 16 index cards with numbers 2 to 9 each written on cards. Have students draw two cards from the deck. The first card represents the length and the second card represents the width. The students work together to find the perimeter of a rectangle with the given dimensions. Have the students draw from the deck at least five different times and record their work. 2w ⫹ 20 ⫽ 50 ft 12. Is the perimeter the same as you found on the previous page? yes A square is a type of rectangle where all of the side lengths are equal. Find a formula for the perimeter of the square by answering 13 to 15. 13. Add to find the perimeter of the square shown at the right. 5 ⫹ 5 5 ⫹ ⫹ 5 ⫽ 14. What could you multiply to find the perimeter of the square? 20 5 cm 4ⴛ5 15. If s equals the length of a side of a square, how could you find the perimeter? P ⫽ 4s Find the perimeter of the rectangle with the given dimensions. 16. ᐉ ⫽ 9 mm, w ⫽ 12 mm 17. ᐉ ⫽ 13 in., w ⫽ 14 in. 42 mm 54 in. 18. ᐉ ⫽ 2 ft, w ⫽ 15 ft 19. ᐉ ⫽ 17 cm, w ⫽ 25 cm 34 ft 84 cm 21. s ⫽ 10 in. 8 yd 22. s ⫽ 31 km 40 in. 124 km 23. s ⫽ 11 m 44 m 24. Reasoning Could you use the formula for the perimeter of a rectangle to find the perimeter of a square? Explain your reasoning. Yes; the formula for the perimeter of a rectangle can be used to find the perimeter of a square because a square is a rectangle. 180 Intervention Lesson I45 Intervention Lesson I45 © Pearson Education, Inc. 20. s ⫽ 2 yd © Pearson Education, Inc. 3 Find the perimeter of the square with the given side. Name Practice F8 Rounding Numbers Through Thousands Round each number to the nearest ten. 1. 326 2. 825 3. 162 4. 97 Round each number to the nearest hundred. 5. 1,427 6. 8,136 7. 1,308 8. 3,656 Round each number to the nearest thousand. 9. 18,366 10. 408,614 11. 29,430 12. 63,239 Round each number to the nearest ten thousand. 13. 12,108 14. 70,274 15. 33,625 16. 17,164 17. What is 681,542 rounded to the nearest hundred thousand? A 600,000 B 680,000 C 700,000 D 780,000 © Pearson Education, Inc. 3 18. Mrs. Kennedy is buying pencils for each of 315 students at Hamilton Elementary. The pencils are sold in boxes of tens. How can she use rounding to decide how many pencils to buy? Practice F8 Name Practice F9 Comparing and Ordering Numbers Through Thousands Use the chart for help if you need to. hundred thousands ten thousands thousands Compare. Write ⬎ or ⬍ for each 1. 54,376 3. 9,635 hundreds tens ones . 45,763 9,536 2. 6,789 9,876 4. 4,125 3,225 Order the numbers from least to greatest. 5. 959,211 936,211 958,211 6. 456,318 408,405 459,751 7. Write three numbers that are greater than 43,000 and less than 44,000. 8. Which number has the greatest value? A 86,543,712 B 86,691,111 C 86,381,211 D 86,239,121 © Pearson Education, Inc. 3 9. Tell how you could use a number line to determine which of two numbers is greater. Practice F9 Name Practice F10 Place Value Through Millions Write the number in standard form and in word form. 1. 300,000,000 ⫹ 70,000,000 ⫹ 2,000,000 ⫹ 500,000 ⫹ 10,000 ⫹ 2,000 ⫹ 800 ⫹ 5 Write the word form and tell the value of the underlined digit for each number. 2. 4,600,028 3. 488,423,046 4. Number Sense Write the number that is one hundred million more than 15,146,481. 5. The population of a state was estimated to be 33,871,648. Write the word form. 86. Which is the expanded form for 43,287,005? A 4,000,000 ⫹ 300,000 ⫹ 20,000 ⫹ 8,000 ⫹ 700 ⫹ 5 B 40,000,000 ⫹ 3,000,000 ⫹ 200,000 ⫹ 80,000 ⫹ 7,000 ⫹ 5 C 400,000,000 ⫹ 30,000,000 ⫹ 2,000,000 ⫹ 8,000 ⫹ 500 © Pearson Education, Inc. 3 D 4,000,000 ⫹ 30,000 ⫹ 2,000 ⫹ 800 ⫹ 70 ⫹ 5 7. In the number 463,211,889, which digit has the greatest value? Explain. Practice F10 Name Practice F11 Rounding Numbers Through Millions Round each number to the nearest thousand. 1. 6,326 2. 2,825 3. 2,162 4. 4,097 Round each number to the nearest ten thousand. 5. 31,427 6. 68,136 7. 76,308 8. 93,656 Round each number to the nearest hundred thousand. 9. 618,366 10. 409,614 11. 229,930 12. 563,239 Round each number to the nearest million. 13. 12,108,219 14. 7,570,274 15. 9,333,625 16. 4,307,164 17. What is1,486,428 rounded to the nearest million? A 1,000,000 B 1,250,000 C 1,500,000 D 2,000,000 18. What is 681,542 rounded to the nearest hundred thousand? A 600,000 B 680,000 C 700,000 D 780,000 ten hundred thousand ten thousand hundred thousand million Practice F11 © Pearson Education, Inc. 3 19. Round 2,672,358 to each place value? Name Practice F29 Patterns and Equations For 1 through 6, complete each table. Find each rule. 1. x y 81 63 45 27 9 7 5 ? 2. Rule: 5. x y 6 8 10 12 42 56 70 ? 3. Rule: 2 22 x y 4 44 x y 36 42 48 54 6 7 8 ? 4. Rule: 6 66 8 ? 6. x y 10 15 20 25 30 45 60 ? Rule: x y 9 3 12 4 15 5 18 ? Rule: Rule: 7. Lucas recorded the growth of a plant. How tall will the plant be on Day 5? Day Height in inches 1 6 2 12 3 18 4 24 5 ? 8. Danielle made a table of the rental fees at a video store. What is the rule? x y A y ⫽ 3x 1 $3 2 $6 C y⫽x⫹3 3 $9 4 $12 B y ⫽ 6x D y ⫽ 4x © Pearson Education, Inc. 3 9. Curtis found a rule for a table. The rule he made is y ⫽ 7x. What does the rule tell you about every y-value? Practice F29 Name Practice G7 Estimating Sums Estimate by rounding to the nearest ten. 1. 51 46 2. 34 71 3. 33 81 4. 53 69 5. 58 47 6. 39 64 7. 88 76 8. 33 23 Estimate by rounding to the nearest hundred. 9. 478 252 _ 10. 680 743 _ 11. 617 358 _ 12. 569 780 _ 13. 840 501 14. 764 571 15. 421 887 16. 458 681 17. 141 370 18. 605 825 19. Corey was a member of the baseball team for 4 years. Dan was a member of the football team for 3 years. The baseball team has 51 members and the football team has 96 members. About how many members do the two groups have together? 20. Karen sold 534 magazines and Carly sold 308. About how many total magazines did the two girls sell? © Pearson Education, Inc. 3 21. What is the largest number that can be added to 28 so that the sum is 50 when both numbers are rounded to the nearest ten? Explain. Practice G7 Name Practice G42 Dividing with Objects Divide. You may use counters or pictures to help. 1. 27 ⫼ 4 2. 32 ⫼ 6 3. 17 ⫼ 7 4. 29 ⫼ 9 5. 27 ⫼ 8 6. 27 ⫼ 3 7. 28 ⫼ 5 8. 35 ⫼ 4 9. 19 ⫼ 2 10. 30 ⫼ 7 11. 17 ⫼ 3 12. 16 ⫼ 9 If you arrange these items into equal rows, tell how many will be in each row and how many will be left over. 13. 26 shells into 3 rows 14. 19 pennies into 5 rows 15. 17 balloons into 7 rows 16. Ms. Nikkel wants to divide her class of 23 students into 4 equal teams. Is this reasonable? Why or why not? 17. Which is the remainder for the quotient of 79 ⫼ 8? A 7 B 6 C 5 D 4 © Pearson Education, Inc. 3 18. Pencils are sold in packages of 5. Explain why you need 6 packages in order to have enough for 27 students. Practice G42 Name Practice G59 Factoring Numbers In 1 through 12, find all the factors of each number. Tell whether each number is prime or composite. 1. 81 2. 43 3. 572 4. 63 5. 53 6. 87 7. 3 8. 27 9. 88 10. 19 11. 69 12. 79 14. 1,212 15. 57 16. 17 13. 3,235 17. Mr. Gerry’s class has 19 students, Ms. Vernon’s class has 21 students, and Mr. Singh’s class has 23 students. Whose class has a composite number of students? A 1, 3, 7, 9 C 0, 2, 4, 5, 6, 8 B 1, 3, 5, 9 D 1, 3, 7 Practice G59 © Pearson Education, Inc. 3 18. Every prime number larger than 10 has a digit in the ones place that is included in which set of numbers below? Name Practice G66 Mental Math: Multiplying by Multiples of 10 Multiply. Use mental math. 1. 4 ⫻ 30 ⫽ 2. 5 ⫻ 90 ⫽ 3. 9 ⫻ 200 ⫽ 4. 6 ⫻ 500 ⫽ 5. 3 ⫻ 600 ⫽ 6. 0 ⫻ 600 ⫽ 7. 90 ⫻ 70 ⫽ 8. 70 ⫻ 400 ⫽ 9. 50 ⫻ 800 ⫽ 10. 30 ⫻ 800 ⫽ 11. 90 ⫻ 500 ⫽ 12. 30 ⫻ 4,000 ⫽ 13. Number Sense How many zeros are in the product of 60 ⫻ 900? Explain how you know. Truck A can haul 400 lb in one trip. Truck B can haul 300 lb in one trip. 14. How many pounds can Truck A haul in 9 trips? 15. How many pounds can Truck B haul in 50 trips? 16. How many pounds can Truck A haul in 70 trips? © Pearson Education, Inc. 3 A 280 B 2,800 C 28,000 D 280,000 17. There are 9 players on each basketball team in a league. Explain how you can find the total number of players in the league if there are 30 teams. Practice G66 Name Practice G67 Estimating Products Round each factor so that you can estimate the product mentally. Use rounding to estimate each product. 1. 38 ⫻ 29 2. 71 ⫻ 47 3. 54 ⫻ 76 4. 121 ⫻ 62 5. 548 ⫻ 28 6. 823 ⫻ 83 7. 67 ⫻ 289 8. 183 ⫻ 34 Use compatible numbers to estimate each product. 9. 28 ⫻ 87 10. 673 ⫻ 85 11. 54 ⫻ 347 12. 65 ⫻ 724 13. 81 ⫻ 643 14. 44 ⫻ 444 15. 72 ⫻ 285 16. 61 ⫻ 761 17. Vera has 8 boxes of paper clips. Each box has 275 paper clips. About how many paper clips does Vera have? A 240 B 1,600 C 2,400 D 24,000 18. Ana can put 27 stickers on each page of her scrapbook. The scrapbook has 112 pages. About how many stickers can Ana put in the scrapbook? A 6,000 B 4,000 C 3,000 D 2,000 © Pearson Education, Inc. 3 19. A wind farm generates 330 kilowatts of electricity each day. About how many kilowatts does the wind farm produce in a week? Explain. Practice G67 Name Practice H1 Equal Parts of a Whole Tell if each shows equal or unequal parts. If the parts are equal, name them. 1. 2. 3. 4. 7. 8. Name the equal parts of the whole. 5. 6. Use the grid to draw a region showing the number of equal parts named. 9. tenths 10. sixths © Pearson Education, Inc. 3 11. Geometry How many equal parts does this figure have? 12. Which is the name of 12 equal parts of a whole? halves tenths sixths twelfths Practice H1 Name Practice H2 Parts of a Region Write a fraction for the part of the region below that is shaded. 1. 2. Shade in the models to show each fraction. 3. 7 4. __ 10 ᎏ2ᎏ 4 5. What fraction of the pizza is cheese? cheese green peppers 6. What fraction of the pizza is mushroom? mushrooms 7. Number Sense Is ᎏ41ᎏ of 12 greater than ᎏ14ᎏ of 8? Explain your answer. 8. A set has 12 squares. Which is the number of squares in ᎏ13ᎏ of the set? A 3 B 4 C 6 D 9 Region A Practice H2 Region B © Pearson Education, Inc. 3 9. Explain why ᎏ12ᎏ of Region A is not larger than ᎏ12ᎏ of Region B. Name Practice H3 Parts of a Set 9 shaded. 1. Draw a group of squares with ___ 10 2. How many squares do you need to draw altogether. 3. How many should be shaded? Write the fraction for each shaded model. 4. 5. 6. 7. 8. 9. © Pearson Education, Inc. 3 Draw a model and shade it in to show each fraction. 8 10. ___ 12 15 11. ___ 20 Practice H3 Name Practice H14 Equivalent Fractions To find an equivalent fraction by multiplying, use this example. To find the equivalent fraction by dividing, use this example. ⫻2 ⫼5 10 ⫽ ____ ___ 2 ⫽ ____ __ 3 15 6 ⫻2 ⫼5 3 Find the equivalent fraction. 1 ⫽ ____ 1. __ 6 2. ___ ⫽ ____ 6 3. __ ⫽ ____ 6 4. ___ ⫽ ____ 8 5. ___ ⫽ ____ 9 ⫽ ____ 6. ___ 6 10 18 10 14 20 5 8 4 11 7 22 Write each fraction in simplest form. 5 8. ___ 9 7. ___ 12 5 9. ___ 10 24 10. ___ 25 36 Multiply or divide to find an equivalent fraction. 6 12. ___ 11 11. ___ 22 5 14. ___ 9 13. ___ 36 10 35 7 15. ___ 12 16. At the air show, _13 of the airplanes were gliders. Which fraction is not an equivalent fraction for _13? 5 A ___ 15 7 B ___ 21 6 C ___ 24 9 D ___ 27 © Pearson Education, Inc. 3 17. In Missy’s sports-cards collection, _57 of the cards are baseball. 12 are baseball. Frank says they have In Frank’s collection, __ 36 the same fraction of baseball cards. Is he correct? Practice H14 Name Practice H18 Mixed Numbers Write _52 as a mixed number without using fraction strips. 1. Divide 5 by 2 at the right. 2 5 2. Fill in the missing numbers below. Quotient Remainder Divisor 3. Write _52 as a mixed number. Write each improper fraction as a mixed number. 12 4. ___ 7 5. __ 9 6. __ 9 7. __ 29 8. ___ 34 9. ___ 7 4 7 3 13 8 10. Write 2_45 as an improper fraction. Whole Number Denominator Numerator __________________________________________ Denominator 4 2 10 ____________________________________________ _______ © Pearson Education, Inc. 3 Change each mixed number to an improper fraction. 4 11. 2__ 7 12. 8__ 6 13. 3__ 1 14. 7__ 3 15. 4__ 1 16. 5__ 5 8 9 7 7 4 Practice H18 Name Practice Congruent Figures and Motions I8 Congruent figures have the same size and shapes, although they may face different directions. Write yes or no to tell if the figures are congruent. 1. 2. 3. 4. 5. 6. Flip Slide Turn Write slide, flip, or turn for each diagram. 7. 8. 10. 11. 12. © Pearson Education, Inc. 3 6. Practice I8 Name Practice I10 Solids and Nets For 1 and 2, predict what shape each net will make. 2. 1. For 3–5, tell which solid figures could be made from the descriptions given. 3. A net that has 6 squares 4. A net that has 4 triangles 5. A net that has 2 circles and a rectangle 6. Which solid can be made by a net that has exactly one circle in it? A Cone B Cylinder C Sphere D Pyramid © Pearson Education, Inc. 3 7. Draw a net for a triangular pyramid. Explain how you know your diagram is correct. Practice I10 Name Practice I11 Views of Solid Figures Draw the front, right, and top views of each solid figure. 2. 1. Front Side Top 3. Front Front Side Top Front Side Top 4. Side Top Side Top 5. © Pearson Education, Inc. 3 Front Practice I11 Name Practice I13 Congruent Figures Congruent figures have the same size and shape, although they may face different directions. Tell if the figures are congruent. 1. 2. 3. 4. 5. 6. 8. Divide this shape into 2 congruent shapes. 9. Divide this shape into 3 congruent shapes. 10. Divide this shape into 8 congruent shapes. © Pearson Education, Inc. 3 7. Divide this shape into 4 congruent shapes. Practice I13 Name Practice I45 Perimeter Look at Rectangle A and Rectangle B. Complete the table. Rectangle A 3 in. Rectangle B 9 in. 4 ft 6 ft Rectangle Length Width Perimeter A B So, Any w 2 ⫹ 2w Find the perimeter of these rectangles. 1. ⫽ 9 w⫽2 2. ⫽ 6 3. ⫽ 11 w ⫽ 12 4. ⫽ 10 w⫽7 w⫽5 Find the perimeter of the square with the given side. 5. s ⫽ 4 6. s ⫽ 2 7. s ⫽ 9 8. s ⫽ 6 9. s ⫽ 20 10. s ⫽ 5 12. s ⫽ 10 © Pearson Education, Inc. 3 11. s ⫽ 8 Practice I45 Answers for Practice F8, F9, F10, F11 Name Name Practice F8 Rounding Numbers Through Thousands 330 2. 825 Use the chart for help if you need to. 3. 162 4. 97 160 830 F9 Comparing and Ordering Numbers Through Thousands Round each number to the nearest ten. 1. 326 Practice hundred thousands 100 ten thousands thousands hundreds tens ones Round each number to the nearest hundred. 5. 1,427 1,400 6. 8,136 7. 1,308 8,100 8. 3,656 1,300 1. 54,376 3. 9,635 Round each number to the nearest thousand. 9. 18,366 18,000 10. 408,614 409,000 11. 29,430 29,000 12. 63,239 10,000 14. 70,274 70,000 15. 33,625 30,000 B 680,000 C 700,000 2. 6,789 4. 4,125 < 9,876 > 3,225 5. 959,211 936,211 958,211 958,211 936,211 6. 456,318 408,405 459,751 16. 17,164 456,318 408,405 20,000 7. Write three numbers that are greater than 43,000 and less than 44,000. 17. What is 681,542 rounded to the nearest hundred thousand? A 600,000 > 45,763 > 9,536 Order the numbers from least to greatest. 63,000 Round each number to the nearest ten thousand. 13. 12,108 . Compare. Write ⬎ or ⬍ for each 3,700 D 780,000 18. Mrs. Kennedy is buying pencils for each of 315 students at Hamilton Elementary. The pencils are sold in boxes of tens. How can she use rounding to decide how many pencils to buy? 959,211 459,751 Answers will vary. 8. Which number has the greatest value? A 86,543,712 Round to the nearest 10. B 86,691,111 C 86,381,211 D 86,239,121 9. Tell how you could use a number line to determine which of two numbers is greater. © Pearson Education, Inc. 3 © Pearson Education, Inc. 3 Answers will vary. Practice F8 F8 6/30/08 12:01:54 PM Name F10 1. 300,000,000 ⫹ 70,000,000 ⫹ 2,000,000 ⫹ 500,000 ⫹ 10,000 ⫹ 2,000 ⫹ 800 ⫹ 5 372,512,805; three hundred seventy-two million, five hundred twelve thousand, eight hundred five Four million, six hundred thousand, twenty-eight; six hundred thousand 2. 4,600,028 Four hundred eighty-eight million, four hundred twenty-three thousand, forty-six; forty Number Sense Write the number that is one hundred million more than 15,146,481. 115,146,481 6,000 2. 2,825 3. 2,162 3,000 2,000 4,000 30,000 6. 68,136 7. 76,308 70,000 80,000 8. 93,656 90,000 Round each number to the nearest hundred thousand. 10. 409,614 400,000 11. 229,930 200,000 12. 563,239 600,000 Round each number to the nearest million. 13. 12,108,219 14. 7,570,274 15. 9,333,625 16. 4,307,164 12,000,000 8,000,000 9,000,000 4,000,000 Thirty-three million, eight hundred seventy-one thousand, six hundred forty-eight 17. What is1,486,428 rounded to the nearest million? A 1,000,000 B 1,250,000 C 1,500,000 D 2,000,000 18. What is 681,542 rounded to the nearest hundred thousand? 86. Which is the expanded form for 43,287,005? A 600,000 A 4,000,000 ⫹ 300,000 ⫹ 20,000 ⫹ 8,000 ⫹ 700 ⫹ 5 B 680,000 C 700,000 19. Round 2,672,358 to each place value? B 40,000,000 ⫹ 3,000,000 ⫹ 200,000 ⫹ 80,000 ⫹ 7,000 ⫹ 5 2,672,360 2,672,000 hundred thousand 2,700,000 C 400,000,000 ⫹ 30,000,000 ⫹ 2,000,000 ⫹ 8,000 ⫹ 500 ten D 4,000,000 ⫹ 30,000 ⫹ 2,000 ⫹ 800 ⫹ 70 ⫹ 5 thousand 7. In the number 463,211,889, which digit has the greatest value? Explain. Practice F10 6/30/08 12:01:57 PM D 780,000 2,672,400 2,670,000 million 3,000,000 hundred ten thousand 4; it is in the hundred millions place. F10 4. 4,097 Round each number to the nearest ten thousand. 600,000 5. The population of a state was estimated to be 33,871,648. Write the word form. © Pearson Education, Inc. 3 1. 6,326 9. 618,366 3. 488,423,046 45095_Practice_F8-I45.indd F10 F11 Round each number to the nearest thousand. 5. 31,427 Write the word form and tell the value of the underlined digit for each number. © Pearson Education, Inc. 3 Practice Rounding Numbers Through Millions Write the number in standard form and in word form. 4. 6/30/08 12:01:56 PM Name Practice Place Value Through Millions F9 45095_Practice_F8-I45.indd F9 © Pearson Education, Inc. 3 45095_Practice_F8-I45.indd F8 Practice F9 Practice F11 45095_Practice_F8-I45.indd F11 F11 6/30/08 12:01:59 PM Answers: F8, F9, F10, F11 Answers for Practice F29, G7, G42, G59 Name Name Practice F29 Patterns and Equations 9 7 5 ? xⴜ9 Rule: 5. 2 22 x y Rule: 3 y 6 8 10 12 42 56 70 ? 7x Rule: 4 44 3. x Estimate by rounding to the nearest ten. 6 66 8 ? 84 x y 36 42 48 54 6 7 8 ? 9 xⴜ6 Rule: 11x 9 3 x y 6. 88 4. Rule: x y 10 15 20 25 30 45 60 ? 12 4 75 1 6 2 12 18 ? A y 3x 2 $6 3 $9 4 24 5 ? B y 6x F29 G42 © Pearson Education, Inc. 3 Dividing with Objects 3 R3 5. 27 8 9 R1 9. 19 2 9 6. 27 3 4 R2 10. 30 7 2 R3 3 R2 5 R3 11. 17 3 14. 19 pennies into 5 rows 15. 17 balloons into 7 rows 8 R3 1 R7 12. 16 9 18. 605 825 1,400 1,300 500 1,400 G7 45095_Practice_F8-I45.indd G7 6/30/08 12:02:02 PM Practice 2. 43 G59 3. 572 1, 43 prime 6. 87 9. 88 1, 2, 4, 4. 63 11, 13, 22, 26, 1, 3, 7, 9, 44, 52, 143, 21, 63 286, 572 composite composite 7. 3 1, 3, 29, 87 composite 10. 19 8. 27 1, 3 11. 69 1, 19 1, 3, 23, 69 22, 44, 88 composite prime composite 3235 composite 14. 1,212 1, 3, 9, 27 prime 1, 2, 4, 8, 11, 13. 3,235 15. 57 composite 12. 79 1, 79 prime 16. 17 1, 2, 4, 6, 12, 1, 3, 19, 57 101, 202, 303, composite 606, 1212 composite 1, 17 prime 17. Mr. Gerry’s class has 19 students, Ms. Vernon’s class has 21 students, and Mr. Singh’s class has 23 students. Whose class has a composite number of students? Ms. Vernon’s D 4 18. Every prime number larger than 10 has a digit in the ones place that is included in which set of numbers below? © Pearson Education, Inc. 3 5 ⴛ 5 ⴝ 25 (not enough) Practice G42 Answers: F29, G7, G42, G59 150 members 800 magazines Practice G7 1, 5, 647, G42 1,400 17. 141 370 prime 18. Pencils are sold in packages of 5. Explain why you need 6 packages in order to have enough for 27 students. 45095_Practice_F8-I45.indd G42 1,000 569 780 _ 16. 458 681 1, 53 17. Which is the remainder for the quotient of 79 8? 6 ⴛ 5 ⴝ 30 12. 15. 421 887 5. 53 8 rows; 2 left over 3 rows; 4 left over 2 rows; 3 left over C 5 617 358 _ 14. 764 571 composite 8. 35 4 No. The teams will not be even. 23 ⴜ 4 ⴝ 5R3 B 6 11. 1,400 1. 81 16. Ms. Nikkel wants to divide her class of 23 students into 4 equal teams. Is this reasonable? Why or why not? A 7 680 743 _ 13. 840 501 1, 3, 9, 27, 81 If you arrange these items into equal rows, tell how many will be in each row and how many will be left over. 13. 26 shells into 3 rows 10. In 1 through 12, find all the factors of each number. Tell whether each number is prime or composite. 4. 29 9 7. 28 5 5 R2 478 252 _ Factoring Numbers Divide. You may use counters or pictures to help. 3. 17 7 50 Name Practice 5 R2 170 24; 28 rounds to 30, so the second number must round to 20, 30 ⴙ 20 ⴝ 50 6/30/08 12:02:00 PM Name 2. 32 6 100 120 21. What is the largest number that can be added to 28 so that the sum is 50 when both numbers are rounded to the nearest ten? Explain. Practice F29 6 R3 110 20. Karen sold 534 magazines and Carly sold 308. About how many total magazines did the two girls sell? D y 4x The y-value is 7 times greater than the x-value. 1. 27 4 8. 33 23 1,200 9. Curtis found a rule for a table. The rule he made is y 7x. What does the rule tell you about every y-value? 45095_Practice_F8-I45.indd F29 7. 88 76 110 19. Corey was a member of the baseball team for 4 years. Dan was a member of the football team for 3 years. The baseball team has 51 members and the football team has 96 members. About how many members do the two groups have together? 4 $12 C yx3 6. 39 64 1,300 8. Danielle made a table of the rental fees at a video store. What is the rule? 1 $3 5. 58 47 800 30 inches x y 4. 53 69 9. 6 xⴜ3 3 18 3. 33 81 100 Estimate by rounding to the nearest hundred. 15 5 7. Lucas recorded the growth of a plant. How tall will the plant be on Day 5? Day Height in inches 2. 34 71 100 3x Rule: 1. 51 46 6/30/08 12:02:04 PM A 1, 3, 7, 9 C 0, 2, 4, 5, 6, 8 B 1, 3, 5, 9 D 1, 3, 7 Practice G59 45095_Practice_F8-I45.indd G59 G59 6/30/08 12:02:06 PM © Pearson Education, Inc. 3 81 63 45 27 2. © Pearson Education, Inc. 3 y © Pearson Education, Inc. 3 x G7 Estimating Sums For 1 through 6, complete each table. Find each rule. 1. Practice Answers for Practice G66, G67, H1, H2 Name Name Practice G66 Mental Math: Multiplying by Multiples of 10 Round each factor so that you can estimate the product mentally. Use rounding to estimate each product. 5. 3 ⫻ 600 ⫽ 7. 90 ⫻ 70 ⫽ 9. 50 ⫻ 800 ⫽ 11. 90 ⫻ 500 ⫽ 450 3,000 6 ⫻ 500 ⫽ 0 0 ⫻ 600 ⫽ 28,000 70 ⫻ 400 ⫽ 24,000 30 ⫻ 800 ⫽ 120,000 30 ⫻ 4,000 ⫽ 4. 6. 8. 10. 12. 3. 54 ⫻ 76 5. 548 ⫻ 28 7. 67 ⫻ 289 13. 3,600 lb 15,000 lb 15. How many pounds can Truck B haul in 50 trips? © Pearson Education, Inc. 3 50 ⴛ 300; 15,000 12. 80 ⴛ 600; 48,000 14. 81 ⫻ 643 72 ⫻ 285 70 ⴛ 300; 21,000 16. A 240 B 1,600 A 6,000 D 280,000 70 ⴛ 700; 49,000 44 ⫻ 444 40 ⴛ 400; 16,000 61 ⫻ 76160 ⴛ 800; 48,000 65 ⫻ 724 C 2,400 D 24,000 B 4,000 C 3,000 D 2,000 19. A wind farm generates 330 kilowatts of electricity each day. About how many kilowatts does the wind farm produce in a week? Explain. 17. There are 9 players on each basketball team in a league. Explain how you can find the total number of players in the league if there are 30 teams. 7 ⴛ 300 ⴝ 2,100 kilowatts Multiply 7 days in one week ⴛ 300. (300 is incompatible to 330) Answers will vary. Sample answer: Multiply 3 ⴛ 9 ⴝ 27; 27 ⴛ 10 ⴝ 270 Practice G66 G66 6/30/08 12:02:07 PM Name H1 Equal Parts of a Whole Practice G67 G67 45095_Practice_F8-I45.indd G67 6/30/08 12:02:09 PM Name Practice Practice H2 Parts of a Region Tell if each shows equal or unequal parts. If the parts are equal, name them. Write a fraction for the part of the region below that is shaded. 1. 2. Equal, halves Answers may vary. 700 ⴛ 90; 6,300 10. 673 ⫻ 85 18. Ana can put 27 stickers on each page of her scrapbook. The scrapbook has 112 pages. About how many stickers can Ana put in the scrapbook? 16. How many pounds can Truck A haul in 70 trips? 1. 3,500 6,000 64,000 6,000 17. Vera has 8 boxes of paper clips. Each box has 275 paper clips. About how many paper clips does Vera have? 14. How many pounds can Truck A haul in 9 trips? 45095_Practice_F8-I45.indd G66 8. 183 ⫻ 34 11. 54 ⫻ 347 Truck A can haul 400 lb in one trip. Truck B can haul 300 lb in one trip. C 28,000 6. 823 ⫻ 83 30 ⴛ 90; 2,700 15. B 2,800 4. 121 ⫻ 62 9. 28 ⫻ 87 Answers will vary. A 280 2. 71 ⫻ 47 Use compatible numbers to estimate each product. 13. Number Sense How many zeros are in the product of 60 ⫻ 900? Explain how you know. 3 1,200 4,000 15,000 21,000 1. 38 ⫻ 29 2. 5 ⫻ 90 ⫽ © Pearson Education, Inc. 3 3. 9 ⫻ 200 ⫽ 120 1,800 1,800 6,300 40,000 45,000 G67 Estimating Products Multiply. Use mental math. 1. 4 ⫻ 30 ⫽ Practice 3. Unequal 2. 4. Equal, eighths ᎏ4ᎏ 8 3 ᎏ4ᎏ Equal, fourths Shade in the models to show each fraction. 3. ᎏ2ᎏ 4 7 4. __ 10 or Name the equal parts of the whole. 5. 6. 7. 8. 5. What fraction of the pizza is cheese? _3 eighths thirds fifths 8 sixths 6. What fraction of the pizza is mushroom? _2 8 Use the grid to draw a region showing the number of equal parts named. 9. tenths cheese green peppers mushrooms Answers will vary. 7. Number Sense Is ᎏ41ᎏ of 12 greater than ᎏ14ᎏ of 8? Explain your answer. 10. sixths Yes. Answers will vary. 1 of 12 is 3 and ᎏ4ᎏ of 8 is 2; 3 > 2. ᎏ1 4ᎏ 8. A set has 12 squares. Which is the number of squares in ᎏ13ᎏ of the set? 11. Geometry How many equal parts does this figure have? A 3 12. Which is the name of 12 equal parts of a whole? 45095_Practice_F8-I45.indd H1 halves tenths sixths B 4 C 6 D 9 9. Explain why ᎏ12ᎏ of Region A is not larger than ᎏ12ᎏ of Region B. twelfths They each have the same _1 region shaded for 2 Practice H1 Practice H2 _1 2 Region A H1 6/30/08 12:02:10 PM 45095_Practice_F8-I45.indd H2 H2 Region B © Pearson Education, Inc. 3 © Pearson Education, Inc. 3 © Pearson Education, Inc. 3 4 6/30/08 12:02:12 PM Answers: G66, G67, H1, H2 Answers for Practice H3, H14, H18, I8 Name Name Practice H3 Parts of a Set Practice To find an equivalent fraction by multiplying, use this example. 10 Answers will vary. 2 3. How many should be shaded? 3 5 4 15 6 2 6 3 18 6 2. ___ ____ 12 8 5. ___ ____ 10 6 4. ___ ____ 10 _2 5 11 11. ___ 6 12. ___ 36 2 9 16 © Pearson Education, Inc. 3 15 11. ___ 20 Practice H3 H3 6/30/08 12:02:14 PM Name H18 Mixed Numbers 35 answers given 7 15. ___ _1 12 7 20 14 __ 24 6 C ___ 7 B ___ 21 9 D ___ 24 27 Practice H14 H14 45095_Practice_F8-I45.indd H14 6/30/08 12:02:16 PM Practice I8 Congruent figures have the same size and shapes, although they may face different directions. 2 Write yes or no to tell if the figures are congruent. 2 5 4 1 1. Remainder 4. 2. No 2. Fill in the missing numbers below. 1 2 5 14. ___ Congruent Figures and Motions Write _52 as a mixed number without using fraction strips. 2 3 36 Name Practice Quotient 18 __ _2 24 10. ___ 5 12 In simplest form, __ ⴝ _13 . The fraction _57 36 is already in simplest form. Since _13 ⴝ _57 , Frank and Missy do not have the same fraction of baseball cards. Draw a model and shade it in to show each fraction. _1 22 17. In Missy’s sports-cards collection, _57 of the cards are baseball. 12 are baseball. Frank says they have In Frank’s collection, __ 36 the same fraction of baseball cards. Is he correct? 4 __ 1. Divide 5 by 2 at the right. 25 18 © Pearson Education, Inc. 3 _7 45095_Practice_F8-I45.indd H3 5 9. ___ 10 4 11 7 9 13. ___ _1 3 8 16. At the air show, _13 of the airplanes were gliders. Which fraction is not an equivalent fraction for _13 ? 15 12 9 ____ 6. ___ 6 5 A ___ Answers will vary. 4 2 10 _1 22 9. 8 10. ___ 3. _6_ ____ Multiply or divide to find an equivalent fraction. Sample 5 8 5 _1 5 8. ___ 4 12 _2 8. _3 9 7. ___ 7. _6 14 20 3 Write each fraction in simplest form. 3 6. 3 5 1. _1_ ____ 5. _4 3 10 ____ ___ Find the equivalent fraction. Write the fraction for each shaded model. 4. To find the equivalent fraction by dividing, use this example. _2_ ____ 10 9 2. How many squares do you need to draw altogether. H14 Equivalent Fractions 9 shaded. 1. Draw a group of squares with ___ 3. Yes 5. No 6. Divisor 2_12 3. Write _52 as a mixed number. Yes No Yes Slide Flip Turn Write each improper fraction as a mixed number. 1_57 4 2_17 6. _9_ 1_27 29 8. ___ 3 2__ 13 34 9. ___ 4_28 ; 4_14 3 2_14 7. _9_ 5. _7_ 13 7 8 10. Write 2_54 as an improper fraction. Write slide, flip, or turn for each diagram. Whole Number Denominator Numerator __________________________________________ 6. Denominator 5 4 14 15 2 4 10 ____________________________________________ _______ 5 slide © Pearson Education, Inc. 3 Change each mixed number to an improper fraction. 11. 2_4_ 5 14. 7_1_ 8 14 __ 5 57 __ 8 12. 8_7_ 9 15. 4_3_ 7 79 __ 9 31 __ 7 13. 3_6_ 7 16. 5_1_ 4 10. 27 __ H18 Answers: H3, H14, H18, I8 8. turn 11. flip 12. 7 turn 21 __ 4 Practice H18 45095_Practice_F8-I45.indd H18 7. 6/30/08 12:02:18 PM slide flip Practice I8 45095_Practice_F8-I45.indd I8 I8 7/1/08 11:40:17 AM © Pearson Education, Inc. 3 7 © Pearson Education, Inc. 3 12 4. ___ Answers for Practice I10, I11, I13, I45 Name Name Practice I10 Solids and Nets Draw the front, right, and top views of each solid figure. 2. 1. 2. Front square pyramid rectangular prism I11 Views of Solid Figures For 1 and 2, predict what shape each net will make. 1. Practice Top Side 3. Front Side Top Front Side Top 4. For 3–5, tell which solid figures could be made from the descriptions given. 3. A net that has 6 squares 4. A net that has 4 triangles 5. A net that has 2 circles and a rectangle cube triangular pyramid cylinder Front Side Top Side Top 6. Which solid can be made by a net that has exactly one circle in it? A Cone B Cylinder C Sphere 5. D Pyramid 7. Draw a net for a triangular pyramid. Explain how you know your diagram is correct. Answers will vary. © Pearson Education, Inc. 3 © Pearson Education, Inc. 3 Front Practice I10 I10 45095_Practice_F8-I45.indd I10 6/30/08 12:02:23 PM Name H11 45095_Practice_F8-I45.indd I11 6/30/08 12:02:25 PM Name Practice I13 Congruent Figures Practice I11 Practice I45 Perimeter Look at Rectangle A and Rectangle B. Complete the table. Congruent figures have the same size and shape, although they may face different directions. 3 in. Rectangle A Rectangle B 9 in. 6 ft Tell if the figures are congruent. 1. 2. yes 4. 3. no 5. no Rectangle Length Width Perimeter A 9 6 3 4 24 20 B 6. no yes 7–10: Answers will vary. 7. Divide this shape into 4 congruent shapes. So, Any 2 ⫹ 2w w Find the perimeter of these rectangles. yes 8. Divide this shape into 2 congruent shapes. 1. ⫽ 9 w⫽2 2. ⫽ 6 3. ⫽ 11 w ⫽ 12 4. ⫽ 10 P ⴝ 22 P ⴝ 46 Find the perimeter of the square with the given side. 10. Divide this shape into 8 congruent shapes. P ⴝ 26 w⫽5 P ⴝ 30 16 6. s ⫽ 2 8 7. s ⫽ 9 36 8. s ⫽ 6 24 9. s ⫽ 20 80 10. s ⫽ 5 20 32 12. s ⫽ 10 40 © Pearson Education, Inc. 3 11. s ⫽ 8 Practice I13 45095_Practice_F8-I45.indd I13 w⫽7 5. s ⫽ 4 © Pearson Education, Inc. 3 © Pearson Education, Inc. 3 9. Divide this shape into 3 congruent shapes. 4 ft I13 6/30/08 12:02:26 PM Practice I45 45095_Practice_F8-I45.indd I45 I45 6/30/08 12:02:29 PM Answers: I10, I11, I13, I45 Grade 3 Name 1. 2. Round 43,864 to the nearest ten thousand. Step Up to Grade 4 Test 4. Round this number to the nearest ten million. 15,679,841 A 40,000 A 5,000,000 B 43,000 B 11,000,000 C 43,900 C 15,000,000 D 44,000 D 16,000,000 Which is the expanded form of 4,321,189? 5. x y 20 12 25 17 30 22 35 ? A 4,000,000 ⫹ 300,000 ⫹ 20,000 ⫹ 1,000 ⫹ 100 ⫹ 80 ⫹ 9 If x = 35, what is the value of y? B 4,000,000 ⫹ 300,000 ⫹ 21,000 ⫹ 100 ⫹ 89 B 27 A 30 C 25 C 4,000,000 ⫹ 300,000 ⫹ 20,000 ⫹ 1,000 ⫹ 90 ⫹ 9 D 23 D 400,000 ⫹ 300,000 ⫹ 21,000 ⫹ 1,000 ⫹ 100 ⫹ 80 ⫹ 9 Which digit is in the thousands place? 128,698,473 6. Estimate by rounding to the nearest hundred. 689 ⫹ 228 A 1 A 628 B 2 B 800 C 6 C 889 D 8 D 900 © Pearson Education, Inc. 3 3. T1 Grade 3 Name 7. Find the quotient and the remainder. 26 ⫼ 4 A 4R2 B 6R2 C 6R4 D 8R2 Step Up to Grade 4 Test 10. Estimate the product by rounding each factor. 28 ⫻ 23 A 900 B 600 C 500 D 400 8. What are all the factors of 12? 11. Name the equal parts of the whole. A 1, 6, 12 B 1, 2, 6, 12 C 1, 2, 3, 6, 12 D 1, 2, 3, 4, 6, 12 A fifths B fourths C thirds D halves 9. The comic book store packs 30 comic books into one envelope. How many comic books will be packed into 30 envelopes? 12. Write the fraction for the shaded part of the region. A 90 B 300 C 600 A _45 D 900 B _58 C _68 © Pearson Education, Inc. 3 D _78 T2 Grade 3 Name 13. Find the fraction for the shaded parts of this set. A _35 B _45 C _56 D _47 14. Which fraction is not equivalent to _23? Step Up to Grade 4 Test 16. What motion does this shape show? A slide B flip C turn D motion 17. Which solid can be made from this net? A _46 8 B __ 12 9 C __ 12 10 D __ 15 A square B cube C triangular prism D rectangular prism 15. What is the mixed number for this 15 improper fraction? __ 8 18. What would the top view of this solid look like? A 2_78 B 2_18 © Pearson Education, Inc. 3 C 1_78 D 1_58 A B C D T3 Grade 3 Name 19. Which set of figures is not congruent? Step Up to Grade 4 Test 20. What is the perimeter of this garden? A 6 ft 3 ft 4 ft 3 ft B 1 ft 3 ft A 12 ft B 20 ft C 22 ft C D 24 ft © Pearson Education, Inc. 3 D T4 Answers for Test T1, T2, T3, T4 Grade 3 Name 1. 4. Round 43,864 to the nearest ten thousand. 2. 7. Round this number to the nearest ten million. 15,679,841 A 5,000,000 A 4R2 B 43,000 B 11,000,000 B 6R2 C 43,900 C 15,000,000 C 6R4 D 16,000,000 D 8R2 5. Which is the expanded form of 4,321,189? A 4,000,000 ⫹ 300,000 ⫹ 20,000 ⫹ 1,000 ⫹ 100 ⫹ 80 ⫹ 9 B 4,000,000 ⫹ 300,000 ⫹ 21,000 ⫹ 100 ⫹ 89 C 4,000,000 ⫹ 300,000 ⫹ 20,000 ⫹ 1,000 ⫹ 90 ⫹ 9 x y 20 12 25 17 30 22 Step Up to Grade 4 Test Find the quotient and the remainder. 26 ⫼ 4 A 40,000 D 44,000 Grade 3 Name Step Up to Grade 4 Test 10. Estimate the product by rounding each factor. 28 ⫻ 23 A 900 B 600 C 500 D 400 35 ? 8. 11. Name the equal parts of the whole. What are all the factors of 12? If x = 35, what is the value of y? A 1, 6, 12 A 30 B 1, 2, 6, 12 B 27 C 1, 2, 3, 6, 12 C 25 D 1, 2, 3, 4, 6, 12 A fifths D 23 B fourths D 400,000 ⫹ 300,000 ⫹ 21,000 ⫹ 1,000 ⫹ 100 ⫹ 80 ⫹ 9 C thirds D halves 3. Which digit is in the thousands place? 128,698,473 6. Estimate by rounding to the nearest hundred. 689 ⫹ 228 9. A 1 A 628 B 2 B 800 The comic book store packs 30 comic books into one envelope. How many comic books will be packed into 30 envelopes? C 6 C 889 A 90 D 8 D 900 B 300 12. Write the fraction for the shaded part of the region. A _45 B _58 C 600 D 900 C _68 © Pearson Education, Inc. 3 © Pearson Education, Inc. 3 D _78 T1 T1 45095_T1-T4.indd T1 T2 7/1/08 2:09:36 PM Grade 3 Name 7/2/08 1:20:15 PM Grade 3 Name Step Up to Grade 4 Test 13. Find the fraction for the shaded parts of this set. T2 45095_T1-T4.indd T2 16. What motion does this shape show? Step Up to Grade 4 Test 19. Which set of figures is not congruent? 20. What is the perimeter of this garden? A 6 ft 3 ft 4 ft 3 ft A _35 A slide B _45 B A 12 ft B flip C _56 B 20 ft C turn D _47 C 22 ft D motion D 24 ft C 14. Which fraction is not equivalent to _23? 1 ft 3 ft 17. Which solid can be made from this net? A _46 8 B __ 12 D 9 C __ 12 10 D __ 15 A square B cube C triangular prism D rectangular prism 15. What is the mixed number for this 15 improper fraction? __ 8 18. What would the top view of this solid look like? A 2_78 C 1_78 © Pearson Education, Inc. 3 © Pearson Education, Inc. 3 D 1_58 A B C D © Pearson Education, Inc. 3 B 2_18 T3 45095_T1-T4.indd T3 T3 T4 7/1/08 2:09:38 PM 45095_T1-T4.indd T4 T4 7/1/08 2:09:39 PM Answers: T1, T2, T3, T4