Please explain all the questions that are circled, and number them correctly.

lov4 = 09 Aloma. Qur 7 Put On Your Thinking Cap! Problem Solving = 08 Make two 3-digit numbers from the numbers below. Use each number only once. What are the two 3-digit numbers that give the greatest answer when you add them? 3 5 2 4 0 Addition up to LOO0808 (d) 3.2 Algorithms for Addition and Subtraction of Whole Numbers . left. (b) place-value cards marked Is, 10s, and 100s from right to 10. The calculation of the difference 30,007 - 1098 might look 3. like this to your class. Jse the instructional algorithm for addition to perform the fol- lowing additions: (a) 23 + 44 -1098 (b) 57 + 84 28,909 Carefully discuss the exchanges indicated. 4. Use the instructional algorithm for addition to perform the fol- ewing additions: 11. While Sylvia was trying to balance her checkbook, her calcu- (a) 324 + 78 lator battery went dead. When she added up the outstanding (b) 608 + 513 checks by hand, her work looked like this: 5. JUse the instructional algorithm for subtraction to perform 2109 these subtractions: 308 Note the (a) 78 - 35 19 exchange from 207 the units b) 75 - 38 129 column to the 208 hundreds Use the instructional algorithm for subtraction to perform the 219 column. following subtractions: 307 (a) 582 - 245 29 b) 414 - 175 108 17 7. Perform these additions and subtractions, being careful not to 209 leave more than 59 seconds or 59 minutes in your answers: 118 (a) 3 hours, 24 minutes, 54 seconds 3987 +2 hours, 47 minutes, 38 seconds (a) Is the addition correct? (b) 7 hours, 56 minutes, 29 seconds (b) Discuss each of the exchanges shown. +3 hours, 27 minutes, 52 seconds c) Would you have proceeded as Sylvia did? (c) 5 hours, 24 minutes, 54 seconds (d) How else might have the addition been carried out? -2 hours, 47 minutes, 38 seconds (e) What would you say to a student of yours who did the d) 7 hours, 46 minutes, 29 seconds computation as Sylvia did? -3 hours, 27 minutes, 52 seconds 12. In a long-distance relay race of 50 miles, the four runners 8. The column-by-column addition of the numbers 36 and 52 is on one team had the following times: 1 hour, 2 minutes, 23 shown next. State the property of the whole numbers that jus- seconds; 51 minutes, 31 seconds; 1 hour, 47 seconds; and ifies each of these steps. We begin with expanded notation as 48 minutes, 27 seconds. What was the total time for the team? a justification of the first line: Comment on the exchanges involved in solving this problem. 36 + 52 = (3.10 + 6) + (5 . 10 + 2) expanded notation Note: The final answer should be stated with the least pos- = 3 . 10 + [6 + (5 - 10 + 2)] sible number of minutes and seconds.) (a) = 3 . 10 + [(6 + 5 .10) + 2] ( b ) 13. (Writing) Read the Number and Operations Standard for Grades = 3 - 10 + [(5 . 10 + 6) + 2] (c) Pre-K-2, pages 78-88 in NCTM's Principles and Standards for School Mathematics, and write a critique of the standard, empha = 3 - 10 + [5 . 10 + (6 + 2)] ( sizing your own reaction to the recommendations. How do the = (3 . 10 + 5 . 10) + (6 + 2) (e) recommendations compare with your own school experience? = (3 + 5) . 10 + (6 + 2) 14. Give each pair of students a set of the 10 digits, each printed = 8 - 10 + 8 addition facts on a square of heavy paper. - 88 expanded notation (a) Have the students choose and place the digits on the desk top to form the greatest four-digit number that is a mult Into the Classroom ple of 6. (b) Can any odd number be a multiple of 6? Why or why 9. The hand calculation of the sum of 279 and 84 involves two not? exchanges and might appear as follows: (c) Have the students choose and place the digits on the 279 top to form the least six-digit number for which the 84 of the digits is at least 20. 363 (d) Have the students choose and place the digits on the top to form the greatest six-digit number for which Carefully describe each of the exchanges. How would you sum of the digits is less than 20. explain these to a third grader?id cover it with their ers, they can add ave more counters ers. Math lovy 40 40 CHAPTER 3 Numeration and Computation 15. Form two four-digit numbers using each of 1. 2. 3. 4, 5. 6.7. and 8 once, and only once, so that (a) the sum of the two numbers is as large as possible. (c) Sandy used the following steps: b) the sum of the two numbers is as small as possible. 10 c) You can do better than guess and check on parts (a) and (b). Explain your solution strategy briefly. (d) Is there only one answer to each of parts (a) and (b)? Explain in two sentences. -558 354 Responding to Students 19. Xavier, a third grader, looks at finding the answer to 523 - 247. After he looks at what the teacher wrote, he asks, "Is 16. How would you respond to one of your students who sub- the answer 4117 The calculation of the difference 523 - 247 tracted 229 from 2003 as might look like this: 20013 -247 - 229 276 1774 saying that he or she had exchanged one of the 200 tens for 10 Carefully discuss the exchanges indicated. How would you units? explain these to Xavier? 20. Ms. Leung asks her fourth-grade class what 273 + 124 is and 17. Examine the given student responses to the same addition gets the correct answer of 397. She then wants them to con- problem below. What possible reason(s) can you give for their sider the problem 274 + 124, but they must think before they errors? How would you help each student correct the work? add. What is the quickest way for the students to do the prob- 426 lem (with understanding)? + 397 21. (Writing) Mrs. Giles writes on the board the equation (a) Thomas, who sometimes isn't careful with routine single- - 152 = 121. She then asks her students if they would digit arithmetic, writes the solution as use that equation to write an explanation as to which of (a) and (b) is correct and why. 426 + 397 (a) 273 - 153 = 120 818 (b) 273 - 153 = 122 (b) Annabelle wrote down Thinking Critically 426 + 397 22) On his way to school, Peter dropped his arithmetic paper in 713 a puddle of water, blotting out some of his work. What digits should go under the blots in these problems? (c) Xiao gives the solution as (a) 6 3 (b) 770 (c) 8. 426 +6510 +362 + 397 2282 871 $43 803 d) 248 (e) 4 (f) 3425 18. Examine the given responses of fourth-grade students to the 122 -1843 -748 subtraction problem. Generally, subtraction errors are more 015 021 common than addition errors. 23. Find the missing digits in each of these addition 722 problems: 558 (a) 437 (b) 721 What errors is each student making, and why is the student 2 1 901 making them? What steps would you take to help the students + 347_ + 713 correct their mistakes? 6 94 0 26 (a) Richard writes the solution as (c) 38_ 5 4 24 3 612 72 2 + 512_ (d) + 81 -558 5_9 76 6 264 (b) Jeff's computation is 24. Fill in the missing digits in each of these subtraction problems: 12 2 (a) (b) 3 4 558 - 21 346 363 594 1753.3 Algorithms for Multiplication and Division of Whole Numbers 173 (c) 74 =54 (d) 212 Movie Times 808 6209 Start End 25. There is a rather interesting addition algorithm called the 3:00 P.M. scratch method that proceeds as follows: Consider the sum 2:45 ext. 5:15 8.M 2 834 6:45.B.M. 9.15 PM. 4 835 2 743 10,988 From the information in the table, which of the following statements is true? Begin by adding from the top down in the units column. When F. The end time is exactly 2 hours and 45 minutes after the you add a digit that makes your sum 10 or more, scratch out start time. the digit as shown and make a mental note of the units digit of your present sum. Start with the digit noted and continue adding G. The end time is exactly 2 hours and 15 minutes after the and scratching until you have completed the units column, writ- start time. ing down the units digit of the last sum as the units digit of the H. The end time is exactly 2 hours and 30 minutes after the answer, as shown. Now count the number of scratches in the start time. units column and, starting with this number, add on down the The end time is exactly 3 hours and 45 minutes after the tens column, repeating the scratch process as you go. Continue start time. the entire process until all the columns have been added. This gives the desired answer. Explain why the algorithm 30. ((Grade 4) works. If you change the digit 2 to 4 in the number 32,314, what will be the difference? A. Three hundred B. Two hundred Making Connections C. Four thousand D. Two thousand 26. Julien spent 1 hour and 45 minutes mowing the lawn and 2 hours and 35 minutes trimming the hedge and some shrubs. 31. (Grade 4) How long did he work altogether? Ann picked pears on her family's farm. She picked 46 pears on Monday, 56 on Tuesday, and 39 on Wednesday. 27. (a) Mr. Kobayashi has four pieces of oak flooring left over What is the total of the pears she picked after the three from a job he just completed. If they are 3' 8", 4' 2", days? 6' 10", and 5' 11" long, what total length of flooring does A. 84 B. 96 he have left over? Make sure that the number of inches in C. 141 D. 102 your answer is less than 12. (b) If Mr. Kobayashi uses 9'10" of the flooring left over in 32. (Grade 4) part (a) to make a picture frame, how much flooring does A skier reached the level of 3776 feet above sea level. he have left over then? She is going up the next part of the mountain and will at the top which is 7248 feet high. Using the ski lift, how 28. It was 25 minutes after 5 in the morning when Ari began many more feet must she go up to get to the top so that she his paper route. If it took him an hour and three-quarters to can ski back? deliver the papers, at what time did he finish? A. 4572 ft B. 4472 ft State Assessments C. 3776 ft D. 3472 ft 29. Grade 5) 33. (California, Grade 4) The movie, Math Teachers Have Fun, is scheduled on March 14. Solve: 619,581 - 23,183 = ? The schedule of the movie starts and ends at the following times. Solve: 6747 + 321,105 = ? 3.3 Algorithms for Multiplication and Division of Whole Numbers In most ancient numeration systems, multiplication and division were quite complicated. The deci- mal system makes these processes much easier, but many people still find them confusing. At least part of the difficulty has been that the ideas are often presented as a collection of rules to be learnek by rote, with little or no effort made to impart understanding. In this section, we will see the concep tual basis of a number of different algorithms for multiplication and division; that is, you will now see why they work!Schmidt (4 110) PREP MICH DUTY WHICH BUTY PREP SYSOP 1 COACH D BEHEADSAL COACH P Listin (2-115) EATER Parr ( 8 EDIA MUSIC PREP AL ARTS COACH D Darrow (8 21) ce Value COACH P Reid (7-2) HEATER PRE Crossword Puzzle Name: MEDIA Date: MUSIC UAL A O 1 2 9 3 AKER 10 4 O 6 SUENCE Across four thousand one hundred five -4 105, fifty-six thousand seven hundred seventy-four five hundred twenty one million four hundred twenty thousand five hundred eighty-seven 5. four thousand seven hundred twenty-three 6. five hundred sixty-nine Down 7. two hundred fifty thousand three hundred thirty- two 8 SCHOO five hundred sixty million one hundred forty-seven thousand eight hundred eighty-nine 9. seventy-eight million nine hundred seventy-one thousand thirty-three 10. eight hundred thirty-two 2014 Shelly Anton, Promoting Success Printables, Inc. - Revised 2021. 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