7. This is how a child added 48 + 27: 48 + 2 = 50 50 + 20 = 70 70 + 5 = 75 a. Explain why the child's solution works. b. Justify the solution path using the commutative and associa- tive properties. c. How might the child add 36 + 84? d. How might the child add 268 + 347? 8. Through illustrations, demonstrate how to solve these problems with manipulatives. a. 76 b. 524 + 47 + 26814. Classroom Connection Identify and explain the errors in each of these computations, all of which have occurred in real classrooms. a. 36 b. 36 C. 365 + 28 + 28 + 287 91 514 74225. Place the digits 1, 2, 3, 6, 7, and 8 in the boxes to obtain + E a. The greatest sum b. The least sum to 1 2 3 4 52. Which model of subtraction best illustrates each of the prob- lems below: a. Reena had 25 quilts and sold 10 of them at the show. How many does she have left? b. The hall holds 100 people. Currently 65 tickets have been sold. How many more tickets can be sold? c. The sixth grade has sold 58 raffle tickets and the fifth grade has sold only 45. How many more has the sixth grade sold?11. Classroom Connection Following are two children's solutions to 73 - 39, taken from the December 2001 issue of Teaching Children Mathematics (p. 231). Study each child's work, and then describe how that child would find the answer to 65 - 28. Then explain why that method works. a. on ban hed a ban slordy s anived to attend Lobing ords 101-010 = 34 lovni Honor = 1 asl Josudug nsublido amos (a) Samantha's solutionswoulechidna .none b. Demon fardi vestrule enedmun nonw. nays lliw aw daidy. .noras we endsb nso sweet jeffT enonsisqo owl off dontwant Jus sol jon Jud nonlibbe not blond (b) Alice's solution Source: Teaching Children Mathematics, by the National Council of Teachers of Mathematics. 12. A child subtracted 53 - 24 this way: 50 - 20 = 30 30 - 4 = 26 26 + 3 = 29 a. Justify the child's solution path.woot or insesigust b. Explain how the child would solve 72 - 38.15. Through illustrations, demonstrate how to solve these prob- lems with manipulatives. a. 524 b. 600 268 -345different ways can you make 234? 28. With three boys on a large scale, it read 170 pounds. When Adam stepped off, the scale read 115 pounds. When both Adam and Ben stepped off, the scale read 65 pounds. What is the weight of each boy?IICIO 6. a. Someone determined 25 X 12 by adding (25 X 10) and (25 X 2). What property were they using? b. Someone determined 8 X 7 X 5 mentally by multiplying 8 X 5 X 7. What properties did they use?In Exercises 11 and 12, determine the answer mentally. 11. A concert hall has 36 seats in a row, and there are 25 rows. How many people can be seated?22. Classroom Connection Identify and explain the errors in the problems below, all of which have occurred in real classrooms. a. 46 b. 46 C. 46 d. 46 X 28 X 28 X 28 X 28 404 3248 368 92 101 812 92 368 1414 4060 460 377224. Classroom Connection When children work to develop meth- ods of multiplying large numbers, the following conceptual error is very common. For example, a child will conclude that 34 X 26 will be equal to (30 X 20) + (4 X 6). Why doesn't this work?36. If a dripping faucet wastes water at the rate of 75 ounces per day, how many gallons does it waste per year? 37. People at the copy center at Keene State College told me that they used 1200 reams of paper last semester at my college