ESSENTIAL QUESTION How can place value help me add larger numbers? watcha video! era opm Scanned with CamScanneri Lesson a ; essenmiat ouestion CUTOUT EI) sitet gtk (Sf In math, properties are rules you can use with numbers. n CEM Example 1 Sid has 4 blue pens and 5 red pens. Mario has 4b 5 blue pens and 4 red pens. How many pens. does each boy have? y eg y Find 4 + 5. Then find 5 + 4. 4+5 ————. Sid has pens. 5+4= __. Mario has ___ pens. This shows the |. The order in which the numbers were added did not change the sum. Example 2 1 Anna practiced the piano for 3 hours on Friday. She did not Practice at all on Saturday. How many hours did she practice i altogether? {Find 3 +0. Then find 0 + 3. Se Anna practiced 3 : 0+3= hours all togeth i ee | i This shows the Identity Property of Addition. The sum of any { fumber and zero is the number. ; g Online Content at <7 connectED.megrew-hillcom Lesson AciditionProperties 61 Scanned with CamScannerS that make Sometimes you may want to group numbers in a Way them easier to add in your head. This is Example 3 Matthew saw 9 sailboats, 4 rowboats, and 6 canoes on the lake. How many boats did he see all together? Helpful Cay 9+446=19i5 a num sentence because it, numbers, operations, andan equals sign. noes Find (9 + 4) +6. how how to group operatior \eses tell you to add 9 + 4 frst. Since 4+6 10, finding 4 + 6 is easier than finding 9 + 4- The way in which the addends are grouped does not change the sum. This is the Associative Property of Addition. (9+4)+6=94+(4+6) Associative Property of Addition =9+10 Add 4 +6 =19 Add 9 and 10. So, (9 + 4) + 6 = ___. There are ___ boats on the lake. A SC ye Tera ie Wi Find each sum. Draw line to the correct / addition property. 1.6455 + Identity 54+6= How can you use the \ Associative Property to add 7,8, and 3? / 2. (5+7)+3 v - Associati 5+(+3)= ative = Commi i Evaro utative 62. Chapter 2 Addition Scanned with CamScannerName Mit Cy raul select te} Find each sum. Draw a line to the correct addition property. 4 (2+5)+8=___ 24+(5+8)= i + Commutative eka Property 8.2-— 6.94+2= * pesociative OL Property 7. 100+0= _ * entity 8.44+(6+3)= Property (4+6)+3= Algebra Use an addition property to complete. 96+ =6 10. (7 +9) + =(9+7+3 1,.94+2=2+ 12. (8+3)+ =8+(3+2) Find each sum mentally. 14, (7+5)+5= ™ 7-479 415. Complete the number sentence for the figures below which shows the Associative Property of Addition. OOOK HHH RAAAA (+5)¢ = 3 + (_ Lesson AdditionProperties 63 Scanned with CamScannerProblem Solving ne property: For Exercises 16-17, write a number sentence and identify the P! uns. 16. In three baseball games, the Tigers scored 7, 4. and 6 r 2 How many runs did the Tigers score in all 3 games: ( +447= Property of Addition Processes tices Model Math Kelly collected 16 vacation brochures last summer, This summer she did not collect any | brochures. How many brochures did she collect all together? Brain Builders 48. Mrs. Jackson bought 27 blue notebooks and some red notebooks. Mr. Mendez bought 19 blue notebooks and 27 red notebooks. They bought the same number of notebooks. How many red notebooks did Mrs. Jackson buy? Explain how you know. Process 19. aPractices Reason Can the Commutative Property be used for subtraction? Give an example to justify your answer. 64 Chapter 2 Addition Scanned with CamScanner_ Lesson { addition Properties Sopa Homework Helper (#)/Mitercor pam ; Jaycee bought 3 yellow apples and 4 green apples. Marshall bought 4 yellow apples and 3 green apples. How many apples did each person buy? 34+4=7 443=7 Commutative Property of Addition They each bought 7 apples. The order in which the addends are added does not change the sum. You learned two other addition properties. The Identity Property shows the The Associative Property shows sum of any number and zero is _ the way the addends are grouped the number. does not change the sum. xi i> Ls Draw lines to match each property of addition with its correct example. 4344=7 443=7 * Commutative Property of Addition 2.74+0=7 * Associative Property of Addition Copyright © McCraw 1 Edvcation 3.74944) =(7+3)+4 * Identity Property of Addition Lesson MyHomework 65 Scanned with CamScannerFi ind each sum. Identity the addition property. 446205 7+O+ 5. (7+9)+3= erty Property ae & Brain Builders Find each sum mentally. Tell someone how you used a property: 6 6+s+2= 23+ 2+4= Processes 8. sPractices D> Make Sense of Problems Pedro and Jamal collected yellow and red leaves. They each collected the same total number of leaves. How many red leaves did Jamal collect? Tell someone how you used a property. Write an equation to support your answer. Pedro's leaves Jamal's leaves Vocabulary Check && Draw a line to match the vocabulary word(s) to its example. 9. Commutative Property + symbols which show grouping 40. parentheses “G4+)+4=8 34044) =8 41. Identity Property ‘St6=1 8 8=6645=1 42. Associative Property -240=2 43. Test Practice Which number sentence is an example of the Associative Property? @ 541=3+3 © @+2+5=84(245) © 583 +0 = 583 © 34+5=543 66 Need more practice? 280558555 EA connected. megraw-hill.com Scanned with CamScanner' i é i i j i i i ; ! TTL} Addition Patterns =e Example 1 ‘The bank book shows how much money was added to Bart’s account each time he visited the bank. How much money did Bart have after each trip to the bank? Complete Bart's bank book. Bart's Bank Book 2[3 i = 5 [s[_[s|7|s 51715 $1 more $ 5|7 <— 1st tip —> 51716 $100 more | $ 716 |+—2nuin—+] |@: 716 $1,000 more |$|_}6| 7/6 40» —|) 676 The circled digits show which place's value changed each time. So, Bart had $ after the first trip, $ after the second trip, and $ after the third trip. Bart added some money to the $1,676 he already had in his account. He now has $1,686. Complete the number sentence to show how much he added. $1676+ = $1,686 Online Content at +9 connectED.megraw-hill.com Lesson 3 AdditionPatterns 73 Scanned with CamScanner ESSENTIAL =?Example Patrick kept Each time they stopped, odometer. Patrick noticed a pa 2 track of the miles hi he wrot Describe the pattern. Each time they stopped, the nu Write the next number in the pattern above: =” +100 So, Patrick's family stopped every Wha ep te fee] Write the number in the place-value chart. PETES 4. 100 more than 3,728 thousands| hundreds} tens ail is family travel ywn the mil ee pers he wrote: ttern in the num! oy Coe Se Se ed on les from miles. imbers increased by miles. 2. 1 more than 281 3 8 9. 7: } 2 1 3. Complete the number sentence. thousands} tens | ones hundreds |_——-¢_—__—_+ 3; 215 6/4i2is5 pa peg 6,325 + = 6,425 7A Chapter 2 Addition Tell what happens to the digits in the number 1,057 if 100 is added to that number. Scanned with CamScannerName Independent Practice Write the number. 4, 1more than 972 6. 10 more than 310 8. 10 more than 1,437 40. 100 more than 173 Complete the number sentence. 12,974+ = 975 14. 8,264 + = 9,264 16. 6,123+ ss = 6,223 Identify and complete the number pattern. 18. 6,282; 7,282; ___; 9,282 The number pattern is —____ 19. 9,379; ; 9,381; 9,382 The number pattern is ______- 20. 7,874; 7,884; 37,904; The number pattern is 21. Add to move up the stairs. 5. 1,000 more than 374 41. 10 more than 6,910 13. 1,234 + 2,234 15. 1,038 + —__—=,1,138 17. 8877+ ____ = 8,887 )) LW Lesson3 AdditionPatterns 75 Scanned with CamScannerProblem Solving ne bag of cllens » Look fora Pattern A fac Lory pack otal balloons each second, Each balloon below roprosen ma umber of balloons packagod after 1 more secon balloons are in each bad? Complete the pattern, ” Asecond Zeeconds Sseconds ‘tseconds Siseconds 6 seconds 23. It takes one second to fill a carton with bags of balloons. Each number below represents the total number of bags of balloons packaged into cartons after 1 more second. Complete the pattern. 4,720; 4,730; 4,740; Wes ess Processes 24, sPractices Brain Builders » Use Number Sense Laurel is playing a hopscotch game. Help her fill in the empty hopscotch spaces by writing the number that is 1, 10, 100, or 1,000 more according to the pattern. Start | 4,500 | 4,600 4,800 5,801 | 5,802 5,804 | 5,805 6,804 | 6,803 6,800 For the last space, write a number sentence to support your answer. 25. GF Building on the Essential Question How does place value help me add mentally? 76 Chapter2 Addition Scanned with CamScannerName Homework | Lesson 3 ‘ Addition | Patterns f J Homework Helper. Need help? 7 connectED.megraw-hill.com | Over several years, Mrs. Bowers’ students made a total of 2,367 paper cranes. This year, she challenged her students to make the new total 2,467 paper cranes. How many paper cranes do they need to make this year to meet the challenge? Use a place-value chart to find which place changed in value. The new number is 100 more. 2,367 + 100 = 2,467 thousands hundreds eee 2 617 21@ 617 So, this year’s class needs to make 100 paper cranes. Write the number in the place-value chart. 1. 10 more than 567 5 6 7 hundreds} tens | ones 3. 1,000 more than 1,529 2. 1 more than 358 | thousands} hundreds tens ones T fe ah eae sis) li t { Ena pay | a Lesson3 MyHomework 77 Scanned with CamScannerCommiete the number sentence. 1 6 [ssn] ees} tere Tones 1 = ] a] 2jf4 14 ‘| : | 1 ; 5 ] 3 i 4a | 4} 3345 J tome asad Write the number, RW 1 mon 8. 100 more than 8,699 9, 1,000 more than 3,097 Identify and complete the number pattern. What would the next number be? 10. 2,378; 2,478; 2,578; ; $2,878; 2,978 The number pattern is 41. 5,903; 5,913; 5,923; : 35,953; 5,963 The number pattern is S Problem Solving Processes 42. Practices Model Math A baby horse weighed 104 pounds at birth. It gained 100 pounds each month. How much does the horse weigh In 4 months? Write a number sentence to support your answer. 43. Test Practice Which pattern shows 100 more? Explain how you know. ® 1,456; 1,556; 1,656; 1,756 © 5,832; 5,833; 5,834; 5,835 4,987; 4,887; 4,787; 4,687 © 6,001; 7,001; 8,001: 9,001 HE sta Picea sJeonnectED megeaw-hill.com Scanned with CamScannerTT ENC Mile et bt eat (Ssh ESSENTIAL oussrion How can place value help | me add larger numbers? _ When you add, you may need to regroup. To Fegreup means to rename a number using place value. Example 1 During a weekend trip to Vermont, the Wildlife Club saw 127 wrens and 58 eagles. How many wrens and eagles did the Wildlife Club see? Find 127 + 58. hundreds! tens | ones ao + 15 18 ' ' Estimate 127 + 58 ——> + = i Add the ones. 7ones + 8 ones = 15 ones Regroup 15 ones as 1 ten and 5 ones. Add the tens and hundreds. ————___________, - 1ten + 2 tens + 5 tens = 8 tens ‘hundred + 0 hundreds = 1 hundred in loo NI 1 Be Check for Reasonableness —= 185 is close to the estimate of ___.. It makes sense. 5 The answer is Feasonable, 127 + 58 = | | | I So, the Wildlife Club saw _ wrens and eagles. Online Content at ¢7 connectED.megraw-hill.com Lesson7 AddThree-DigitNumbers 99 Scanned with CamScannerYou can write a number sentence to fad tho GAKAOWA, oF missing number Example 2 (| One box of butterfly nets costs $175, Another box costs $225, How much do the boxes of nets cost all together? Write a number sentence to find the unknown. $175 4 $225 = aw 17 2/2 jn or + Add the ones. Sones ‘+ 5 ones = 10 ones Regroup 10 ones as 1 ten and O ones, a 1 Add the tens and hundreds. Tten + 7 tens + 2 tens = 10 tens Regroup 10 tens as 1 hundred and 0 tens. ‘Thundred + 1 hundred ++ 2 hundreds = 4 hundreds Check for Accuracy $225 Use the Commutative Property to check your answer, + 3 75 400 No matter in which order you add, the sum Is the same. So, $175 + $225 = . The unknown is . The nets cost Add. i a Why is iti heck 1 6] 4 1 sle6 f y important to ches ‘ Al + 2] 2[ 9 \ frreasonableness? 100 Chapter2 Addition Scanned with CamScanner; WY Add. Check for reasonableness. 3. 4. 5, 7)5)9 4]4]s5 $|3]4]5 + 1|9 + 2|6 $ 9|3 Estimate: Estimate: Estimate: 6. $427 7 597 8. 279 + $217 + 51 + 19 Estimate: Estimate: Estimate: Add. Use the Commutative Property of Addition to check for accuracy. 9. 228 149 10. 231 596 + 149 +228 + 596 + 231 Algebra Add to find the unknown. 1. 434+21I7=0 12. 607+ 27=8 43, $173 + $591 The unknown Is ___—- The unknown is... The unknown is Lesson 7 Add Three-Digit Numbers 101 Scanned with CamScanner& Problem Solving Write a number sentence with a symbol for the unknown. Then solve. 14, A10-speed bike Is on sale for $199, and a 12-speed racing bike Is on sale for $458. How much do the two bikes cost all together? Processes 15. «Practices Use Algebra A newspaper surveyed 475 students about their favorite sport. A magazine surveyed 189 students about their favorite snack, How many students were surveyed by the magazine and newspaper? ce Brain Builders Processes | 16. aPractices Use Number Sense Use the digits 3, 5, and 7 to make two three-digit numbers with the greatest possible sum. Use each digit one time in each number. Write a number sentence. Explain your reasoning. 17. & Building on the Essential Question How can | use place value to add three-digit numbers? 102 Chapter 2 Addition Scanned with CamScannerName Lesson 7 ‘ Add Three-Digit Numbers / “f Homework Helper Atoy store sold 223 robots last year. This year, they sold 198 robots. How many robots did they sell over the two years? Find 223 + 198. Need help? 5] connectED.megra Estimate 223 +198 ———+ 200 + 200 = 400 q Add the ones. 3 ones + 8 ones = 11 ones Regroup 11 ones as 1 ten and 1 one. 2 Add the tens and hundreds. ————————> 1; Tten + 2 tens +9 tens = 12 tens 223 Regroup 12 tens as 1 hundred and 2 tens. +198 ‘hundred + 2 hundreds + 1 hundred = 4 hundreds 421 Check for reasonableness 421is close to the estimate of 400. The answer is reasonable. So, 223 + 198 = 421. The store sold 421 toy robots over the two years. Add. Check for reasonableness. 1. 2. 3, Tile 6jo|s s|3|2|7 + 9]9 +1fata +$ 5|6 > all Estimate: Estimate: Lesson? MyHomework 103 Scanned with CamScannerAdd. Use the Commutative Property to check for accuracy. 1}9]6 21816 4. ac |53:), 60.0 $]4jo]s 5 . h4 +slalels vif fele +21 8/6 1246 $ $ ders Algebra Add to find the unknown. Explain how you used place value to find the unknown. 6. 661+ 99 = 7. $258 + $337 = 8, $739 + $81= + + + The unknown is| . The unknown is| ~The unknown is fi Processes 9. aPractices Make a Plan The principal ordered 215 muffins and 155 bagels, Then he ordered 45 more bagels. How many muffins and bagels were ordered in all? [seh Vocabulary Check (Gj Choose the correct word to complete each sentence, reasonable regroup unknown 10, To____ means to rename a number using place value. 11. A missing number is the 42. If an answer makes sense, it is _ 13. Test Practice Mrs. Lewis bought two statues for her garden. One cost $145 and one cost $262. What was the total cost of the statues? @® $117 © $407 $317 ® $410 104 Needmore practice? Downlol tc at g7conneetED megraw-hil.com Scanned with CamScanneraddend addition sentence estimate reasonable ‘earoup round sum ak | Label each with the correct vocabulary word(s). i 1° 139» 100 2. 139 +273 = 412 | +273——> +300 412 is close to the estimate of 400. : 400 i The answer is __ 3. 148 + 153 = 301<— __ 4.543 + 281 = © aaa poh 4 5. Exchange 10 ones as 1 ten. 6. 153 to the nearest ten is 150. 153 to the nearest hundred is 200. hundreds tens ‘ones Concept Check Estimate, Round each addend to the indicated place value. 8. 483 + 112; hundreds 7. 214 + 62; tens Check My Progress 105 Scanned with CamScannerUse models to add. Draw the sum, 14. 377 + 308 9. 99 + 209 40. 316 + 284 Add. Check for reasonableness, Explain how you know your answers are reasonable, 12. 3447275 43, 528 +149 = 14, $193 + $619 = + + + Estimate: Estimate: Estimate: Brain Builders 18. Dory's Farm has 468 apple trees and 224 pear trees, To the nearest ten, how many apple and pear trees are there all together? To the nearest hundred, how many apple and pear trees are there all together? Which estimate is better? Explain. 16. There are 369 boys and 421 girls signed up for Adventure Camp this summer. There are 75 counselors. How many people will be at camp? 17. Test Practice It will cost $177 a night to stay at a hotel Friday and Saturday. It will cost $159 to stay on Sunday. The Taylors want to stay three nights. How much will it cost to stay three nights? ® $336 $344 © $513 © $531 106 Chapter 2 Addition Scanned with CamScanner