Use Strategies and Properties to Add and Subtract Home-School Connection Topic 8 Dear Family, Your child is learning strategies to add and subtract numbers using mental math. One strategy for solving addition problems using mental math is to break apart numbers to make a ten, because the ten is easier to add. Here s an example: Find 157 + 34. You can make a 10 by adding 3 to 157. 157 + 3 = 160 Break apart 34 into 3 + 31. 160 + 31 = 191 So, 157 + 34 = 191. For subtraction, you can use the same strategy of making a ten. Find 378-195. It is easier to subtract 200. 378-200 = 178 If you subtract 200, you subtract 5 more than 195. You must add 5 to the answer. 178 + 5 = 183 So, 378-195 = 183. Help your child practice using mental math to add and subtract. Here are activities you can do together. Use Mental Math to Add and Subtract Materials paper and pencil Write different 3-digit numbers on eight slips of paper. Place the numbers in a bag and select two numbers at random. Add the two numbers by making a ten and breaking apart numbers. Then, subtract the lesser number from the greater number using the same mental math strategy. Observe Your Child Provide your child with two 3-digit numbers to subtract. Then have him or her check the answer by using addition.
Nombre Usar estrategias y propiedades para sumar y restar De la escuela al hogar (en español) Tema 8 Estimada familia: Su niño(a) está aprendiendo estrategias para sumar y restar números usando el cálculo mental. Una estrategia para resolver problemas de suma usando el cálculo mental es descomponer números para formar una decena, porque es más fácil sumar una decena. Aquí se muestra un ejemplo: Halla 157 + 34. Puedes formar un 10 sumando 3 a 157. 157 + 3 = 160 Descompón 34 en 3 + 31. 160 + 31 = 191 Por tanto, 157 + 34 = 191. Para la resta, puedes usar la misma estrategia de formar una decena. Resta 378-195. Es más fácil restar 200. 378-200 = 178 Si restas 200, restas 5 más que 195. Debes sumar 5 a la respuesta. 178 + 5 = 183 Por tanto, 378-195 = 183. Ayude a su niño(a) a practicar cómo calcular mentalmente para sumar y restar. A continuación se muestran actividades que pueden realizar juntos. Calcular mentalmente para sumar y restar Materiales papel y lápiz Escriba distintos números de 3 dígitos en ocho pedazos de papel. Coloque los números en una bolsa y saque dos números al azar. Sumen los dos números formando una decena y descomponiendo números. Luego, resten el número menor del número mayor usando la misma estrategia de cálculo mental. Observe a su niño(a) Dele dos números de 3 dígitos para restar y, luego, pídale que use la suma para comprobar la respuesta.
Vocabulary 1. The Commutative (Order) Property of Addition states that you can add numbers in any order and the sum will be the same. Reteach to Build Understanding 8-1 + = 3 + 4 = 7 + = + = 2. The Associative (Grouping) Property of Addition states that you can group numbers in any way and the sum will be the same. = (4 + 2) + 1 = 4 + ( + ) 3. The Identity (Zero) Property of Addition states that the sum of any number and zero equals that same number. 5 + = 4. Draw pictures to complete the model of the Commutative Property of Addition. Complete the equation. + = 5 + 3 = 8 + = 3 + = On the Back! 5. Draw a picture that shows the Associative Property of Addition. Use 9 objects, 6 objects, and 4 objects in your picture. Include equations for the picture. R 8 1
Tic Tac Toe Partner Talk Share your thinking while you work. Get Started or For Each Round Get 20 squares in one color and 20 in another color. Get two number cubes. Take turns. Toss two cubes. Toss again if you get a double. Apply the Commutative Property of Addition. Explain how to add your numbers in two different ways. Find the sum. Cover your answer on the game board. If the answer is taken, lose your turn. Change the Order! Example If you toss: 3 + 5 = 8 and 5 + 3 = 8 The sum is 8. How to Win The first player or team to cover a row, column, or diagonal in one of the four sections of the game board wins. 6 9 6 4 6 5 8 7 3 7 3 8 7 5 4 6 5 7 8 11 8 8 9 11 7 6 7 9 5 7 7 10 9 6 8 10 If you have more time Play again! Center Game 8 1
Tic Tac Toe Partner Talk Share your thinking while you work. Get Started or For Each Round Get 20 squares in one color and 20 in another color. Get two number cubes. Take turns. Toss two cubes. Add your two numbers and 9. Apply the Associative Property of Addition. Explain how to group your addends in two different ways. Find the sum. Cover your answer on the game board. If the answer is taken, lose your turn. Example If you toss: (3 + 5) + 9 = 8 + 9 and 3 + (5 + 9) = 3 + 14. The sum is 17. How to Win Change the Grouping! The first player or team to cover a row, column, or diagonal in one of the four sections of the game board wins. 12 14 13 18 14 16 19 15 17 11 15 13 18 20 16 19 17 16 17 18 16 21 20 15 14 13 19 12 16 18 16 17 15 17 14 15 If you have more time Play again! Center Game 8 1
Vocabulary 1. An even number can be shown as two equal groups or as doubles. Circle all the examples of even numbers. Reteach to Build Understanding 8-2 6 + 7 8 + 8 24 107 2. An odd number cannot be shown as two equal groups or as doubles. Circle all the examples of odd numbers. 2 + 2 3 + 2 28 19 When you add even and odd numbers, you can see patterns. 3. An even number plus an even number has an even sum. + = 4. An number plus an number has an sum. + = On the Back! 5. Describe a pattern shown by the sums that are shaded. Explain why the pattern is true. + 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 3 3 4 5 6 7 8 9 10 11 12 4 4 5 6 7 8 9 10 11 12 13 5 5 6 7 8 9 10 11 12 13 14 R 8 2
Vocabulary 1. Place value is the value of the place a digit has in a number. Use the number 753. Write the digit in each place value. Reteach to Build Understanding 8-3 7 is in the hundreds place. It has a value of 700. is in the tens place. It has a value of 50. is in the ones place. It has a value of. 2. When you round a number, you find another number that is close to your number. Look at the digit to the right of the place you are rounding. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the digit alone. Change digits to the right of the rounding place to 0. Round 549 to the nearest ten and hundred. is in the ones place. So, the tens digit rounds up to. 549 rounded to the nearest ten is. is in the tens place. So, the hundreds digit stays the same. 549 rounded to the nearest hundred is. You can use a number line and what you know about place value to help round numbers. 3. Round 487 to the nearest ten. 480 481 482 483 484 485 486 487 488 489 490 Between which two multiples of ten is 487 located? 480 and Is 487 closer to 480 or to 490? 487 rounds to. 4. Round 487 to the nearest hundred. 400 410 420 430 440 450 460 470 480 490 500 Between which two multiples of one hundred is 487 located? and 487 is closer to. 487 rounds to. On the Back! 5. Draw number lines to round 445 to the nearest ten and to the nearest hundred. R 8 3
The Giraffe Math and Science Activity 8-3 Did You Know? The giraffe is the tallest living land mammal. It ranges in height from about 6 ft (180 cm) at birth to about 18 ft (550 cm) at full maturity. Its neck can be up to 7 ft (210 cm) long. Its diet mainly consists of leaves from trees, which is why some people believe the giraffe has such a long neck. A zoologist records the heights in centimeters of some giraffes she is studying. Adult Female Adult Male Young Male Baby Female Height 445 cm 525 cm 256 cm 195 cm ➊ She estimates that the baby female giraffe is about 200 cm. What place could she have rounded to? ➋ She rounds the heights of the adult male and adult female to the nearest hundred. The height of the adult male is about The height of the adult female is about centimeters. centimeters. ➌ Another zoologist recommends that they round the heights to the nearest ten for more accuracy. What is the height of the young male rounded to the nearest ten? ➍ Extension A zoologist estimates that the leaves of a tree are about 400 centimeters off the ground. Which giraffes are most likely to be able to reach the leaves? Explain. Math and Science Activity 8 3
Vocabulary Reteach to Build Understanding 8-4 1. When you use mental math to find 24 + 17, you do not need paper and pencil. You can use place value to break apart the addends into tens and ones. tens ones 24 = 20 + 4 17 = + Add the tens: 20 + 10 = Add the ones: 4 + 7 = Add the sums of the tens and ones: + = So, 24 + 17 =. 2. You can break apart numbers to make them easier to add mentally. Find 336 + 142 by breaking apart the addends into hundreds, tens, and ones. hundreds tens ones 336 = 300 + + 142 = + + Add the hundreds: + = Add the tens: + = Add the ones: + = Add the sums: + + = 3. Find 517 + 238 by breaking apart numbers to make a ten. Break 238 into 200 + 35 +. Add 3 to 517 to make a ten. 517 + 3 = Add 200 to 520. 520 + 200 = Add 35 to 720. 720 + 35 = So, 517 + 238 =. On the Back! 4. Use mental math to find 129 + 436. Write the steps you used. R 8 4
Clip and Cover Partner Talk Share your thinking while you work. Get Started or At Your Turn How to Play How to Win Get 10 squares in one color and 10 in another color, two paper clips, and two number cubes. Take turns. Toss two cubes to find your ovals. EXAMPLE: Choose the 3rd oval on the left and the 5th oval on the right, or choose the 5th oval on the left and the 3rd oval on the right. Mark your ovals with paper clips. Explain how to add the numbers by breaking apart both addends. EXAMPLE: 114 + 503 = (100 + 500) + (10) + (4 + 3) = 600 + 10 + 7 = 617 Find and cover the answer. Lose your turn if the answer is taken. The first player or team to get any three connected squares in a row or column wins. 114 355 221 380 631 603 514 765 561 469 524 248 503 410 402 114 355 617 812 650 724 362 273 858 905 159 503 410 If you have more time Play again! Talk about how you break apart the addends. Center Game 8 4
Clip and Cover Partner Talk Share your thinking while you work. Get Started or At Your Turn How to Play How to Win Get 10 squares in one color and 10 in another color, two paper clips, and two number cubes. Take turns. Toss two cubes to find your ovals. EXAMPLE: Choose the 3rd oval on the left and the 5th oval on the right, or choose the 5th oval on the left and the 3rd oval on the right. Mark your ovals with paper clips. Explain how to add in two different ways. EXAMPLE: 276 + 192 = (200 + 100) + (70 + 90) + (6 + 2) = 468 276 + 192 = 276 + 100 + 90 + 2 = 376 + 90 + 2 = 466 + 2 = 468 Find and cover the answer. Lose your turn if the answer is taken. The first player or team to get any three connected squares in a row or column wins. 276 451 329 790 468 777 719 674 592 975 643 192 448 398 527 276 329 899 521 724 539 714 727 925 849 192 263 448 If you have more time Play again! Talk about your strategies as you play. Center Game 8 4
Vocabulary 1. The difference is the answer when subtracting two numbers. Reteach to Build Understanding 8-5 Look at the problem 45-10 = 35. The difference is. 2. Use mental math to find 356-128. Make a simpler problem by changing each number in the same way. If you add the same amount to each number, it does not change the difference. Look at the number being subtracted. Change 128 to 130 because it is easier to subtract 130. Add 2 to both 128 and 356. 356 + 2 = 128 + 2 = Now subtract: 358-130 = So, 356-128 =. 3. Find 453-196 using mental math. It is easier to subtract 200. 453-200 = If you subtract 200, you subtract 4 more than 196. You must add 4 to the answer. 253 + 4 = So, 453-196 =. On the Back! 4. Use mental math to find 651-328. Write the steps you used. R 8 5
Vocabulary 1. When you round a number, you replace it with a number that tells about how much or how many it is to the nearest ten or hundred. Round 54 and 27 to the nearest ten. 54 Reteach to Build Understanding 8-6 54 rounds to. 27 rounds to. 50 60 27 20 30 2. When you estimate a sum, you find about how much the sum is. Estimate 54 + 27 by rounding each addend to the nearest ten. 3. Compatible numbers are close to the addends, but are easy to add mentally. 50 and 25 are compatible numbers. Estimate the sum of 54 + 27 using compatible numbers. 54 S + 27 S 54 S + 27 S 4. Estimate 465 + 123. Show each addend on a number line. 400 500 100 200 Round to the nearest hundred to estimate. 465 S + 123 S What are two estimates for 465 + 123? Round to the nearest ten to estimate. 465 S + 123 S and On the Back! 5. Estimate 107 + 182 by rounding to the nearest hundred and then to the nearest ten. Show your work. R 8 6
Clip and Cover Partner Talk Share your thinking while you work. Get Started or At Your Turn How to Play How to Win Get 10 squares in one color and 10 in another color, one paper clip, and one number cube. Take turns. Toss one cube to find your oval. EXAMPLE: Choose the 3rd oval on the left, or choose the 3rd oval on the right. Mark your oval with a paper clip. Explain how to estimate the sum by rounding. Say your estimate. Find the rounded numbers you used to make your estimate. Cover the rounded numbers. Lose your turn if the answer is taken. The first player or team to get any three connected squares in a row or column wins. 380 + 270 450 + 345 400 + 200 500 + 300 400 + 500 400 + 400 380 + 466 450 + 359 380 + 590 500 + 400 400 + 300 500 + 700 500 + 600 450 + 189 540 + 492 500 + 700 500 + 200 400 + 300 400 + 600 375 + 225 540 + 598 540 + 652 400 + 600 500 + 500 500 + 400 400 + 200 375 + 359 375 + 289 If you have more time Play again! Explain how to round each addend. Center Game 8 6
Clip and Cover Partner Talk Share your thinking while you work. Get Started or At Your Turn How to Play How to Win Get 10 squares in one color and 10 in another color, two paper clips, and two number cubes. Take turns. Toss two cubes to find your ovals. EXAMPLE: Choose the 3rd oval on the left and the 5th oval on the right, or choose the 5th oval on the left and the 3rd oval on the right. Mark your ovals with paper clips. Explain how to estimate the sum. Use compatible numbers. Find the compatible numbers you can use to estimate. Cover the compatible numbers. Lose your turn if the answer is taken. The first player or team to get any three connected squares in a row or column wins. 179 120 256 250 + 125 425 + 325 375 + 425 175 + 425 228 368 425 + 425 175 + 225 250 + 325 375 + 325 432 429 250 + 425 375 + 225 175 + 125 425 + 125 317 255 367 175 + 325 375 + 125 425 + 225 250 + 225 435 229 If you have more time Play again! Talk about your strategies as you play. Center Game 8 6
Vocabulary 1. A number line can show numbers you are rounding. You can round numbers to different place values. Use the number line to round 322 and 587 to the nearest hundred. 322 rounds to. Reteach to Build Understanding 8-7 322 587 300 400 500 600 587 rounds to. Show 322 and 587 on these number lines. Round each number to the nearest ten. 320 330 580 590 322 rounds to. 587 rounds to. 2. Estimate 587-322 by rounding to the nearest hundred. Then estimate by rounding to the nearest ten. Nearest hundred 587 S - 322 S Nearest ten 587 S - 322 S 3. Use compatible numbers to estimate. Compatible numbers are close to the original number, but are easier to add or subtract mentally. 4 5 1-2 0 2 4 5 0-1 7 7-1 2 4 - On the Back! 4. Estimate 644-229 by rounding to the nearest hundred and then to the nearest ten. Show your work. R 8 7
Teamwork Partner Talk Share your thinking while you work. Get Started or Put 0 1 2 3 4 5 6 7 8 9 in a bag. Repeat for Each Round Pick six tiles. Display two 3-digit numbers. Make sure that the 3-digit number you place in the boxes on the left is larger than the 3-digit number you place in the boxes on the right. Round each number to the nearest ten to answer the question. Then round each number to the nearest hundred to answer the question. Number of Pages in a Book Number of Pages Someone Has Read in that Book - Question About how many more pages are there to read in the book? If you have more time Answer the question for a book that someone in your class is reading. Center Game 8 7
Teamwork Partner Talk Share your thinking while you work. Get Started or Put 0 1 2 3 4 5 6 7 8 9 in a bag. Repeat for Each Round Pick six tiles. Display two 3-digit numbers, making sure that the 3-digit number you place in the boxes on the left is larger than the 3-digit number you place in the boxes on the right. Find two different ways to estimate with compatible numbers. Answer the question. Number of Pages in a Book Number of Pages in a Different Book - Question About how many more pages are there in the first book than in the second book? If you have more time Answer the question for two different books in your classroom. Center Game 8 7
Vocabulary 1. You can use a bar diagram to represent addition and subtraction. Reteach to Build Understanding 8-8 Complete the addition equation for the bar diagram. +? = 825 337? Complete the subtraction equation for the bar diagram. -? = 2. Operations that undo each other are inverse operations. Addition and subtraction are inverse operations. If you subtract 68-15 = 53, you can add 53 + 15 to check your work. 6 8 5 3 Complete the addition to check. - 1 5 + 1 5 5 3 3. You can check a subtraction problem by using addition. Subtract. Then complete the addition to check. 3 7 9-1 0 8 + 1 0 8 4. You can check an addition problem by using subtraction. Add first. Then complete the subtraction to check. 5 3 3 + 3 2 4-3 2 4 5. Complete the bar diagram and solve. Alisha reads a book that has 478 pages. She has read 199 pages. How many more pages does she need to read to finish the book? 478 On the Back! 6. Find 289-164. Show how you checked your answer. If your answer is incorrect, correct it. R 8 8
Battle of the Beaks Math and Science Activity 8-8 Did You Know? A bird s beak helps it pick up food. Most birds eat both plants and animals. Many ducks and geese have wide, flat beaks. These beaks sift food from the water. Eagles have beaks with a sharp curved point for tearing meat. While most woodpeckers eat insects, they eat other things too. Their beaks come in handy for cracking nuts! woodpecker duck A class wanted to know what the shape of a bird s beak tells about its diet. Students chose kitchen tools similar in shape to those of birds beaks. Two teams of students had 3 minutes to use their tools to pick up food similar in shape or texture to what the birds might eat. The table shows the results. egret eagle Puffed Rice (Water Plants) Gummy Worms (Fish) Nuts in Shell (Nuts) Chopsticks (egret) 248 526 0 Nutcracker (woodpecker) 98 186 352 Slotted spatula (duck) 627 119 8 ➊ How many items did the teams pick up with the slotted spatula? ➋ Why does the slotted spatula work best at picking up puffed rice? ➌ Extension The table shows the total number of food items picked up by two teams using each tool. One team used chopsticks to pick up 99 pieces of puffed rice and 314 gummy worms. How many pieces of puffed rice and gummy worms did the other team pick up with chopsticks? Show your work. Math and Science Activity 8 8
Vocabulary 1. A bar diagram can be used to represent math problems. Bar diagrams show how the numbers in a word problem are related. This bar diagram models addition. 110 88 22 Reteach to Build Understanding 8-9 The parts represent the addends. What are the addends? and The whole represents the sum. What is the sum? Write an addition equation for the bar diagram. Mike has $350. He spends $62 on a computer game and $124 on clothes. How much money does Mike have left? 2. Answer the hidden question. How much money has Mike spent in all? Complete the bar diagram and write an equation. Total amount spent $62 Mike spent + = in all. Amount spent on computer game Amount spent on clothes 3. Use the answer to the hidden question to solve the problem. How much money does Mike have left? Complete the bar diagram and write an equation. Total amount of money $350 - = Amount spent Amount left Mike has left. On the Back! 4. There are 745 students at Highland Elementary School in Grades 3, 4, and 5. There are 225 students in Grade 3. There are 240 students in Grade 4. How many students are in Grade 5? Write and answer the hidden question. Then draw bar diagrams to solve the problem. R 8 9
Teamwork Partner Talk Share your thinking while you work. Get Started or Put 1 2 3 4 in a bag. Repeat for Each Round Choose a, b, c, or d. Pick a tile. Pick two tiles if your group has only two students. Do the jobs listed below in order. To find your job, find the number that matches the tile you chose. 1 2 3 4 Read the problem. Tell your team what you know and what you need to find. Explain how to use the bar diagram. Work with your team to solve the problem. Answer the question. Check the answer. Make sure it is reasonable. Explain your thinking. Talk about another way to solve the problem. a. Jamie goes to the sports store. He buys a jacket and a pair of shoes. How much money does Jamie spend?? Cost in all $329 $125 b. Wendy and her two friends collect dolls. How many dolls do Wendy and her friends have?? Total Number of Dolls 55 dolls 193 dolls 349 dolls Cost of a jacket Cost of shoes Wendy Susie Betty c. Mia goes to the store. She estimates the cost of her supplies. About how much money does Mia plan to spend?? Cost in all d. Bill, John, and Tim collect baseball cards. How many baseball cards do these three friends have?? Total Number of Baseball Cards about $239 about $82 712 cards 209 cards 477 cards Computer software Headphones Bill John Tim If you have more time Draw a bar diagram. Tell a story with the numbers in your diagram. Ask your team to use your diagram to answer a question. Center Game 8 9
Teamwork Partner Talk Share your thinking while you work. Get Started or Get paper and a pencil. Put 1 2 3 4 in a bag. Repeat for Each Round Choose a, b, c, or d. Pick one tile. Pick two tiles if your group has only two students. Do the jobs listed below in order. To find your job, find the number that matches the tile you chose. 1 2 3 4 Read the problem. Tell your team what you know and what you need to find. Draw a bar diagram to show what you know. Label each part. Explain how to use the bar diagram to solve the problem. Work with your team to solve the problem. Check the answer. Make sure it is reasonable. Explain your thinking. a. Corey s school has 462 students. Abe s school has 328 students. Gail s school has 591 students. How many students are in these three schools? b. Faisal buys a video game system and a game. The video game system costs $299 and the game costs $39. How much does Faisal spend? c. A snow blower costs $655. A lawn mower costs $222. A wheel barrow costs $49. How much do these three items cost? d. An airplane ticket costs $462. A train ticket costs $119. About how much do both tickets cost in all? If you have more time Make up a problem that can be solved by making a bar diagram. Ask a partner to solve your problem. Center Game 8 9