Series Student Addition and Subtraction My name F
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Series F Contents Topic Addi on mental strategies (pp. 8) jump strategy split strategy compensa on strategy checkerboard race apply crack the city code apply Date completed Topic Subtrac on mental strategies (pp. 9 6) jump strategy split strategy compensa on strategy snakes but no ladders apply darts apply Topic Wri en methods (pp. 7 5) addi on subtrac on adding and subtrac ng decimals word problems slippery dip race apply subtrac on puzzles solve Series Authors: Rachel Flenley Nicola Herringer Copyright
Addition mental strategies jump strategy When we add we can use the jump strategy to help us. Look at 57 + : First we jump up by the tens. Then we jump up by the ones. + 0 + 0 + 0 + 57 67 77 87 88 89 57 + = 89 Warm up with jumping by tens up and down these ladders: 4 5 5 4 59 49 84 75 Use the jump strategy to complete these addi ons: a 575 + 5 = + 0 + 0 + 0 + 0 + 0 + 575 585 b 759 + 4 = 759 c 5 + 7 = 5 F
Addition mental strategies jump strategy A group of friends each bought some school supplies. Prac se using the jump strategy to solve each problem. Write your answer and any working out in the space below each problem: pencil 55 pen 75 eraser 90 glue s ck 95 a How much did Liam spend if he bought a pencil and an eraser? b How much did Ruby spend if she bought a glue s ck and a pen? Remember with addi on, you can start with either number. c How much did Rea spend if she bought one of each item? d Rachel spent $.85 on items. Use guess, check and improve to work out which items she could have bought. 4 Use the jump strategy to help you finish these addi on walls. Can you see how they work? a b 5 5 60 4 0 5 40 0 c 5 60 F
Addition mental strategies split strategy 8 can be spilt into 00, 0 and 8. When adding large numbers in our heads it can be easier to split one of the numbers into parts and add each part separately. 00 4 + 8 0 4 + 00 = 4 4 + 0 = 44 44 + 8 = 5 8 4 + 8 = 5 Use the split strategy to add the numbers. The first one has been done for you. 0 a 6 + 8 b 8 + 6 c 56 + 4 8 6 + 0 = 64 64 + 8 = 65 6 + 8 = 65 8 + 6 = 56 + 4 = These problems have been split and some have been solved already. Lucky, hey? You just have to work out what the second numbers were before they were split and answer any unsolved problems: a 46 + 90 + = 507 b 0 + 0 + = c 8 + 60 + 7 = was was was 46 + 9 0 + 8 + d 5 + 60 + = e 45 + 00 + 40 + = f 9 + 00 + 40 + 6 = was was was 5 + 45 + 9 + Work out the answers to these ques ons by using the split strategy. See if you can do the working in your head. If it helps, make notes as you go: a 7 + 6 = b 446 + 5 = c + 8 = d 74 + 7 = e 475 + = f + 64 = F
Addition mental strategies split strategy 4 Bu erflies can fly great distances. Use the map and the split strategy to calculate the total distance flown by each bu erfly in the table below: Seaport 5 km Effe 75 km Kia 45 km Villa km 45 km 54 km 55 km Truss 45 km 85 km *not to scale Lotor 476 km Sept Flight Path Distances to add Total distance The Field Crescent flies from Lotor to Villa and then to Seaport 55 + 45 The Painted Lady flies from Sept to Lotor and then to Villa The Fawn flies from Seaport to Effe and then to Kia The Monarch flies from Sept to Kia and then to Effe We o en use the split strategy when adding money. We split the amounts into dollars and cents, work out each part and then add the two answers together: $8.50 + $6.80 = ($8 + $6) + ($0.50 + $0.80) = $44 + $.0 = $45.0 5 Match the price tags with the bills: $8.5 + $.75 Total: $ $64.70 + $.0 Total: $46 Total: $76 $.85 + $4.5 Total: $0 $56.5 + $7.65 4 F
Addition mental strategies compensation strategy Some mes we round one number in the problem to make it easier to do in our heads. Then we adjust our answer to compensate: 405 + 69 = 474 405 + 70 I rounded up by 475 = 474 so I subtract. I added extra to round to 70 so I have to take off my answer. Warm up by rounding these numbers to the closest ten: a 48 b 67 c d 74 e 89 f 456 g 955 h 786 Solve these problems using compensa on: a 45 + 7 = b 66 + 8 = 45 + 40 66 + = = c 86 + 49 = d 4 + 57 = 86 + 4 + = = We can also round down to the closest ten. When we do this we add to compensate. Round these numbers to the closest ten. Then compensate by adding: a 6 + 4 = b 5 + 6 = 6 + 40 5 + = = c 96 + = d 45 + 4 = 96 + 45 + = = F 5
Addition mental strategies compensation strategy 4 Connect the statements with their answer: When we round down we compensate by When we round up we compensate by subtrac ng adding 5 Solve these addi on problems using compensa on. Decide if you need to round up or down and compensate accordingly. Make as many notes as you need to: a 45 + 67 b 67 + 98 c 75 + 9 d 784 + e 6 + 7 f 5 + 79 6 A website tracked the number of visitors over 5 days: Monday Tuesday Wednesday Thursday Friday 4 99 58 6 Use the compensa on method to answer the following ques ons. Try to do the sum in your head, then show how you did it in the space below: a How many people looked at the website on Monday and Tuesday? b How many people looked at the website on Thursday and Friday? c On which days did the total reach 449 visitors? 6 F
Checkerboard race apply Ge ng ready This is a game for players. You will need a counter each, a die and some paper to keep score. What to do Choose the best addi on mental strategy. Each of you will choose a star ng square on the top row. The object of this game is to get to the finish line first with the largest total. Roll a die. If you throw: a or, you can only move one square across the row in either direc on; a or 4 means you can move one square diagonally; a 5 or 6 means you move one downwards. Add the two numbers using a strategy of your choice. Record your total as you go. Who will arrive at the finish with the largest score? Good luck! 8 76 9 4 89 50 66 74 6 8 54 7 6 45 95 9 87 70 69 8 75 57 49 6 9 5 44 86 67 7 58 8 47 8 7 95 7 49 56 90 7 68 9 54 85 4 Can you find the route that would give you the largest possible score? 4 6 5 9 78 66 7 6 8 7 44 46 50 74 FINISH F 7
Crack the city code apply Ge ng ready Work out the answers to these sums in your head. Each answer matches a le er in the list on the right. Write the le ers next to your answers, then unjumble the le ers to find the name of a city. What to do Try compe ng with a friend to be the fastest to do all of the sums and work out the names of the three ci es. a 70 + 6 = Le er Code 50 + 8 = Le er 80 + 7 = Le er 04 + 05 = Le er 80 + 7 = Le er 0 + 66 = Le er The city is b 9 + 6 = Le er 8 + = Le er 650 + 0 = Le er 60 + 57 = Le er 80 + = Le er The city is c 86 + 40 = Le er 9 + 6 = Le er 75 + 05 = Le er 80 + 79 = Le er 88 + 9 = Le er 47 + = Le er The city is A = 9 B = 754 C = 4 D = 58 E = 97 F = 75 G = H = 58 I = 780 J = 989 K = 48 L = 909 M = 98 N = 856 O = 975 P = 667 Q = 555 R = 4 S = 509 T = 58 U = 656 V = 0 W = 50 X = 76 Y = 87 Z = 907 8 F
Subtraction mental strategies jump strategy When we subtract we can use the jump strategy to help us. Look at 89 5: First we jump back by the tens. Then we jump back by the ones. 0 0 0 5 Start 54 59 69 79 89 89 5 = 54 Warm up with these subtrac on wheels: 0 60 80 5 5 75-50 40 75 00 70 0 0 70 80 5 0 0-40 50 75 00 60 0 Use the jump strategy to complete these subtrac on problems. The first one has been started for you: Start a 586 55 = 0 0 0 0 0 5 586 b 88 45 = Start 88 c 64 = Start 64 d 55 95 = Start 55 F 9
Subtraction mental strategies jump strategy Work out the answers to these by using the jump strategy. See if you can do the working in your head: a 74 0 = b 87 6 = c 444 50 = d 784 6 = e 89 5 = f 85 60 = 4 An electronics store had a sale on the following video games. Use the jump strategy to work out the savings on each item: Bionic Bozo Revenge of the Ponies Fitness Frenzy Taekwondo Team Was $05 Was $5 Was $0 Was $55 Now $75 Now $60 Now $9 Now $ Save Save Save Save 5 Use the prices above and the jump strategy to solve these problems. Show your answer and any working out: a Tahlia saved her pocket money for weeks to buy Fitness Frenzy. She had $0 saved and bought Fitness Frenzy in the sale. How much money did she have le a er the purchase? b Mar n saved up especially for the sale and bought items for $86. He bought Bionic Bozo and which other game? c Dana bought Taekwondo Team for her husband before the sale. What change did she receive if she paid with $00 bills? 0 F
Subtraction mental strategies split strategy Remember that 5 is 00 + 0 + 5 When subtrac ng large numbers in our heads it can be easier to split the number to be subtracted into parts and work with each part separately. 00 468 5 0 468 00 = 68 68 0 = 58 58 5 = 5 5 468 5 = 5 Prac se spli ng these numbers into hundreds, tens and ones. The first one is done for you. a 56 = 00 + 50 + 6 b 89 = c 867 = d 9 = e 44 = f 94 = Use the split strategy to subtract: a 468 6 b 574 55 c 457 468 00 = = = 0 = = = 6 = = = 468 6 = 574 55 = 457 = Work out the answers to these ques ons then cross out the le er above each answer in the puzzle. The le ers that remain will form the answer to the riddle. a 484 74 = b 400 80 = c 406 06 = d 40 40 = e 40 = f 455 60 = g 497 9 = h 505 5 = i 50 5 = j 795 50 = k 40 00 = S Y H O U E R X E L A 00 95 40 05 50 0 505 70 595 405 00 K Z R I D R J U M V A 90 495 0 95 0 85 480 500 05 645 0 Riddle: What is the most rhythmic part of your body? F
Subtraction mental strategies split strategy 4 These problems have been completed. Are they correct? If not, circle where it all began to go wrong: 00 00 00 a 75 64 60 b 49 4 40 c 79 58 50 4 8 75 00 = 75 49 00 = 79 00 = 79 75 60 = 5 4 = 9 79 50 = 9 5 4 = 9 = 6 9 8 = 75 64 = 49 4 = 6 79 58 = 5 The following problems require you to add and subtract. Use the split strategy to help you solve them: Four different families went on a holiday over Easter. Work out the distance that each car has travelled on the missing days: Robertsons Pankhursts Cailes Darnleys Day 5 km 5 km 0 km Day 75 km 55 km Day 0 km 5 km 70 km Total distance 75 km 86 km 950 km 695 km Make as many notes as you need to help you: 6 Assuming that each family started their holiday from the same place, work out where each family was at the end of Day. Connect the place with the family by drawing a line: Family Robertsons Darnleys Pankhursts Cailes Place Damp n Crazy Water Park 76 km The Big Baboon 85 km Insect Museum 45 km The Giant Toothbrush 500 km F
Subtraction mental strategies compensation strategy Some mes we round one number in the problem to make it easier to do in our heads. Then we adjust our answer to compensate: 486 59 = 47 486 60 + I rounded up by, which means I subtracted 46 + = 47 extra so we need to add back. I took off extra so I have to add back. Round these numbers to the closest ten. Then compensate by subtrac ng or adding to get back to the first number. The first one is done for you. a 9 = 90 + b 48 = c 5 = d 76 = e 57 = f 7 = g 7 = h 68 = Solve these subtrac on problems using compensa on. Show all your working out: a 585 78 = b 894 7 = c 6 49 = 585 80 + 894 70 6 50 + = = = Solve these problems using compensa on. Decide if you need to round up or down and compensate accordingly: a 555 6 b 775 98 c 644 9 d 594 9 e 4 04 You can solve these in your head or make notes as you go. Do whatever works for you. F
Subtraction mental strategies compensation strategy 4 Wally the work experience boy has solved these. He is very chuffed because he solved them all correctly. Can you use his working out to establish what the original ques ons were? a 454 = 47 b = 454 0 = 44 + = 47 568 0 = 58 + = 60 c = d = 994 80 = 94 + = 96 678 450 = 8 = 6 e = f = 684 60 = 64 + = 65 48 0 = 8 + = 0 5 Use the compensa on method to count backwards and complete these number pa erns. 7 is close to 0 so I will subtract 0 and add. 7 600 4 98 95 800 58 0 99 549 6 These subtrac on problems have been par ally solved using compensa on. Colour match the steps that were used and complete the missing parts. The first one has been done for you: $4.50 $.75 $5.70 $.00 = $.70 $.45 + = $0.00 $6.5 $4.50 $.00 = $.50 $4.5 + = $5.70 $.05 $7.5 $.00 = $4.5 $.50 + = $7.5 $.90 $9.45 $7.00 = $.45 $4.00 = $9.45 $6.85 $0.00 $6.00 = $4.00 $.70 = $.75 4 F
Snakes but no ladders apply Ge ng ready You can play with to 4 players and you will need two dice and a love of snakes! What to do Start at 00. Throw the dice and add the numbers. The answer is the number of spaces you can move. Follow the numbers. If you land on a square with a snake you must work out the answer to the subtrac on and move back to that square! The winner is the first to finish alive! 6 Finish 6 ( 5) 6 60 59 ( ) 58 57 56 48 49 ( 4) 50 5 5 5 ( 50) 54 55 ( 7) 47 46 45 44 ( 9) 4 4 4 40 ( 0) 4 5 6 ( ) 7 8 ( 4) 9 0 9 ( ) 8 7 6 ( ) 5 4 6 ( 8) 7 8 9 ( 5) 0 ( 7) 5 4 ( 0) 0 09 ( 6) 08 00 Start 0 0 0 04 ( ) 05 06 07 F 5
Darts apply Ge ng ready A game of darts is usually scored by subtrac ng the number that you throw from 0. Throwing darts can be dangerous in a classroom so you will be throwing dice instead! You can play with to 4 people. You will take turns. You will need a copy of this page, two dice, a pencil and paper to keep score. copy What to do Throw two dice, find the total and look for the number in the inner ring. The number next to it in the outer ring is the one that you will subtract from. Start subtrac ng from 0, keeping score as you go. The winner is the first to get past 0! 4 5 56 4 0 8 6 46 4 7 8 5 67 56 9 7 9 6 F
Written methods addition H T O 5 + 4 8 9 7 4 How do we add using a wri en strategy? First we es mate: 5 + 500 = 75. Our answer will be around 75. We start with the ones. 5 + 9 is 4 ones. We rename this as ten and 4 ones. We put the 4 in the ones column and carry the to the tens column. tens plus 8 tens plus the carried ten is tens. We rename this as hundred tens We put the in the tens column and carry the to the hundreds column. We add the hundreds. We put 7 in the hundreds column. Finally we check against our es mate do they match? Solve these addi on problems. First es mate the answers: e: e: e: e: a H T O b H T O c H T O d H T O 5 4 7 8 4 6 8 + + 5 9 + + 4 9 e: e: e: e: e Th H T O f Th H T O g Th H T O h Th H T O 7 4 5 6 5 8 9 8 + 4 0 8 + 4 + 7 4 + 4 8 Use these cards to make 5 different addi on problems using and digit numbers. Show your working out: 4 5 6 7 8 9 = + F 7
Written methods addition H T O 5 6 + 4 5 7 0 0 6 0 0 7 0 7 We can also add each place value separately and then add these together: + 5 = 7 60 + 40 = 00 500 + 00 = 600 7 + 00 + 600 = 707 Solve these addi on problems using a wri en strategy of your choice: e: e: e: a H T O b H T O c H T O 8 5 4 9 + 4 + 8 + 6 9 e: e: e: d H T O e H T O f H T O 8 8 7 4 6 + 4 4 + 9 + 4 4 4 Can you work out what the missing numbers should be? Remember there may have been some regrouping! Guess, check and improve will help me here. a H T O b H T O c H T O 4 5 5 9 5 6 7 + + 4 + 9 8 5 7 0 6 9 9 8 F
Written methods subtraction H T O 9 9 4 7 8 7 6 8 First we es mate: 000 00 = 700 We start with the ones. We can t take 8 away from 4 so we must rename one of the tens as ones. We now have 4 ones. 4 subtract 8 is 6 so we put the 6 in the ones column. 8 tens subtract 7 tens is ten so we put a in the tens column. We subtract the hundreds. 9 hundred subtract hundred is 7 hundred. Put a 7 in the hundreds column. We check the answer against our es mate. Complete the subtrac on problems: e: e: e: a Th H T O b Th H T O c Th H T O 4 9 8 9 5 8 7 5 8 7 8 5 8 6 When a problem asks us to find the difference, we subtract. We always start with the larger number. Showtown 49 km Normanville 6 km Roper 749 km Ace Bay 6 km Tidings km Ringer 7869 km Harpville 486 km Eagle Bay 595 km Solve these problems to find the difference: a How far from Showtown to Ringer? Th H T O b What is the distance from Normanville to Tidings? Th H T O c What is the distance from Roper to Eagle Bay? Th H T O d How far from Normanville to Ace Bay? Th H T O F 9
Written methods subtraction Use a calculator to add each group of numbers. Turn your calculator upside down to see a word on the screen. Use the key below to help you iden fy the le ers. Write each word in the correct place in the crossword puzzle. 6 4 5 CLUES Across. 05 + 589 = 4. 4 456 + 07 = 5. 776 + 86 = 6. 84 + 5 = Down. 4 569 + 4 047 =. 0 786 + 6 548 =. 456 789 + 0 556 = Key 0 4 5 6 7 8 O I E H S G L B 4 The answer is 4. What could the missing numbers be? Come up with 5 possibili es: H T O H T O H T O 4 4 4 H T O H T O 4 4 0 F
Written methods adding and subtracting decimals When we add and subtract decimals we follow the same rules we use when working with whole numbers. We need to make sure we line up the place values and the decimal points: T O t 4 7 6 Es mate and solve these addi on problems. Remember to put the decimal point into your answers: e: e: e: e: a T O t b T O t c T O t d T O t 5 4 4 8 4 7 8 + + 5 8 + 4 + 9 e: e: e: e: e T O t h f T O t h g T O t h h T O t h 5 7 4 5 5 8 9 4 + 5 9 + 4 0 5 + 4 + 9 Es mate and solve these subtrac on problems. Remember to put the decimal point into your answers: e: e: e: e: a O t h b O t h c O t h d O t h 8 4 9 0 8 7 6 9 7 5 0 4 Bart finished his race in a me of 0.67 secs. Lisa finished in.4 secs. How much faster was Bart? F
Written methods adding and subtracting decimals 4 You bought the following. Find the difference between the discount price and regular price for each item, then calculate your total savings. Show all your working out: Was $9.99 Now $8.50 Save $ Was $8.50 Now $7.99 Was $7.5 Now $6.85 Save $ Save $ Was $.89 Now $.65 Was $8.95 Now $6.50 Save $ Save $ Was $4.66 Now $.89 Save $ Total savings: F
Written methods word problems Solve the following word problems using addi on or subtrac on. Circle the opera on you use to calculate the answer: a Joe scored 46 more points than Zac. Joe scored 589 points. How many points did Zac score? + Answer b Jenny is cm taller than Jaala. Jaala is 4 cm tall. How tall is Jenny? + Answer c Maitland recorded 7 mm of rain. Balaklava recorded 58 mm more. How much rain did Balaklava record? + Answer d Wayne has $7. How much more money does he need to buy a t-shirt that costs $9? + Answer e Charlene had $. A er she paid for a cket, she had $84. How much did the cket cost? + Answer f Sanjay spent $4 and had $9 le. How much did he have before the purchase? + Answer g Jarred s bike cost $89. Molly s bike cost $6. What is the price difference between the two bikes? + Answer h The rainfall in Two Wells was 7 mm. Gawler recorded 6 mm less. How much rainfall did Gawler record? + Answer i Write your own word problem and solve it. + Answer F
Slippery dip race apply Ge ng ready Players Objec ve To be the first to slide all the way down the slippery dip and land in the sand. Materials Game marker for each player, scrap paper, pencils, deck of cards with tens and picture cards taken out. Ace has a value of. What to do To play Mix up the cards and place them face down in a pile. Players place the game markers at the Start. Each player draws 6 cards arranging them to make two digitnumbers. Arrange the cards as shown: Remember, the first card drawn is in the hundreds place for the first number. The fourth card drawn is in the hundreds place for the second number. + Varia ons 4 Add the numbers. The player with the larger total moves the game marker one space down the slippery dip. 5 Play un l someone lands in the sand. Change the number of cards laid out. Start 4 5 6 Finish 4 F
Subtraction puzzles solve What to do Puzzle Place the numbers to 6 in the grey circles so that each number is the difference between the two numbers just below it. 4 5 6 Puzzle Place eight digits from to 8 in each circle. Numbers with a difference of cannot be placed in circles directly connected by a straight line. HINT: Place some s ckers over a set of counters and write the digits to 8 on each counter. Now you can move them around. F 5