SERIES Addition and Subtraction

Transcription

1 F Teacher Student Book SERIES Addition and Subtraction Name

2 Series F Addition and Subtraction Contents Topic Section Addition Answers mental (pp. 5) strategies (pp. 8) jump addition strategy mental strategies subtraction split strategy mental strategies 9 written compensation methods_ strategy 7 checkerboard race apply / / / / / / / / crack the city code apply Section Assessment with answers (pp. 6 ) Topic Subtraction mental strategies (pp. 9 6) Section Objectives (p. ) addition mental strategies 6 subtraction mental strategies 8 written jump strategy methods 0 / / word split strategy problems using addition and subtraction_ / / compensation strategy / / snakes but no ladders apply darts apply Date completed / / / / / / Topic Written methods (pp. 7 5) addition subtraction adding and subtracting decimals word problems slide race apply subtraction puzzles solve / / / / / / / / / / / / Series Authors: Rachel Flenley Nicola Herringer Copyright

3 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 units = 89 Warm up with jumping by tens up and down these ladders: Use the jump strategy to complete these additions: a = b = c = Addition and Subtraction F SERIES TOPIC

4 Addition mental strategies jump strategy A group of friends each bought a bag of mixed sweets at a sweet shop. Practise using the jump strategy to solve each problem. Write your answer and any working out in the space below each problem: Choc mints 90p per scoop Jellybeans 55p per scoop Cream chocs 95p per scoop Chocolate bonbons 75p per scoop a How much did Liam spend if he bought a scoop of jellybeans and a scoop of choc mints? p 65p 75p 85p 95p b How much did Ruby spend if she bought a scoop of cream chocs and a scoop of chocolate bonbons?.70 Remember with addition, you can start with either number. c How much did Rea spend if she bought one scoop of each type?.5 d Rachel spent.85 on scoops of sweets. Use guess, check and improve to work out which scoops she could have bought. Choc mints and cream chocs. Use the jump strategy to help you finish these addition walls. Can you see how they work? a 86 b c F SERIES TOPIC Addition and Subtraction

5 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 = + 0 = + 8 = = 5 Use the split strategy to add the numbers. The first one has been done for you a b c = = = = = = = = = = 98 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 = 507 b = 6 c = 50 was was was d = 59 e = 567 f = 75 was was was Work out the answers to these questions by using the split strategy. See if you can do the working in your head. If it helps, make notes as you go: a = 09 b = 97 c + 8 = 95 d = 796 e 75 + = 597 f + 6 = 87 Addition and Subtraction F SERIES TOPIC

6 Addition mental strategies split strategy Butterflies can fly great distances. Use the map and the split strategy to calculate the total distance flown by each butterfly in the table below: Seaport 5 km Effe 75 km Kia 5 km Villa km 5 km 5 km 55 km Truss 5 km 85 km *not to scale Lotor 76 km Sept Flight path Distances to add Total distance The Field Crescent flies from Lotor to Villa and then to Seaport km 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 km 0 km 57 km We often use the split strategy when adding money. We split the amounts into pounds and pence, work out each part and then add the two answers together: = ( 8 + 6) + ( ) = +.0 = Match the price tags with the bills: Total: Total: 6 Total: Total: F SERIES TOPIC Addition and Subtraction

7 Addition mental strategies compensation strategy Sometimes we round one number in the problem to make it easier to do in our heads. Then we adjust our answer to compensate: = I rounded up by 75 = 7 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 8 50 b c 0 d 7 70 e f g h Solve these problems using compensation: a = 8 b = = 8 86 = 8 c = 5 d + 57 = = 5 8 = 8 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 + = 68 b = = = 98 c 96 + = 7 d 5 + = = = 79 Addition and Subtraction F SERIES TOPIC 5

8 Addition mental strategies compensation strategy Connect the statements with their answer: When we round down we compensate by When we round up we compensate by subtracting adding 5 Solve these addition problems using compensation. Decide if you need to round up or down and compensate accordingly. Make as many notes as you need to: a b c = 9 = 77 = 66 d 78 + e f = 86 = 89 = 9 6 A website tracked the number of visitors over 5 days: Monday Tuesday Wednesday Thursday Friday Use the compensation method to answer the following questions. 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? 9 c On which days did the total reach 9 visitors? Wednesday and Friday 6 F SERIES TOPIC Addition and Subtraction

9 Checkerboard race apply Getting 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 addition mental strategy. Each of you will choose a starting 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 direction; a or 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! Can you find the route that would give you the largest possible score? FINISH Addition and Subtraction F SERIES TOPIC 7

10 Crack the city code apply Getting ready Work out the answers to these sums in your head. Each answer matches a letter in the list on the right. Write the letters next to your answers, then unjumble the letters to find the name of a city. What to do Try competing with a friend to be the fastest to do all of the sums and work out the names of the three cities. a = 87 Letter Y Code = 58 Letter D = 97 Letter E = 509 Letter S = 87 Letter Y = 856 Letter N The city is S Y D N E Y b = 509 Letter S 8 + = 9 Letter A = 780 Letter I = 667 Letter P 80 + = Letter R The city is P A R I S c = 856 Letter N = 975 Letter O = 856 Letter N = 909 Letter L = 975 Letter O 7 + = 58 Letter D The city is L O N D O N A = 9 B = 75 C = D = 58 E = 97 F = 75 G = H = 58 I = 780 J = 989 K = 8 L = 909 M = 98 N = 856 O = 975 P = 667 Q = 555 R = S = 509 T = 58 U = 656 V = 0 W = 50 X = 76 Y = 87 Z = F SERIES TOPIC Addition and Subtraction

11 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 units Start = 5 Warm up with these subtraction wheels: Use the jump strategy to complete these subtraction problems. The first one has been started for you: Start a = b 88 5 = Start c 6 = Start 6 d = 60 Start 55 Addition and Subtraction F SERIES TOPIC 9

12 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 7 0 = b 87 6 = 8 c 50 = 9 d 78 6 = 7 e 89 5 = 5 f = 765 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 0 Save 75 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 left after the purchase? 9 b Martin saved up especially for the sale and bought items for 86. He bought Bionic Bozo and which other game? Taekwondo Team c Dana bought Taekwondo Team for her husband before the sale. What change did she receive if she paid with 00? 5 0 F SERIES TOPIC Addition and Subtraction

13 Subtraction mental strategies split strategy Remember that 5 is When subtracting large numbers in our heads it can be easier to split the number to be subtracted into parts and work with each part separately = = = = 5 Practise splitting these numbers into hundreds, tens and units. The first one is done for you. a 56 = b 89 = c 867 = d 9 = e = f 9 = Use the split strategy to subtract: a b c = = = = = 57 0 = = 5 5 = 9 7 = 68 6 = = 9 57 = Work out the answers to these questions then cross out the letter above each answer in the puzzle. The letters that remain will form the answer to the riddle. a 8 7 = 0 b = 0 c = d 0 0 = 70 e 0 = 90 f = g 97 9 = 05 h = 80 i 50 5 = j = 65 k 0 00 = 0 S Y H O U E R X E L A K Z R I D R J U M V A Riddle: What is the most rhythmic part of your body? Y O U R E A R D R U M Addition and Subtraction F SERIES TOPIC

14 Subtraction mental strategies split strategy These problems have been completed. Are they correct? If not, circle where it all began to go wrong: a b 9 0 c = = = = 5 = = 9 5 = 9 = = 75 6 = 9 = = 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 00 km 0 km Day 75 km 50 km 55 km 95 km Day 5 km 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 5 km The Giant Toothbrush 500 km F SERIES TOPIC Addition and Subtraction

15 Subtraction mental strategies compensation strategy Sometimes we round one number in the problem to make it easier to do in our heads. Then we adjust our answer to compensate: = I rounded up by, which means I subtracted 6 + = 7 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 subtracting or adding to get back to the first number. The first one is done for you. a 9 = 90 + b 8 = 50 c 5 = 50 + d 76 = 80 e 57 = 60 f 7 = 0 g 7 = 0 h 68 = 70 Solve these subtraction problems using compensation. Show all your working out: a = 507 b 89 7 = 8 c 6 9 = = = 8 + = Solve these problems using compensation. Decide if you need to round up or down and compensate accordingly: a b c = = = 505 d 59 9 e = 65 = 8 You can solve these in your head or make notes as you go. Do whatever works for you. Addition and Subtraction F SERIES TOPIC

16 Subtraction mental strategies compensation strategy Wally the work experience boy has solved these. He is happy because he solved them all correctly. Can you use his working out to establish what the original questions were? a 5 7 = 7 b = = + = = 58 + = 60 c = 96 d = = 9 + = = 8 = 6 e = 65 f 8 8 = = 6 + = = 8 + = 0 5 Use the compensation method to count backwards and complete these number patterns. 7 is close to 0 so I will subtract 0 and add These subtraction problems have been partially solved using compensation. Colour match the steps that were used and complete the missing parts. The first one has been done for you: = = = = = = = = = =.75 F SERIES TOPIC Addition and Subtraction

17 Snakes but no ladders apply Getting ready You can play with to 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 subtraction and move back to that square! The winner is the first to finish alive! 6 Finish 6 ( 5) ( ) ( ) ( 50) 5 55 ( 7) ( 9) 0 ( 0) 5 6 ( ) 7 8 ( ) ( ) ( ) 5 6 ( 8) ( 5) 0 ( 7) 5 ( 0) 0 09 ( 6) Start ( ) Addition and Subtraction F SERIES TOPIC 5

18 Darts apply Getting ready A game of darts is usually scored by subtracting 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 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 subtracting from 0, keeping score as you go. The winner is the first to get past 0! F SERIES TOPIC Addition and Subtraction

19 Written methods addition H T U How do we add using a written strategy? First we estimate: = 75. Our answer will be around 75. We start with the units is units. We rename this as ten and units. We put the in the units column and carry the to the tens column. tens plus 8 tens plus the carried ten is tens. We rename this as hundred and 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 estimate do they match? Solve these addition problems. First estimate the answers: e: 850 e: 800 e: 600 e: 700 a H T U b H T U c H T U d H T U e: e: e: e: 600 e Th H T U f Th H T U g Th H T U h Th H T U Use these cards to make 5 different addition problems using and digit numbers. Show your working out: = + Answers will vary. Addition and Subtraction F SERIES TOPIC 7

20 Written methods addition H T U We can also add each place value separately and then add these together: + 5 = = = = 707 Solve these addition problems using a written strategy of your choice: e: 800 e: 600 e: 990 a H T U b H T U c H T U e: 600 e: 750 e: 80 d H T U e H T U f H T U 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 U b H T U c H T U F SERIES TOPIC Addition and Subtraction

21 Written methods subtraction H T U First we estimate: = 700 We start with the units. We can t take 8 away from so we must rename one of the tens as units. We now have units. subtract 8 is 6 so we put the 6 in the units 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 estimate. Complete the subtraction problems: e: 800 e: 00 e: 00 a Th H T U b Th H T U c Th H T U When a problem asks us to find the difference, we subtract. We always start with the larger number. Showtown 9 km Normanville 6 km Roper 79 km Ace Bay 6 km Tidings km Ringer 7869 km Harpville 86 km Eagle Bay 595 km Solve these to find the difference problems: a How far from Showtown to Ringer? Th 7 H 8 T 6 U 9 9 b What is the distance from Normanville to Tidings? 7 0 km Th H T U km c What is the distance from Roper to Eagle Bay? Th H T U d How far from 7 9 Normanville to Ace Bay? km Th H T U km Addition and Subtraction F SERIES TOPIC 9

22 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 identify the letters. Write each word in the correct place in the crossword puzzle. 6 S G H I G H I E G E G G S 5 G L L O S H S H E L L E G S CLUES Across = 6 E S Down = = = = = = Key O I E H S G L B The answer is. What could the missing numbers be? Come up with 5 possibilities: H T U H T U H T U H T U H T U Answers will vary. 0 F SERIES TOPIC Addition and Subtraction

23 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 U T 7 6 Estimate and solve these addition problems. Remember to put the decimal point into your answers: e: 85 e: 90 e: 90 e: 70 a T U T b T U T c T U T d T U T e: 90 e: 60 e: 65 e: 50 e T U T H f T U T H g T U T H h T U T H Estimate and solve these subtraction problems. Remember to put the decimal point into your answers: e: 5 e: e: 5 e: 6 a T U T b T U T c T U T d T U T Bart finished his race in a time of 0.67 secs. Lisa finished in. secs. How much faster was Bart? 0.57 secs Addition and Subtraction F SERIES TOPIC

24 Written methods adding and subtracting decimals 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.9 Was 8.50 Now 7.99 Was 7.5 Now 6.85 Save 0.5 Save 0.50 Was 8.95 Now 6.50 Was.89 Now.65 Save.5 Save. Was.66 Now.89 Save 0.77 Total savings: 6.96 F SERIES TOPIC Addition and Subtraction

25 Written methods word problems Solve the following word problems using addition or subtraction. Circle the process you use to calculate the answer: a Joe scored 6 more points than Zac. Joe scored 589 points. How many points did Zac score? + + Answer b Jenny is cm taller than Jaala. Jaala is cm tall. How tall is Jenny? + Answer 7 5 cm c Maitland Manchester recorded 7 7 mm mm of rain. of rain. Balaklava recorded Birmingham 58 mm recorded more. 58 How mm much more. rain How did Balaklava much rain record? did Birmingham record? + Answer mm d Wayne has 7. How much more money does he need to buy a t-shirt that costs 9? + + Answer 9 7 e Charlene had. After she paid for a a ticket, she she had had 8. How much did did the the ticket cost? + Answer 8 8 f Sanjay spent and had 9 left. How much did he have before the purchase? + Answer 9 6 g Jarred s bike cost 89. Molly s bike cost h The rainfall in Two Wells was 7 mm. 6. What is the price difference between Gateshead recorded 6 mm less. How the two bikes? much rainfall did Gateshead record? Answer mm 6 mm Answer 7 mm 6 i Write your own word problem and solve it. + Answer Answers will vary. Addition and Subtraction F SERIES TOPIC

26 Slide race apply Getting ready Players Objective To be the first to slide all the way down the slide and land in the sand. Materials Game markers for each player, scrap paper, pencils, a deck of cards with the tens and the picture cards taken out. The 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 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. + Answers will vary. Add the numbers. The player with the larger total moves the game marker one space down the slide. 5 Play until someone lands in the sand. Variations Change the number of cards laid out. Start 5 6 Finish F SERIES TOPIC Addition and Subtraction

27 Subtraction puzzles solve What to do HINT: Place some stickers over a set of counters and write the digits to 8 on each counter. Now you can move them around. Puzzle Place the numbers to 6 in the grey circles so that each number is the difference between the two numbers just below it. 5 6 Two possibilities are : Puzzle Place the digits from to 8 in each circle. Numbers with a difference of cannot be placed in circles directly connected by a straight line. Sample answer: Addition and Subtraction F SERIES TOPIC 5

28 Addition mental strategies Name Complete these addition wheels Show how you would solve using: Jump strategy Split strategy Compensation strategy Skills Not yet Kind of Got it Calculates basic addition facts Demonstrates mental addition strategies for: Jump Split Compensation 6 Series F Topic Assessment

29 Addition mental strategies Name Complete these addition wheels Show how you would solve using: = Jump strategy = = = Split strategy = 5 = = Compensation strategy Skills Not yet Kind of Got it Calculates basic addition facts Demonstrates mental addition strategies for: Jump Split Compensation Series F Topic Assessment 7

30 Subtraction mental strategies Name Complete this subtraction grid: Show how you would solve 6 66 using: Jump strategy Split strategy Compensation strategy Skills Not yet Kind of Got it Calculates basic subtraction facts Demonstrates mental subtraction strategies for: Jump Split Compensation 8 Series F Topic Assessment

31 Subtraction mental strategies Name Complete this subtraction grid: Show how you would solve 6 66 using: = 95 Jump strategy = = = 9 + = = 95 Split strategy Compensation strategy Skills Not yet Kind of Got it Calculates basic subtraction facts Demonstrates mental subtraction strategies for: Jump Split Compensation Series F Topic Assessment 9

32 Written methods Name Complete these algorithms. Write an estimate for each: e: e: e: a H T U b Th H T U c Th H T U e: e: e: d Th H T U e H T U f Th H T U e: e: e: g H T U T H h T U T H i T U T H Skills Not yet Kind of Got it Solves addition and subtraction problems using a written algorithm Adds and subtracts decimals in an algorithm Provides a reasonable estimate 0 Series F Topic Assessment

33 Written methods Name Complete these algorithms. Write an estimate for each: e: 800 e: e: 800 a H T U b Th H T U c Th H T U e: 000 e: 000 e: 00 d Th H T U e H T U f Th H T U e: 0 e: 0 e: g H T U T H h T U T H i T U T H Skills Not yet Kind of Got it Solves addition and subtraction problems using a written algorithm Adds and subtracts decimals in an algorithm Provides a reasonable estimate Series F Topic Assessment

34 Word problems using addition and subtraction Name Read the problems below carefully. Complete each section of each problem. Use any strategy or written method that you find the easiest. a Max is reading an exciting book that is 6 pages long. If he has read 8 pages, how many does he have left to read? My estimate: My working out: What do I need to find out? b Baz is training for a fun run. On Monday he ran km, Thursday 9 km and on the weekend he ran km. How far did he run altogether? My estimate: My working out: What do I need to find out? c Bella went to the shops and bought a magazine for.75 and a drink for.0. How much change does she get back from 0? My estimate: My working out: What do I need to find out? Skills Not yet Kind of Got it Solves addition and subtraction problems using own strategy or written method Identifies the question Provides a reasonable estimate Series F Topic Assessment

35 Word problems using addition and subtraction Name Read the problems below carefully. Complete each section of each problem. Use any strategy or written method that you find the easiest. a Max is reading an exciting book that is 6 pages long. If he has read 8 pages, how many does he have left to read? What do I need to find out? My estimate: 76 My working out: 6 8 = = 78 The pages left to read. Max has 78 pages left to read. b Baz is training for a fun run. On Monday he ran km, Thursday 9 km and on the weekend he ran km. How far did he run altogether? What do I need to find out? Total distance. My estimate: My working out: 50 km Baz ran 5 km altogether. c Bella went to the shops and bought a magazine for.75 and a drink for.0. How much change does she get back from 0? What do I need to find out? The change Bella should get. My estimate: My working out: = = 85p =.5 Bella gets.5 change. Skills Not yet Kind of Got it Solves addition and subtraction problems using own strategy or written method Identifies the question Provides a reasonable estimate Series F Topic Assessment

36 Series F Addition and Subtraction 006 Primary Framework Core Objectives Topic Addition mental strategies Topic Subtraction mental strategies Topic Written methods Using and applying mathematics Solve one- and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use Knowing and using number facts Use knowledge of place value and addition and subtraction to derive sums and differences, doubles and halves of decimals, e.g. 6.5 ±.7, halve 6.5, double 0. Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations Counting Use efficient written methods to add and subtract whole numbers and decimals with up to two places Using and applying mathematics Solve one- and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use Knowing and using number facts Use knowledge of place value and addition and subtraction to derive sums and differences, doubles and halves of decimals, e.g. 6.5 ±.7, halve 6.5, double 0. Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations Counting Use efficient written methods to add and subtract whole numbers and decimals with up to two places Using and applying mathematics Solve one- and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use Knowing and using number facts Use knowledge of place value and addition and subtraction to derive sums and differences, doubles and halves of decimals, e.g. 6.5 ±.7, halve 6.5, double 0. Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations Counting Use efficient written methods to add and subtract whole numbers and decimals with up to two places Series F Objectives