D Teacher Student Book Name
Series D Contents Topic Section Addition Answers mental (pp. 48) strategies (pp. 4) look addition for a mental ten strategies_ look subtraction for patterns_ mental strategies 5 doubles written methods and near doubles 3 bridge money to ten_ 4 jump strategy split strategy version Section 2 Assessment with answers (pp. 49 64) split strategy version 2 addition mental strategies 49 word problems subtraction mental strategies 55 double or nothing apply written methods 59 two card sum apply money 63 first to 50 apply Date completed / / / / / / / / / / / / / / / / / / / / / / Section 3 Outcomes (pp. 65 66) Topic 2 Subtraction mental strategies (pp. 5 30) Series Author: related facts patterns bridge to ten counting on doubles and near doubles the jump strategy the split strategy lowest score apply subtract from 00 apply / / / / / / / / / / / / / / / / / / Nicola Herringer Copyright
Addition mental strategies look for a ten Let s warm up with some addition grids. Write these answers as fast as you can by counting on: a + 2 3 0 b + 3 0 2 c + 2 3 0 6 8 9 6 9 2 9 7 9 0 7 7 9 20 7 6 9 6 8 3 5 6 3 3 5 6 3 4 3 8 0 8 2 4 5 2 4 7 4 6 5 7 8 5 2 Adding more than two numbers together is easier if we look for a ten. Circle the numbers that add to 0 first, then add what is left: a 6 3 4 = c 9 5 = 3 b 5 5 = 5 d 7 6 3 = 6 e 5 6 4 = 5 f 2 8 = 3 Loop the numbers that make 0. Look for sets going across and down. One set has been looped for you. How many more can you find? 6 3 6 9 2 8 5 Some numbers may be in more than one set. 4 3 3 3 8 3 5 3 7 4 6 2 5 3 3 3 9 6 3 2 7 4 Look for a ten and change the order of the numbers in each addition problem to make it faster to add. a 4 + 5 + 3 + 5 + 6 b 9 + 3 + 7 + + 5 4 + 6 + 5 + 5 + 3 = 23 9 + + 3 + 7 + 5 = 25 D
Addition mental strategies look for patterns Number patterns are useful. You can build on basic addition facts. Add 0 each time: 2 Add 00 each time: a 0 b 5 c 7 20 30 40 a 0 0 20 30 25 35 45 b 5 5 25 35 7 27 37 c 7 07 207 307 3 Use patterns to complete this addition table: a 3 + 5 = 8 30 + 50 = 80 300 + 500 = b 6 + 2 = 8 60 + 20 = 80 600 + 200 = c 4 + = 5 40 + 0 = 50 400 + 00 = d 7 + 3 = 0 70 + 30 = 00 700 + 300 = 800 800 500 000 4 Complete this addition trail: 357 + 0 367 + 0 377 + 0 + 00 257 Start here 7 + 0 7 + 0 247 + 200 47 + 20 27 2 D
Addition mental strategies doubles and near doubles Doubles facts are the same number added together. 3 + 3 = 6 is the same as saying double 3 is 6. Write a doubles fact to match each picture: a Double the fingers: b Double the pencils: If I double 5 I will get 0 If I double 6 I will get 2 c Double the spots: d Double the lace holes: If I double 7 I will get 4 If I double 4 I will get 8 2 Use these addition frames to double each of these numbers as quickly as you can: 5 7 9 2 2 8 5 + 5 = 0 7 + 7 = 4 9 + 9 = 8 2 + 2 = 4 2 + 2 = 24 8 + 8 = 6 3 Complete the grid below so that the question in the top row matches the answer in the bottom row. The first one has been done for you. 2 + 2 5+5 3 + 3 4 + 4 + 6+6 7 + 7 8 + 8 9+9 = 4 = 0 =6 =8 = 2 = 2 =4 =6 = 8 Once you know your basic double facts, you can use them to double bigger numbers e.g. 2 + 2 = 20 + 4 = 24 4 Double these: a 0 20 b 2 24 c 6 32 d 4 28 D 3
Addition mental strategies doubles and near doubles Near doubles strategy is when you double a number and adjust. See: 5 + 6 See: 7 + 6 Think: double 5 + = Think: double 7 = 3 5 Complete the near double strategy for these. The first one has been done for you. a 2 + 3 = double 2 + = 5 b 4 + 5 = double 4 + = 9 c 6 + 7 = double 6 + = e 8 + 9 = double 8 + = 3 d 3 + 4 = double 3 + = 7 7 f 7 + 8 = double 7 + = 5 6 Complete the near double strategy for these. This time you are calculating a near double that is less. a 8 + 7 = double 8 = 5 b 6 + 5 = double 6 = c 5 + 4 = double 5 = 9 d 2 + = double 2 = 23 e 5 + 4 = double 5 = 29 f 6 + 5 = double 6 = 3 7 Complete these near double tables based on the double fact in the top row: a 2 + 2 = 24 b 5 + 5 = 30 c 6 + 6 = 32 2 + 3 = 25 5 + 4 = 29 6 + 9 = 35 2 + = 23 5 + 6 = 3 6 + 2 = 28 2 + 4 = 26 5 + 8 = 33 6 + 7 = 33 8 Who said what? Write the initials after each statement: 7 Sweet Seven (SS) 0 Terrific Ten (TT) 5 Famous Fifteen (FF) 9 Nifty Nine (NN) a Double me and 4 you get 0. SS b Double me and + 2 you get 22. TT c Double me and you get 7. NN d Double me and 3 you get 27. FF 4 D
Addition mental strategies bridge to ten Bridge to ten is when we make the first number up to 0 and then add what is left. Let s start by using ten frames: = 8 4 0 2 8 + 4 = 0 + 2 = 2 Look carefully at the first set of ten frames. Bridge to ten on the second set and complete the addition. a = 8 + 6 = 0 + 4 = 4 b = 7 + 4 = 0 + = c = 9 + 5 = 0 + 4 = 4 d = 9 + 8 = 0 + 7 = 7 D 5
Addition mental strategies bridge to ten We can also use number lines to bridge to the next ten and then add what is left. 22 + 6 = 38 +8 +8 22 30 38 2 Practise bridging to ten with each addition set. The first one has been done for you. Set : a 8 + 6 0 + 4 = 4 Set 2: a 6 + 5 20 + = 2 b 7 + 5 0 + 2 = 2 b 7 + 6 20 + 3 = 23 c 6 + 7 0 + 3 = 3 c 9 + 6 20 + 5 = 25 3 Use the number lines to bridge to ten. Fill in the missing numbers each time. To help you get started, the first number line has 2 numbers filled in. + 3 + 5 a 47 + 8 = 55 47 50 55 + 4 + 5 b 56 + 9 = 65 56 60 65 + 7 + 8 c 73 + 5 = 88 73 80 88 Continued on page 7. 6 D
Addition mental strategies bridge to ten Continued from page 6. 3 Use the number lines to bridge to ten. Fill in the missing numbers each time. + 6 + 6 d 44 + 2 = 56 44 50 56 + 6 + 5 e 84 + = 95 84 90 95 + 8 + 7 f 32 + 5 = 47 32 40 47 4 Write a problem that matches this number line. +6 +7 24 + 3 = 37 24 30 37 5 Complete these addition tables by bridging to the next ten in your head. a Add 2 b Add 7 c Add 3 49 6 36 53 77 90 56 68 7 34 48 6 38 50 58 75 59 72 D 7
Addition mental strategies jump strategy The jump strategy is when you use a number line to jump in and then. 32 + 25 = 57 +0 +0 +5 32 42 52 57 Practise jumping along the number line in : +0 +0 +0 +0 a 5 6 7 8 9 +0 +0 +0 +0 b 78 88 98 08 8 2 Add these using the jump strategy. Show your working on each number line: +0 +0 +0 +5 a 57 + 35 = 92 57 67 77 87 92 +0 +0 +8 b 54 + 28 = 82 54 64 74 82 +0 +0 +0 +5 c 62 + 35 = 97 62 72 82 92 97 8 D
Addition mental strategies split strategy version When adding large numbers in our heads, it can be easier to split one of the numbers into parts and add each part separately. 40 57 + 46 57 + 40 = 97 97 + 6 = 03 6 Practise separating these numbers into and ones. The first one has been done for you. a 22 20 2 50 60 b 57 c 65 d 96 7 5 90 6 2 Practise adding to these numbers: + 0 50 20 30 60 2 3 7 4 5 8 48 58 98 68 78 08 3 Use the split strategy with these problems: 30 a 38 + 34 38 + 30 = 68 4 68 + 4 = 72 20 b 29 + 28 29 + 20 = 49 8 49 + 8 = 57 0 c 75 + 4 75 + 0 = 85 4 85 + 4 = 89 0 d 94 + 7 94 + 0 = 04 7 04 + 7 = D 9
Addition mental strategies split strategy version 2 Here is another way to use the split strategy. 42 + 32 = (4 + 3 ) + (2 + 2 ) = 7 + 4 = 74 Use this way to add these: a 53 + 56 = ( 5 + 5 ) + ( 3 + 6 ) = 0 + 9 = 09 b 35 + 24 = ( 3 + 2 ) + ( 5 + 4 ) = 5 + 9 = 59 c 78 + = ( 7 + ) + ( 8 + ) = 8 + 9 = 89 d 45 + 24 = ( 4 + 2 ) + ( 5 + 4 ) = 6 + 9 = 69 2 Use either version of the split strategy to complete this table: + 65 85 36 23 4 2 77 97 48 35 53 34 99 9 70 57 75 0 D
Mental addition strategies word problems Solve these word problems using either the jump or the split strategies. Show all your working. a Mitch and Anna held a lemonade stall over the weekend. They sold 25 cups on Saturday and 8 cups on Sunday. How many cups did they sell altogether? +0 +8 25 35 43 25 + 8 = 43 cups b I practised my guitar for 48 minutes before school and 34 minutes after school. How many minutes did I practise altogether? +0 +0 +0 +4 48 58 68 78 82 48 + 34 = 82 minutes c Charlotte received $5 for her birthday from her grandmother. She added this to her savings account which has $53. How much does Charlotte have now? +0 +0 +0 +0 +0 +3 5 25 35 45 55 65 68 $5 + $53 = $68 D
Double or nothing apply Getting ready This is a game for two players. You will each need two copies of the set of cards below. So, a total of four pages per pair. Cut out your cards, then join them so that you have a deck of 36 cards. copy What to do Shuffle the cards well and place face down in the centre. Player turns over two cards and calls out the total. If the cards are a double (e.g. 4 and 4) or a near double and the total they have called out is correct, Player keeps the cards. (For the cards to be a near double, there needs to be a difference of, e.g. 3 + 4, 6 + 5.) If the cards are not a double or near double they are put to one side. Player 2 repeats these steps. Continue taking turns until there are no cards left. The winner is the player with the most cards. 2 3 4 5 6 7 8 9 2 D
Two card sum apply Getting ready This is a game for two players. You will each need a copy of the set of cards below. Cut out your cards then join them so that you have a deck of 24 cards. copy What to do Shuffle the cards well and place face down in the centre. Each player turns over two cards and calls out the total. The player with the largest total wins that round and takes all four cards. If players have the same answer, they tie, no one wins the round and these cards are put aside. Continue taking turns until there are no cards left. The winner is the player who wins the most rounds. 5 2 3 4 5 6 7 8 2 0 6 8 D 3
First to 50 apply Getting ready This is a game for two players. You will need four dice and a copy of this page to record your totals. copy What to do The aim of this game is to reach a total of 50. Each player takes a turn to roll a die four times and records the total in a row in one of the tables below. If your running score goes over 50, you strike out. You may choose to freeze after the first or second roll if you are getting close to 50. Take turns until the table is full. The player who finishes the round closest to 50, but not over 50, scores 5 points. The player who finishes the round exactly on 50, scores 0 points. Player Rolled numbers ROUND Running total Rolled numbers ROUND 2 Running total Rolled numbers ROUND 3 Running total Player 2 Rolled numbers ROUND Running total Rolled numbers ROUND 2 Running total Rolled numbers ROUND 3 Running total 4 D
Subtraction mental strategies related facts Knowing one addition fact means you also know two related subtraction facts. Because 7 + 3 = 0 you also know that 0 7 = 3 and 0 3 = 7 Show the related addition and subtraction facts for each set of digits. The first one is partially completed for you. a 8 4 2 b 7 9 6 8 + 4 = 2 7 + 9 = 6 4 + 8 = 2 9 + 7 = 6 2 4 = 8 6 7 = 9 2 8 = 4 6 9 = 7 c 3 7 20 d 0 8 8 3 + 7 = 20 0 + 8 = 8 7 + 3 = 20 8 + 0 = 8 20 3 = 7 8 0 = 8 20 7 = 3 8 8 = 0 2 Ring a section of the dots in each box and write a related number sentence for each. The first one is partially done for you. Answers will vary. a 8 + = 9 b + = 8 c + = 6 D 2 5
Subtraction mental strategies patterns Recognising patterns in subtraction is useful in extending known facts. Can you see the pattern in this set of facts? 7 3 = 4 37 3 = 34 27 3 = 24 47 3 = 44 Extend each set of subtraction patterns in the sets below and then shade the answers on this grid: a Set 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 25 26 27 28 29 30 3 32 33 34 35 36 37 38 39 40 4 42 43 44 45 46 47 48 49 50 5 52 53 54 55 56 57 58 59 60 6 62 63 64 65 66 67 68 69 70 7 72 73 74 75 76 77 78 79 80 8 82 83 84 85 86 87 88 89 90 9 92 93 94 95 96 97 98 99 00 b Set 2 c Set 3 8 2 = 6 25 4 = 2 9 6 = 3 8 2 = 6 35 4 = 3 29 6 = 23 28 2 = 26 45 4 = 4 39 6 = 33 38 2 = 36 55 4 = 5 49 6 = 43 48 2 = 46 65 4 = 6 59 6 = 53 58 2 = 56 75 4 = 7 69 6 = 63 68 2 = 66 85 4 = 8 79 6 = 73 78 2 = 76 95 4 = 9 89 6 = 83 2 Extend this subtraction pattern beyond the hundred grid: a 88 7 = 8 b 98 7 = 9 c 08 7 = 0 d 8 7 = e 28 7 = 2 f 38 7 = 3 6 D 2
Subtraction mental strategies bridge to ten A ten frame is useful to show the bridge to ten strategy when subtracting. Here are 7 counters in 2 frames. When you see 7 8 =?, cross out 8 from the first ten frame then add what is left. 7 8 = 9 Use each ten frame to subtract using bridge to ten. Cross out the number of counters that are subtracted from the first ten frame: a 6 9 = 7 b 3 7 = 6 c 4 9 = 5 d 5 8 = 7 2 Write a subtraction fact that matches each ten frame: a 5 7 = 8 b 9 5 = 4 c 6 7 = 9 d 9 8 = D 2 7
Subtraction mental strategies bridge to ten 3 Complete the subtraction wheels. Use a ten frame in your mind. 8 6 9 2 a 5 7 9 6 2 0 7 5 3 3 3 b 8 6 0 5 8 7 3 3 0 3 4 8 0 0 9 0 8 4 Find the mystery number. Use the clues to write a matching subtraction fact. Add the answers for a to c, and then subtract from 50. This is the mystery number. a 6 5 = b 7 4 = 3 c 9 6 = 3 Show your working here: + 3 + 3 = 37 50 37 = 3 The mystery number is: 3 5 Complete these subtraction squares. Subtract the rows and columns as shown by the arrows: a 5 5 0 b 30 8 2 8 3 5 5 9 6 7 2 5 5 9 6 8 D 2
Subtraction mental strategies bridge to ten Bridge to the next ten and then count on what is left. 25 6 = 9 +4 +5 6 20 25 6 Use the number lines to bridge to ten: + 5 + 32 a 52 5 = 37 5 20 52 + 7 + 42 b 62 3 = 49 3 20 62 + 8 + 55 c 75 2 = 63 2 20 75 + 6 + 72 d 92 4 = 78 4 20 92 D 2 9
Subtraction mental strategies bridge to ten 7 Complete the subtraction frame to match this number line: 27 2 = 5 +8 +7 2 20 27 8 Here is a jar of 65 shells. Three kids guessed how many shells were in the jar. Use bridge to ten on the number lines to show how close each guess was. The first one is done for you. a Jo s guess: 52 65 52 = 3 +8 +5 52 60 65 b Liam s guess: 58 65 58 = 7 +2 +5 58 60 65 c Joel s guess: 54 65 54 = +6 +5 54 60 65 d Whose guess was the closest? Liam's 20 D 2
Subtraction mental strategies counting on If there is only a small difference between the numbers, use counting on to find the difference. See: 32 28 =? Think: What can you add to 28 to get 32? Count on by 4. + 4 20 2 22 23 24 25 26 27 28 29 30 3 32 33 34 35 36 37 38 39 40 Find the difference between these by counting on. a 32 29 = d 7 68 = g 83 77 = 3 b 33 28 = 5 c 34 27 = 7 3 e 82 76 = 6 f 73 69 = 4 5 h 2 09 = 3 i 20 96 = 5 2 Use counting on to complete these function machines. a In Rule Out b In Rule Out With function machines, numbers go in, have the rule applied and then come out. 4 4 7 3 44 42 37 7 5 73 75 68 5 7 45 8 72 4 c In Rule Out d In Rule Out e In Rule Out 22 3 0 3 96 7 25 24 9 6 5 05 07 98 7 9 93 92 89 4 3 23 4 03 5 94 5 D 2 2
Subtraction mental strategies counting on 3 Complete each table of subtraction facts by counting on. Look for the pattern in each table. a Table b Table 2 c Table 3 2 9 = 2 33 28 = 5 20 7 = 3 33 29 = 4 42 38 = 4 0 97 = 4 48 39 = 9 5 48 = 3 33 27 = 6 64 59 = 5 95 88 = 7 52 47 = 5 4 Complete each table of subtraction facts. Can you still use counting on? a Table b Table 2 c 42 23 5 33 38 = 4 9 = 4 47 = 4 29 = 4 2 73 02 8 8 = 3 69 = 4 98 = 4 77 = 4 85 54 45 25 Table 3 79 = 6 48 = 6 39 = 6 9 = 6 5 Roll a die and write this number in the triangle, then complete the subtraction: a 56 = b 76 = c 283 = d 9 = e 292 = g 48 = Answers will vary. f 00 = h 90 = Answers will vary. i 93 = j 200 = k 86 = l 94 = 22 D 2
Subtraction mental strategies doubles and near doubles As long as you know addition doubles, you will know subtraction doubles. 5 + 5 = 0 so 0 5 = 5 Answer the addition doubles and write a matching subtraction double. a 6 + 6 = 2 so 2 6 = 6 b 9 + 9 = 8 so 8 9 = 9 c 2 + 2 = 24 so 24 2 = 2 d 8 + 8 = 6 so 6 8 = 8 2 Play this game with a partner. Make copies of this page so you can play this game again. Player chooses a subtraction double by tossing a counter onto the grid. Player then ticks a circle in the column that has the answer. Player 2 repeats these steps. Take turns until someone has ticked a whole column on their own page. copy 24 2 22 20 0 8 9 6 8 4 7 2 6 0 5 8 4 6 3 4 2 2 2 3 4 5 6 7 8 9 0 2 D 2 23
Subtraction mental strategies doubles and near doubles With near doubles subtraction, think of the doubles fact when you subtract, and then adjust. See: 5 7 See: 3 7 Think: (4 7) + Think: (4 7) 3 Here s a doubles and near doubles addition chart. Remember, you need to know the addition doubles to use near doubles subtractions. Circle the doubles facts. The first two are circled for you + = 2, 2 + 2 = 4. Next, shade all the doubles facts +. Then all the double facts. + 0 2 3 4 5 6 7 8 9 0 0 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 0 2 2 3 4 5 6 7 8 9 0 3 3 4 5 6 7 8 9 0 2 4 4 5 6 7 8 9 0 2 3 5 5 6 7 8 9 0 2 3 4 6 6 7 8 9 0 2 3 4 5 7 7 8 9 0 2 3 4 5 6 8 8 9 0 2 3 4 5 6 7 9 9 0 2 3 4 5 6 7 8 See Think Answer 7 8 (6 8) + 9 5 7 (4 7) + 8 3 6 (2 6) + 7 5 (0 5) + 6 9 4 (8 4) + 5 See Think Answer 3 2 (4 2) 5 3 7 4 9 5 6 (6 3) (8 4) (0 5) (2 6) 2 3 4 5 4 With this table, you need to think of doubles outside the grid. See Think Answer 3 5 (30 5) + 6 37 8 (36 8) + 9 5 25 0 50 6 30 (50 25) + 26 (00 50) + 5 (60 30) + 3 24 D 2
Subtraction mental strategies the jump strategy The jump strategy is when you use a number line to jump in and then. Look at 79 34. First we jump back in and then. So, 79 34 = 45. 4 0 0 0 45 49 59 69 79 Subtract these using the jump strategy: a 78 25 = 53 5 0 0 53 58 68 78 b 93 3 = 62 0 0 0 62 63 73 83 93 c 84 2 = 63 0 0 63 64 74 84 d 79 36 = 43 6 0 0 0 43 49 59 69 79 e 95 42 = 53 2 0 0 0 0 53 55 65 75 85 95 D 2 25
Subtraction mental strategies the jump strategy 2 Use the jump strategy to calculate how much more each person needs to purchase a family pass. SPECIAL DEAL! day family pass $98 a The Darnley family have saved $56. 6 0 0 0 0 0 42 48 58 68 78 88 98 They need another: $42 b The Sommers family have saved $34. 4 0 0 0 64 68 78 88 98 They need another: $64 c The Griffiths family have saved $49. 9 0 0 0 0 49 58 68 78 88 98 They need another: $49 26 D 2
Subtraction mental strategies the split strategy The split strategy is where we make the subtraction easy by splitting the second number into and ones. We then subtract each part separately. 20 68 22 68 20 = 48 48 2 = 46 2 Practise subtracting from these numbers: 0 30 20 30 50 96 7 86 66 76 66 46 6 4 5 4 2 2 Use the split strategy with these problems: 30 a 73 34 73 30 = 43 4 43 4 = 39 60 b 96 65 96 60 = 36 5 36 5 = 3 20 c 8 24 8 20 = 6 4 6 4 = 57 20 d 69 23 69 20 = 49 3 49 3 = 46 40 e 06 43 06 40 = 66 3 66 3 = 63 D 2 27
Subtraction mental strategies the split strategy 3 Use the split strategy to solve this cross number puzzle: 2 3 4 3 2 2 5 7 5 9 0 2 6 7 5 8 6 4 8 9 0 5 3 3 2 5 2 6 4 8 9 3 4 5 7 3 6 6 7 6 2 4 3 Across 50 8 = 32 2 64 6 = 48 5 200 02 = 98 3 00 43 = 57 4 72 36 = 36 6 89 36 = 53 5 35 45 = 90 6 05 43 = 62 8 88 32 = 56 6 70 2 = 58 7 60 7 = 43 9 50 2 = 38 7 87 23 = 8 86 33 = 64 53 Down 2 88 68 = 20 60 0 = 3 33 57 = 59 76 0 78 53 = 25 4 28 56 = 72 5 99 35 = 64 28 D 2
Xxxxxxxx Lowest score xxxxxxxx apply Getting ready This is a game for two players. You will need a die and a copy of this page to record your answers. You may like to make a few copies so you can play again. copy Player What to do The aim of this game is to get the lowest finishing score. Player rolls the die and writes this number in the first column. Next, they decide whether to add 0 or multiply by 5 and subtract this number from 00. The result will be their running score and Player will subtract from their running score on their next turn. Player 2 repeats these steps. Continue taking turns until the table is filled. The lowest finishing score wins. Player 2 I have to be careful when choosing whether to + 0 or 5 because I don t want to get below zero but I want to get close to zero! Number on die Number used Running score Number on die Number used Running score Finishing score Finishing score D 2 29
Xxxxxxxx Subtract from 00 xxxxxxxx apply Getting ready This is a game for two players. You will need two dice and 0 counters each, in two different colours. copy What to do The aim of the game is to use all your counters first. Player rolls the two dice and makes a 2 digit number from the numbers rolled. They subtract this 2 digit number from 00, find the answer on the grid and cover the number with a counter. Player 2 repeats this process. The winner is the first player to get rid of all their counters. 85 38 39 79 86 59 68 55 57 69 37 54 34 87 36 44 56 47 58 49 64 66 77 46 45 78 67 75 76 89 74 88 84 65 48 35 30 D 2
Written methods addition to 99, no regrouping Using a written method to add is very similar to this version of the split strategy: 42 + 3 = (4 + 3 ) + (2 + unit) = 7 + 3 = 73 The difference is that we set the numbers up in place value columns and add the first. 4 2 + 3 7 3 For each addition, complete it with the split strategy and then use the written method. a 55 + 23 = ( 5 + 2 ) + ( 5 + 3 ) = 7 + 8 5 5 + 2 3 = 78 7 8 b 42 + 35 = ( 4 + 3 ) + ( 2 + 5 ) = 7 + 7 + 4 2 3 5 = 77 7 7 c 6 + 8 = ( 6 + ) + ( + 8 ) = 7 + 9 + 6 8 = 79 7 9 d 65 + 32 = ( 6 + 3 ) + ( 5 + 2 ) = 9 + 7 + 6 5 3 2 = 97 9 7 D 3 3
Written methods addition to 99, no regrouping 2 Add these using the written method. Add the, then the. Write your answer neatly in line with the place value columns. a b c 4 3 0 3 6 + 3 2 + 4 9 + 5 2 7 5 5 9 8 8 d e f 6 4 3 3 9 2 + 5 + 4 + 6 6 9 4 7 9 8 3 Now try adding three 2 digit numbers using the written method: a b c 3 0 2 + 2 6 7 7 3 4 4 + 2 3 9 8 2 3 3 5 + 3 0 8 8 4 Write the missing digits in these problems: a b c 2 3 4 3 2 3 2 2 3 3 2 + 4 9 6 + 2 7 8 + 4 5 9 8 32 D 3
Written methods addition to 99 with regrouping Here is a place value board that shows how regrouping works. If we have 0, we should regroup into a ten. On the first place value board we can see that there are 3 and. We regroup 0 into ten and we get 4 and unit. = 0 = ten For each set of place value boards, regroup the into a ten and show the regrouped amount on the next board. Just use straight lines for (longs) and squares for (shorts). a b 2 Add the numbers shown in longs and shorts. Use the first place value board to show the longs and shorts combined and regroup them on the second board. Record the addition problem in the squares: a + 26 + 28 = 54 b + 37 + 9 = 56 D 3 33
Written methods addition to 99 with regrouping Now that you have practised regrouping on place value boards, we are going to apply this to a written strategy of addition where you have to regroup. Let s look at 53 + 9. If we use longs and shorts in columns, it looks like this. Then, we regroup the and to get the answer 72. Now look at the written method for addition when regrouping: + e: 70 5 3 + 9 7 2 First, estimate the answer: 50 + 20 = 70. You estimate by rounding to the nearest 0. Add the : 3 + 9 = 2 Think of this as ten and 2. Write the 2 in the column and put the in the column. Now add the and write 7 in the column. Is our answer reasonable? Yes, because it is close to our estimate. 3 Try adding these 2 digit numbers using the written method. Start by writing your estimate: a e: 70 b e: 80 c e: 80 3 8 4 9 2 9 + 2 9 + 2 7 + 4 9 6 7 7 6 7 8 Continued on page 35. 34 D 3
Written methods addition to 99 with regrouping Continued from page 34. 3 Try adding these 2 digit numbers using the written method. Start by writing your estimate: d e: 60 e e: 90 f e: 80 4 4 4 9 9 + 7 6 + 4 3 9 2 + 6 2 8 g e: 70 h e: 70 i e: 80 4 8 3 8 9 + 8 6 6 + 2 9 6 7 + 5 9 7 8 4 Solve these word problems using the written method: a I drove 39 km on Thursday and 58 km on Friday. How far did I drive altogether? b Our class sold 9 raffle tickets during the first week of sales and 59 raffle tickets during the second week. How many were sold altogether? e: 00 e: 80 3 9 9 + 5 8 + 5 9 9 7 7 8 D 3 35
Written methods subtraction to 99, no regrouping Here is the written method for subtraction. The longs and shorts show you the place value. But you actually use digits. 3 8 5 2 3 Subtract these using the written method. Subtract the then the. Write your answer neatly in line with the place value columns: a b c 6 3 8 7 7 7 3 2 4 3 5 3 3 4 4 2 4 d e f 5 8 4 2 6 7 8 3 2 4 6 6 8 3 5 3 3 g h i 6 7 2 5 5 3 4 3 2 9 7 2 6 7 36 D 3
Written methods subtraction to 99 with regrouping These place value boards show how we can regroup a ten into. 4 and unit is now 3 and. For each set of place value boards, regroup a ten into and show the new amount on the next board. Just use straight lines for and squares for. a b 2 Complete this subtraction problem shown in longs and shorts. Regroup a ten into and then subtract. Show your answer in longs and shorts: = D 3 37
Written methods subtraction to 99 with regrouping Now that you can regroup a ten on the place value board, we can look at written subtraction with regrouping. Here is 62 8 shown in longs and shorts. If we regroup a ten into, we can now subtract the. Now look at the written method for subtraction when regrouping. e: 40 5 6 2 8 4 4 First, estimate the answer: 60 20 = 40. You estimate by rounding to the nearest 0. Look at the. We can t subtract 8 from 2, so we regroup a ten into. We now have 2. 2 subtract 8 is 4, so we write 4 in the column. Now subtract the. 5 subtract ten is 4. Write 4 in the column. Is our answer reasonable? Yes, because it is close to our estimate. 3 Complete these written subtraction problems with regrouping. Start by writing your estimate: a e: 40 b e: 0 c e: 30 6 4 5 7 2 5 2 6 2 8 4 3 3 4 4 4 9 2 7 Continued on page 39. 38 D 3
Written methods subtraction to 99 with regrouping Continued from page 38. 3 Complete these written subtraction problems with regrouping. Start by writing your estimate: d e: 40 e e: 30 f e: 70 4 5 6 8 3 8 5 6 2 3 3 2 9 8 9 6 2 8 6 8 g e: 20 h e: 40 i e: 30 3 4 6 7 6 8 9 7 2 4 7 3 9 3 7 6 8 2 9 4 What is the digit behind the star? a 7 2 b 8 c 7 9 5 5 9 5 6 2 5 2 4 = 6 = 4 = 5 D 3 39
Rolling subtraction apply Getting ready This is a game for two players. You will need two dice and each player needs a copy of this page to record their answers. You may like to make a few copies so you can play again. copy What to do The aim of the game is to get as close as possible to zero. Roll the dice and write this number in the first row under 99. Subtract and record the answer in the next row. Roll the dice again to create another 2 digit number and subtract again. If you can t make a 2-digit number to subtract, you miss a turn. Players take turns and may subtract only one number on the dice once they get closer to zero. The winner of a round is the player who gets the closest to zero. Play the best out of three. Example Number on die Number on die 2 9 9 3 4 6 5 4 2 4 3 5 6 6 0 Round 9 9 Round 2 9 9 Round 3 9 9 40 D 3
Money coin combinations It is important to be able to recognise coins and add different combinations quickly. Label each of these coins: $2 $ 50 20 0 5 2 Add each amount of coins: a b $3 $2 c d $ $0 3 Show $0 using a combination of all the coins in question. Answers will vary 50 has twelve sides, so just use circles with the amount inside. D 4 4
Money coin combinations 4 Cross out all the coins you trade for each amount shown at the top of each group of coins. How much is left over each time? a Trade for $ Amount left over $ b Trade for $2 Amount left over 50 c Trade for $5 Amount left over $5 d Trade for $0 Amount left over $ 42 D 4
Money coin combinations 5 Show how you pay for these party supplies using exact amounts. Place the same number of ticks in the column of the coin you would use. The first one has been done for you. Answers may vary. a Confetti $.60 b Balloons $.75 c Streamers $2.40 d e Glow sticks $4.5 Party hats $3.25 6 You have this amount to spend: List the party supplies that you can buy. Spend as close to the full amount as you can. Answers will vary. D 4 43
Money note combinations These are the notes in our currency. How much money is there? a = $ 90 b = $ 60 c = $ 35 2 Link the price tags that add to $00 by connecting them with a line. $27 $3 $35 $5 $39 $46 $54 $50 $45 $5 44 D 4
Money finding change When you buy something and you don t have the exact combination of notes and coins, you can pay with a larger amount and get the difference back. This is called change. For example, if I buy some fruit that costs $2.85 with a $5.00 note, I would get back $2.5 in change. Bridge to the next dollar and then add the rest. +5 +$2 $2.85 $3.00 $5.00 Practise bridging to the next dollar: +25 +75 a b $3.75 $4.00 $.25 $2.00 c +40 +65 d $4.60 $5.00 $6.35 $7.00 2 Bridge to the next dollar on these number lines to find the change: +5 +$0 a $9.85 $0 $20.00 Change is: $0.5 +25 +$2 b $2.75 $3 $5.00 Change is: $2.25 +5 +$2 c $7.95 $8 $0.00 Change is: $2.05 D 4 45
Money adding dollar amounts Over the weekend Jo and Barney held a lemonade stall at the corner of the street where they live. This table shows how much profit they made each day. Saturday Sunday Large $5.25 $24.75 Small $2.80 $36.20 Find each of these totals. The split strategy would be useful. a What was the profit on large lemonades? $5.25 + $24.75 = ($5 + $24) + (25 + 75 ) = $39 + $ = $40 b What was the profit on Saturday? $5.25 + $2.80 = ($5 + 2) + (25 + 80 ) = $27 + $.05 = $28.05 c What was the total profit on large and small lemonades over the whole weekend? Sunday s profit $24.75 + $36.20 = ($24 + 36) + (75 + 20 ) = $60 + 95 = $60.95 Add this to $28.05 (Saturday s profit) $60.95 + $28.05 = ($60 + $28) + (95 + 5 ) = $88 + $ = $89 46 D 4
Claim the totals apply Getting ready This is a game for two players. You will need a copy of this page and page 48; and three same colour counters each. copy What to do Use the game board below. Then cut out the coin cards on page 48 and shuffle well. Take turns turning over four cards at a time. Add the coins and look for the total on the grid. If the total is on the grid, then place a counter on it. The first player to place a counter on three amounts next to each other in any direction, wins. $5.50 $3.70 $6.0 $.80 $2.20 $3.20 $.70 $.80 $6.20 $4.20 $5.50 $4.0 $.80 $3.70 $.50 $.70 D 4 47
Claim the totals apply 48 D 4
Addition mental strategies Name Complete these addition grids: a + 8 3 9 0 b + 4 8 2 5 52 72 7 25 3 6 2 Show how to use bridge to ten to add these: a 48 + 3 = + + b 56 + 6 = + + Skills Not yet Kind of Got it Recalls addition facts 2 digit plus digit to 99 Uses mental strategies to solve addition or subtraction problems: bridge to ten Series D Topic Assessment 49
Addition mental strategies Name 3 Add these using the jump strategy: a 28 + 22 = b 52 + 3 = 4 Add these using both methods of the split strategy: a 34 + 25 = ( + ) + ( + ) = + = b 42 + 37 Skills Not yet Kind of Got it Uses mental strategies to solve addition or subtraction problems: the jump and the split strategy 50 Series D Topic Assessment
Addition mental strategies Name Complete these addition grids: a + 8 3 9 0 b + 4 8 2 5 52 60 55 6 62 72 76 80 74 77 7 25 20 26 27 25 29 33 27 30 3 2 6 22 23 6 65 69 63 66 2 Show how to use bridge to ten to add these: a 48 + 3 = 6 + 2 + 48 50 6 b 56 + 6 = 72 + 4 + 2 56 60 72 Skills Not yet Kind of Got it Recalls addition facts 2 digit plus digit to 99 Uses mental strategies to solve addition or subtraction problems: bridge to ten Series D Topic Assessment 5
Addition mental strategies Name 3 Add these using the jump strategy: a 28 + 22 = 50 +0 +0 +2 28 38 48 50 b 52 + 3 = 83 +0 +0 +0 + 52 62 72 82 83 4 Add these using both methods of the split strategy: a 34 + 25 = ( 3 + 2 ) + ( 4 + 5 ) = 5 + 9 = 59 30 b 42 + 37 42 + 30 = 72 72 + 7 = 79 7 Skills Not yet Kind of Got it Uses mental strategies to solve addition or subtraction problems: the jump and the split strategy 52 Series D Topic Assessment
Addition mental strategies Name Solve one word problem with the jump strategy and one with the split strategy (either method). a Holly and Tom went on a mini-beast hunt. Holly counted 38 slaters and Tom counted 7 snails. How many mini-beasts did they see altogether? b Harry saved $35 in June and $27 in July. How much did he save altogether? c Which strategy do you like best and why? Skills Not yet Kind of Got it Uses the jump and the split strategy to solve word problems Reflects upon their own thinking with mental addition strategies Series D Topic Assessment 53
Addition mental strategies Name Solve one word problem with the jump strategy and one with the split strategy (either method). a Holly and Tom went on a mini-beast hunt. Holly counted 38 slaters and Tom counted 7 snails. How many mini-beasts did they see altogether? 55 slaters Working will vary. b Harry saved $35 in June and $27 in July. How much did he save altogether? $62 Working will vary. c Which strategy do you like best and why? Answers and workings will vary. Skills Not yet Kind of Got it Uses the jump and the split strategy to solve word problems Reflects upon their own thinking with mental addition strategies 54 Series D Topic Assessment
Subtraction mental strategies Name Complete these subtraction wheels: a 5 7 9 7 3 0 8 b 78 6 0 6 9 4 3 4 3 5 2 Show how to use bridge to ten to subtract these: a 73 5 = + + b 46 7 = + + Skills Not yet Kind of Got it Recalls subtraction facts 2 digit subtract digit to 99 Uses mental strategies to solve addition or subtraction problems: bridge to ten Series D Topic 2 Assessment 55
Subtraction mental strategies Name 3 Subtract these using the jump strategy: a 79 27 = b 84 3 = 4 Subtract these using the split strategy: a 79 25 b 95 32 Skills Not yet Kind of Got it Uses mental strategies to solve addition or subtraction problems: the jump and the split strategy 56 Series D Topic 2 Assessment
Subtraction mental strategies Name Complete these subtraction wheels: 76 74 69 7 a 5 7 9 7 70 78 68 75 3 0 3 8 b 78 6 0 6 5 75 9 4 7 72 3 4 73 72 77 65 74 2 Show how to use bridge to ten to subtract these: a 73 5 = 58 + 5 + 53 5 20 73 b 46 7 = 29 + 3 + 26 7 20 46 Skills Not yet Kind of Got it Recalls subtraction facts 2 digit subtract digit to 99 Uses mental strategies to solve addition or subtraction problems: bridge to ten Series D Topic 2 Assessment 57
Subtraction mental strategies Name 3 Subtract these using the jump strategy: a 79 27 = 52 7 0 0 52 59 69 79 b 84 3 = 53 0 0 0 53 54 64 74 84 4 Subtract these using the split strategy: 20 a 79 25 79 20 = 59 5 59 5 = 54 30 b 95 32 95 30 = 65 2 65 2 = 63 Skills Not yet Kind of Got it Uses mental strategies to solve addition or subtraction problems: the jump and the split strategy 58 Series D Topic 2 Assessment
Written methods Name Add these using the written method: a b c 4 4 + 2 5 3 0 + 4 9 7 2 + 3 2 d e f 8 4 + 3 5 5 4 + 5 9 3 + 4 2 Add these using the written method. Estimate the answer first: a e: b e: c e: 6 3 + 8 3 8 + 2 8 7 9 + 5 9 Skills Not yet Kind of Got it Uses written methods to add 2 digit numbers including regrouping Series D Topic 3 Assessment 59
Written methods Name 3 Subtract these using the written method: a b c 8 4 3 2 9 5 6 2 4 5 2 2 d e f 6 3 2 5 4 3 2 6 7 4 5 4 Subtract using the written method. Estimate the answer first: a e: b e: c e: 6 8 9 8 6 2 8 7 3 5 9 Skills Not yet Kind of Got it Uses written methods to subtract 2 digit numbers including regrouping 60 Series D Topic 3 Assessment
Written methods Name Add these using the written method: a b c 4 4 + 2 5 6 9 3 0 + 4 9 7 9 7 2 + 3 2 0 4 d e f 8 4 + 3 5 5 4 + 5 9 3 + 4 9 6 9 9 7 2 Add these using the written method. Estimate the answer first: Estimates may vary. a e: 80 b e: 70 c e: 40 6 3 + 8 8 3 8 + 2 8 6 6 7 9 + 5 9 3 8 Skills Not yet Kind of Got it Uses written methods to add 2 digit numbers including regrouping Series D Topic 3 Assessment 6
Written methods Name 3 Subtract these using the written method: a b c 8 4 3 2 5 2 9 5 6 2 3 3 4 5 2 2 2 3 d e f 6 3 2 5 5 4 3 2 2 2 6 7 4 5 2 2 4 Subtract using the written method. Estimate the answer first: Estimates may vary. a e: 50 b e: 60 c e: 0 5 7 6 6 8 8 6 7 3 9 4 9 2 8 5 8 5 9 4 Skills Not yet Kind of Got it Uses written methods to subtract 2 digit numbers including regrouping 62 Series D Topic 3 Assessment
Money Name Circle the coins you would need to make each amount. How much is left over each time? a Make $2: Amount left over b Make $0: Amount left over 2 Bridge to the next dollar on these number lines to find the change: a $5.60 $0.00 Change is: b $6.75 $20.00 Change is: Skills Not yet Kind of Got it Represents money values in multiple ways using coins and notes or just coins Calculates the change from whole dollar amounts Series D Topic 4 Assessment 63
Money Name Circle the coins you would need to make each amount. How much is left over each time? a Make $2: Amount left over 70 b Make $0: Amount left over $ 2 Bridge to the next dollar on these number lines to find the change: +40 +$4 a $5.60 $6 $0.00 Change is: $4.40 +25 +$3 b $6.75 $7 $20.00 Change is: $3.25 Skills Not yet Kind of Got it Represents money values in multiple ways using coins and notes or just coins Calculates the change from whole dollar amounts 64 Series D Topic 4 Assessment
Series D Region NSW VIC QLD SA WA NT ACT Outcomes NS2.2 uses mental and written strategies for addition and subtraction involving two-, three- and fourdigit numbers VELS Level 3 Measurement devise and use written methods for whole number problems of addition and subtraction involving numbers up to 999 devise and use algorithms for the addition and subtraction of numbers to two decimal places, including situations involving money N 3.2 students identify and solve addition and subtraction problems involving whole numbers and decimal fractions in context, selecting from a range of computation methods, strategies and known number facts 2.8 uses a variety of estimating and calculating strategies, including memorising addition and subtraction facts with whole numbers, and with money represented as decimals Students use mental, written and calculator strategies including: ways to use basic facts to assist with standard and non-standard partitioning to calculate mentally addition and subtraction of whole numbers addition and subtraction of two digit numbers, through the use of partitioning (e.g. 69 + 54 = 60 + 9 + 50 + 4) strategies for solving addition and subtraction of money and measurements to two decimal places (e.g. mental, written and calculator) strategies for solving addition and subtraction of fractions with the same denominator (e.g. visualising, using pattern blocks, drawing, counting forward and back in fractions) N 2.2 Calculating recall basic addition and subtraction facts to 20 use mental strategies to calculate multiplication facts to 0 0 use a range of mental strategies to add and subtract numbers up to two-digits add and subtract whole numbers to thousands and decimals with money add and subtract simple fractions expressed in words use informal written strategies for multiplying and dividing a two- and three-digit by a one-digit number use the relationship between multiplication and division to solve simple problems estimate both sums and products by rounding to a single digit or multiples of ten 6.LC.8 computation using mental, written and electronic methods, and forming estimates to check the reasonableness of answers 6.LC.6 recall addition and subtraction facts, recall or use suitable strategies to work out multiplication and related division facts and apply facts to calculate mentally with larger numbers Series D Outcomes 65
Series D Region TAS Outcomes Stage 6 add and subtract two-digit numbers using mental and informal written methods e.g. To add 7 and 25, I split the 0 from the 7 and the 20 from the 5 and I added 20 + 0 and then 5 + 7 is 2 so it s 42 Stage 8 calculate mentally or by written methods total and change for purchase of multiple objects < $0 ACARA M3NA4 Model, represent and solve problems involving additive situations using efficient mental and written strategies and calculators 66 Series D Outcomes