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T 0845 630 33 33 F 0845 630 77 77 www.pearsonschools.co.uk [email protected] ALWAYS LEARNING Part of the Abacus toolkit, the textbooks and workbooks provide: • the perfect balance of practice and problem solving for each area of maths • pictorial representations to support children’s conceptual understanding • clearly laid out questions with instructions that are easy to follow • a self-assessment opportunity on every page • colour to indicate the different maths areas within the programme. Abacus is a unique maths toolkit for inspiring a love of maths and ensuring progression for every child. Written by an expert author team for the 2014 curriculum for England, it has been carefully crafted on a robust approach to creating inspired and confident young mathematicians. Freedom when you want it, structure where you choose it. Series Editor: Ruth Merttens Authors: Jennie Kerwin and Hilda Merttens Textbook and workbook sample pages

Abacus Textbook and Workbook Sample Booklet

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  • T 0845 630 33 33F 0845 630 77 77

    [email protected]

    A LWAY S L E A R N I NG

    Part of the Abacus toolkit, the textbooks and workbooks provide:theperfectbalanceofpracticeandproblemsolvingforeachareaofmaths

    pictorialrepresentationstosupportchildrensconceptualunderstanding

    clearlylaidoutquestionswithinstructionsthatareeasytofollow

    aself-assessmentopportunityoneverypage

    colourtoindicatethedifferentmathsareaswithintheprogramme.

    Abacus is a unique maths toolkit for inspiring a love of maths and ensuring progression for every child. Written by an expert author team for the 2014 curriculum for England, it has been carefully crafted on a robust approach to creating inspired and confident young mathematicians.

    Freedom when you want it, structure where you choose it.

    Series Editor: Ruth Merttens Authors: Jennie Kerwin and Hilda Merttens

    Textbook and workbook sample pages

  • 3

    Pick up a handful of counters. Estimate how many. < 10? 1020? >20? Now count them.

    Cross out each grape as you count it.

    Count the grapes in each bunch. How many are there?

    Counting grapesContents

    Key of page coloursNumber and Place value

    Shape and Measure

    Multiplication and Division

    Addition and Subtraction

    Fractions

    Mixed Operations

    Year 1 Workbook 1 pages:

    Counting grapes p3

    Adding 2; 1 more p1213

    Straight or curved; Monster sort p1819

    Write numbers to 20; Ordering numbers to 20 p2021

    Addition facts; Bonds to 20 p1011

    Counting in 10s; More and less p2829

    Counting in 2s, 5s and 10s; 2s, 5s and 10s p6061

    Year 3 Textbook 1 pages:

    Multiplying and dividing by 3, 4, 5 and 10 p2223

    Subtract by counting up p4647

    Finding fractions of shapes and amounts p5455

    Puzzles p9495

    Year 4 Textbook 1 pages:

    Metres, centimetres and millimetres p4041

    Column addition of 3-digit numbers p4243

    Unit fractions and equivalence p5455

    Rounding 4-digit numbers p7475

    Year 5 Textbook 1 pages:

    Two decimal places p2224

    Length and perimeter p3335

    Mental multiplication strategies p2829

    Year 2 Workbook 1 pages:

    Finding missing numbers; Comparing 2-digit numbers p45

    Comparing fractions and fi nding equivalents p5253

  • 12

    Adding 2

    Write your own additions adding 2. Make them different from the ones on this page.

    Use a number track to help you.

    Write the next two numbers on the tracks. Complete all the additions.

    13 14 15

    25 26 27

    17 18 19

    20 21 22

    14 15 16

    23 24 25

    26 27 28

    15 + 2 =

    27 + 2 =

    19 + 2 =

    22 + 2 =

    16 + 2 =

    25 + 2 =

    28 + 2 =

    13

    Text... Text...

    1 more

    6 4

    10 14

    12 17

    15 20

    Write numbers where the next number ends in 0.

    Use a bead string to help you.

    Draw one more bead and write the next number.

  • Join each shape to its correct place in the hoops.

    18

    Straight or curved

    Make a collection of shapes with curved sides.

    Draw different shapes that have both straight and curved sides.

    straight sides curved sides

    Join each monster to its correct place in the hoops.

    19

    Monster sort

    Make a monster from circles, squares, triangles and rectangles. How many arms does your monster have? How many eyes does it have?

    Draw a monster which belongs in both hoops.

    two arms three eyes

  • Write the missing numbers on the track starting each digit at the dot given.

    20

    Write numbers to 20

    Use a number track to help you. Choose three numbers to write in words.

    1

    1112

    19

    2021

    Write the sets of three numbers in order.

    21

    Ordering numbers to 20

    Use a number track to help you. Choose three cards from a shuffled pack of 120 cards. Put them in order.

    6

    7

    9

    69

    7 1210

    11

    1411

    161315

    18

    1619

    1535

    4

    179

    211820

    15

  • 4

    Write the next ten numbers after 100 on the square.

    Use counters to cover numbers on the 100-square. Ask your partner to work out what the numbers are.

    Write in the missing numbers on the 100-square.

    Finding missing numbers

    1

    11

    21

    31

    41

    51

    61

    71

    81

    91

    2

    12

    32

    42

    52

    82

    92

    3

    43

    53

    63

    83

    93

    4

    14

    34

    44

    54

    64

    74

    84

    94

    5

    15

    25

    35

    45

    55

    65

    75

    85

    95

    6

    16

    26

    36

    66

    76

    86

    96

    7

    17

    27

    37

    67

    77

    8

    18

    28

    38

    68

    78

    88

    19

    29

    39

    49

    59

    69

    79

    89

    99

    10

    20

    30

    40

    50

    60

    70

    80

    90

    100

    5

    Comparing 2-digit numbers

    Your partner shows you a number on a bead string. Write a bigger number. Write the pair down.

    Work with a partner. Each secretly make a number on a bead string. Compare numbers. Which is bigger?

    Circle the biggest number in each pair.

    28 32

    18 15

    27 24

    75 71

    58 72

    43 55

    30 13

    26 62

    33 42

    81 18

  • 10

    Addition facts

    Can you make 10 with two even numbers? Two odd numbers? An odd number and an even number?

    Use your fingers to help you find the answers.

    Complete the additions. Add the numbers across and down to fill the grid.

    + 5 6 7 8 912345

    2 + = 10

    + 7 = 9

    + 6 = 7

    5 + = 10

    6 + = 8

    9 + 1 =

    + 3 = 10

    + 6 = 9

    5 + 4 =

    6 + 4 =

    3 + = 8

    + 5 = 6

    5 + 2 =

    7 + 1 =

    1 + = 9

    11

    Text... Text...

    Bonds to 20

    + = 20 +

    = 20 +

    = 20

    + = 20 +

    = 20 +

    = 20

    + = 20 +

    = 20 +

    = 20

    + = 20 +

    = 20 +

    = 20

    What do you add to: 1 to make 20?2 to make 20?Write the next five of these.

    Use interlocking cubes in two colours to help you.

    Complete the additions to match the cubes.

    11 9

  • Fill in the missing numbers on each snake.

    28

    Use the columns on a 100-square to help you.

    Draw your own snake with numbers missing for your partner to complete.

    Counting in 10s

    11121

    61718191

    41424

    44

    6474

    94

    6

    364656

    7686

    515

    5565

    95

    2737

    5767

    87

    1929

    49

    7989

    29

    Text... Text...Copy one of these crosses. Try to fill in the numbers that sit diagonally to the middle number. What is the pattern for diagonal numbers?

    Use a 100-square to help you.

    Write the numbers 10 more and 10 less and 1 more and 1 less.

    More and less

    26 72

    55

    83

    5814

    35

    41 19

    45

    54 56

    65

  • Fill in the missing numbers to continue the patterns.

    60

    Use a bead string or a 100-square to help you.

    Draw more trains starting at 0 and counting in steps of different numbers. Which numbers appear on more than one train?

    Counting in 2s, 5s and 10s

    32 34

    4035

    105

    20 30

    108

    40 50

    61

    Text... Text...Find a number that is in all three counts and show how to make it from 2s, 5s and 10s.

    Use coins to help find the answers.

    Continue to count on in 2p, 5p and 10p coins up to 10 times.

    2s, 5s and 10s

    p p p p p

    p p p p p

    p p p p p

    p p p p p

    p p p p p

    p p p p p

    2 4

    5 10

  • Complete these divisions.

    Solve these problems.

    Complete these multiplications.

    15 4 4 =

    16 8 4 =

    17 20 4 =

    18 28 4 =

    19 32 4 =

    20 48 4 =

    1 3 4 =

    2 5 4 =

    3 7 4 =

    4 2 4 =

    5 1 4 =

    6 10 4 =

    7 9 4 =

    8 4 4 =

    9 4 = 24

    10 4 = 12

    11 4 = 44

    12 4 = 48

    13 4 = 32

    14 4 = 36

    I am confi dent with multiplying and dividing by 4.I am confi dent with multiplying and dividing by 5 and 10. 2322

    A bead string

    7 5 = 35

    6 6 5 =

    7 10 = 60

    8 5 = 40

    9 10 = 40

    10 50 5 =

    11 80 10 =

    21 Cows have 4 legs. How many legs on 12 cows?

    22 There are 24 children. They get into groups of 4. How many groups?

    How many multiples of 4 under 50 are also multiples of 10?

    1

    2

    3

    4

    5

    6 10 =

    9 5 =

    7 10 =

    5 = 25

    10 = 90

    Multiplying and dividing by 3, , 5 and 10

  • Complete these subtractions.

    I am confi dent with subtracting by counting up.

    A number line

    Subtract by counting up

    I am confi dent with subtracting by counting up.

    46 47

    A bead string

    8 854 849 = 9 992 983 =

    Complete these subtractions.

    32 27 = 5

    27 320 40

    3 2

    1 23 16 =

    2 34 28 =

    3 31 26 =

    4 53 47 =

    5 42 35 =

    6 54 46 =

    23160 40

    ? ?

    0 40

    ? ?

    0 40

    0 6047 53

    ? ?

    0 60

    ? ?

    35 42

    0 60

    ? ?

    46 54

    48 34 = 14

    0 100

    6 8

    4834

    1 164 156 =

    2 223 215 =

    3 377 364 =

    4 486 478 =

    5 535 527 =

    6 649 636 =

    7 768 753 =

    100 200

    ? ?

    156 164

    200 300

    ? ?

    300 400

    ? ?

    400 500

    500 600

    600 700

    700 800

  • Finding fractions of shapes and amounts

    Write > or < between each pair of fractions.

    What fraction of each shape is shaded?

    I am confi dent with recognising fractions as equal parts of a whole.

    Can you write any of the fractions above using smaller numbers?

    Is this statement true or false? For unit fractions (those that have the numerator 1) the larger the denominator, the smaller the fraction.

    I am confi dent with recognising fractions as equal parts of a whole, and comparing fractions.54 55

    1 Which shape is divided into s?

    2 Which shape is divided into s?

    3 Which shape is divided into s?

    14

    16

    15

    Write the fraction that is shaded for each shape.

    2 6 10

    3 7 11

    2 8 11

    1 5 9

    13

    14

    15

    16

    17

    18

    16

    14

    13

    18

    13

    15

    16

    18

    16

    15

    13

    14

    a c e

    b d f

    5 8 11

    6 9 12

    4 7 10

  • Grid puzzles Cube puzzles

    1 Choose a pair of 2-digit numbers from the cube and fi nd their total and their difference.

    94 95

    You can use any method you think best. For example:

    Can you fi nd a pair of numbers from the cube that has:

    2 the total 100 and the difference 42?

    3 the total 110 and the difference 4?

    4 the total 93 and the difference 35?

    5 Choose three 2-digit numbers from the cube and fi nd the total.

    6 Can you fi nd three 2-digit numbers from the cube that have a total that is a multiple of 10?

    20 + 80 = 100 9 + 8 = 1 7 1 1 7

    29 + 88

    88 30 = 5858 + 1 = 59

    88 29

    29 and 88: total 117, difference 59

    Four numbers are written in a square. Four products can be found, multiplying across and diagonally.

    2 50, 40, 10 and 8?

    3 20, 12, 35 and 21?

    4 75, 85, 30 and 34?

    Can you fi nd four numbers that give these products:

    1 Choose four different numbers to write in a square. Find the products. Do this several times.

    5 6 7

    Find the four products for each of these.

    12 3

    10 4

    3 5

    9 4

    11 4

    7 3

    5 7

    4 8

    4 7 = 28

    5 7 = 35

    4 8 = 32

    5 8 = 40

  • Metres, centimetres and millimetres

    I am confi dent with estimating measurements in metres, centimetres and millimetres.

    Answer these length questions.

    1 Which of these animals could measure 123 cm in length?

    2 Which of these could measure 2 m 15 cm in length?

    3 Which of these could measure 50 mm in length?

    4 Which of these could measure 34 cm 2 mm in length?

    Make up several puzzles of your own like these.

    I am confi dent with converting between centimetres and millimetres.

    1 3 cm = mm

    2 cm = 40 mm

    3 6 cm 4 mm = mm

    4 9 cm 3 mm = mm

    5 cm mm = 39 mm

    6 72 cm = mm

    7 cm = 39 mm

    8 10 cm 4 mm = mm

    9 cm = 600 mm

    10 cm = 124 mm

    11 cm mm = 203 mm

    12 102 cm = mm

    Write these lengths in order, starting with the smallest.

    240 mm 23 cm 2 mm 25 cm 229 cm 30 mm

    40 41

    Copy and convert these lengths.

    13 194 cm = cm mm

    14 23 cm 2 mm = cm

    15 20 cm 6 mm = cm

    16 289 cm = cm mm

    17 16 cm 1 mm = cm

    18 253 cm = cm mm

    a b c

    a b c

    a b c

    a b c

    0 cm1

    23

    45

    0 mm

    1020

    3040

    50

    67

    8

    6070

    80

  • Use this method to do these additions.

    I am confi dent with adding 3-digit numbers using column addition.

    Column addition of 3-digit numbers

    Use this method to do these additions.

    1 273 + 54 =

    2 645 + 38 =

    3 772 + 83 =

    4 326 + 45 =

    5 482 + 264 =

    6 354 + 185 =

    7 634 + 238 =

    8 381 + 357 =

    I am confi dent with adding 2- and 3-digit numbers using the expanded method.

    Write an addition question that has an answer between 830 and 870.

    42 43

    482 + 64 =

    +400 80 2 60 4400 140 6 = 546

    327 + 254 =

    +300 20 7200 50 4500 70 1 1 = 581

    1 181 312 + 425

    2 217

    444 + 135

    3 363

    342 + 283

    4 282

    162 + 474

    5 554 162 + 245

    6 661

    128 + 165

    7 483

    312 + 412

    8 566

    303 + 625

    9 373 114 + 413

    10 817 336 + 327

    11 784

    552 + 527

    12 868 616 + 917

    1 2320845 1 1782

    +

    Answer these and explain what patterns you notice.

    123 + 987

    456 + 654

    789 + 321

    1 2320845 1

    +

  • 23

    >

    35

    13

    13

    13

    12

    12

    110

    110

    110

    110

    110

    110

    110

    110

    110

    110

    19

    19

    19

    19

    19

    19

    19

    19

    19

    18

    18

    18

    18

    18

    18

    18

    18

    17

    17

    17

    17

    17

    17

    17

    16

    16

    16

    16

    16

    16

    15

    15

    15

    15

    15

    14

    14

    14

    14

    111

    111

    111

    111

    111

    111

    111

    111

    111

    111

    111

    112

    112

    112

    112

    112

    112

    112

    112

    112

    112

    112

    112

    1 Whole

    I am confi dent with fi nding equivalent fractions and simplifying fractions.

    Copy these pairs of fractions and write > or < between them.

    I am confi dent with ordering unit and non-unit fractions and recognising fractions of a shape.54 55

    What fraction of each shape is shaded?

    Can you write any of the fractions above using smaller numbers?

    9 12 15

    10 13 16

    11 14 17

    Complete the equivalent fraction pairs.

    1 36 =

    1

    2 34 = 8

    3 15 = 10

    4 4 = 28

    5 26 =

    1

    6 4

    = 810

    7 46 = 3

    8 48 = 6

    Simplify these fractions.

    9 68 11

    410 13

    36 15

    28

    10 24 12

    26 14

    810 16

    610

    1

    2

    3

    4

    5

    6

    7

    8

    16

    110

    15

    110

    19

    112

    18

    25

    34

    27

    47

    78

    77

    58

    39

    112

  • I am confi dent with rounding 4-digit numbers.

    Round each number to the nearest 10, 100 and 1000.

    Write a number to match each description.

    Rounding 4-digit numbers

    I am confi dent with rounding 4-digit numbers.

    74 75

    A number lineRound these to the nearest 10.

    3 7450 74607455

    1

    2

    1230 1240

    1237

    2660 2670

    2668

    4 1287

    5 6844

    6 8304

    Round these to the nearest 100.

    7 1200 13001237

    8 4578 10 5885

    11

    Round these to the nearest 1000.

    1000 2000

    1237

    12 4578 14 1885

    Write a number which rounds to 5000 to the nearest 1000, 4500 to the nearest 100 and 4520 to the nearest 10.

    1 1287

    2 3623

    3 2535

    4 6729

    5 4572

    6 4302

    7 3608

    8 5937

    9 6851

    10 7777

    11 9440

    12 5781

    13 3514

    14 8535

    15 8448

    16 It rounds to 2570 to the nearest 10.

    17 It rounds to 8300 to the nearest 100.

    18 It is less than 3600 but rounds to 4000 when rounded to the nearest 1000.

    19 It rounds to 4000 to the nearest 1000 and to 3500 to the nearest 100.

    20 It rounds to 3500 to the nearest 100 and to 3000 to the nearest 1000.

    9 2845

    13 5145

  • Write the outputs for each input.

    I am confi dent with place-value multiplications and divisions involving decimals.

    Two decimal places

    I am confi dent with place value of decimals to two decimal places.

    1 The 2 in 4721.

    2 The 3 in 6387.

    3 The 1 in 791.

    4 The 6 in 2236.

    5 The 0 in 3705.

    6 The 8 in 38329.

    7 The 6 in 13761.

    8 The 9 in 24519.

    9 the tenths digit is two more than the tens digit.

    10 the hundredths digit is one less than the tenths digit.

    11 the tens digit is fi ve more than the hundredths digit.

    12 the hundreds digit is double the hundredths digit.

    13 the tenths digit is three times the tens digit.

    Write a number where:

    2322

    A place-value grid

    Write what the given digit represents in each number.

    100s 10s 1s 0.1s 0.01s

    3 7 0 5

    The 5 in 37.05. The 5 represents fi ve hundredths, or fi ve 0.01s or 0.05.

    .

    .

    A number less than 50 has a hundredths digit. The tenths digit and the ones digits have a total that is the same as the tens digit. If the number has no zero digits, what could it be? Find four different answers.

    1 25

    2 027

    3 047

    4 125

    5 003

    6 28

    7 71

    8 124

    9 8

    10 12

    11 140

    12 9

    13 101

    14 3206

    314 314

    10

    100

    10

    100

    10 then 10 again

  • I am confi dent with place-value multiplications and divisions involving decimals.

    Write the missing outputs or inputs.

    24

    1

    2

    3 2046

    4

    5

    6 72

    7

    8

    9 03

    10 126

    11

    12 007

    13 341

    14

    1357 1357

    32

    104

    44

    160

    066

    19

    140

    9036

    10

    100

    100

    10 then 100

    100 then 10

    Length and perimeter

    I am confi dent with measuring in centimetres and millimetres.

    Measure each creature and write the length in millimetres and then in centimetres. Use the red dots to help you.

    2

    3 4 5

    8

    33

    6 7

    1

  • Measure the perimeter of each rectangle in centimetres. Then write it in metres.

    I am confi dent with measuring and fi nding perimeters and converting centimetres into metres.34 35

    Calculate the perimeter of each photo and write it in centimetres and then in metres.

    Measure each creature and write the length in millimetres and then in centimetres.

    I am confi dent with measuring in centimetres and millimetres and converting between units.

    1

    2

    3

    4

    5

    Write each height in centimetres.

    6 1250 mm 7 1370 mm 8 1955 mm

    Write each length in millimetres.

    9 274 cm 10 75.5 cm 11 240 cm Draw a rectangle with a perimeter of 28 cm.

    4 7 10

    5 8 11

    6 9 12

    1250 mm 1370 mm 1955 mm

    274 cm 75.5 cm

    240 cm

    1 2 3

    8 cm

    5 cm

    8 cm

    5 cm

    12 cm

    6 cm

    6 cm

    12 cm

    37 cm

    21 cm

    37 cm

    21 cm

    12 cm

    20 cm20 cm

    12 cm 23 cm

    14 cm

    23 cm

    14 cm 31 cm

    25 cm

    31 cm

    25 cm

    15 cm

    8 cm

    15 cm

    8 cm

    30 cm

    16 cm

    16 cm

    30 cm42 cm

    21 cm

    42 cm

    21 cm

  • Multiply these numbers by 25.

    Multiply these numbers by 9.

    Multiply these numbers by 20.

    1 24

    2 35

    3 48

    4 72

    5 57

    6 86

    7 95

    8 76

    9 68

    I am confi dent with using mental strategies to multiply by 20, 25 and 9.

    Use mental strategies to answer these questions.

    I am confi dent with using mental strategies to multiply by 20, 25 and 9. 2928

    10 32

    11 16

    12 52

    13 62

    14 34

    15 56

    16 85

    17 72

    18 66

    19 38

    20 49

    21 56

    22 47

    23 66

    24 89

    25 35

    26 92

    27 71

    Would you prefer to use the grid method or the mental strategy you have been learning to multiply by 9? Explain why.

    It is easier to do these in two steps!

    1 69 9 =

    2 48 25 =

    3 39 20 =

    4 81 9 =

    5 38 25 =

    6 86 20 =

    7 74 9 =

    8 67 25 =

    9 77 20 =

    10 63 9 =

    11 91 25 =

    12 97 20 =

    13 72 9 =

    14 79 25 =

    15 89 20 =

    16 87 9 =

    17 69 = 1725

    18 71 = 639

    19 42 = 1050

    20 58 = 522

    Find the missing numbers.

    Write a method explaining to a Year 4 pupil how to multiply by 20 or 25. Explain why it works.

    These are easier than they look!

  • Write pairs of letters for the equivalent fractions.

    Copy and complete. Use the number lines to help you.

    I am confi dent with fi nding equivalent fractions and simplifying fractions.

    Use these number lines to write some pairs of equivalent fractions:

    I am confi dent with recognising equivalent fractions.

    Write the equivalent fractions shown in each pair of shapes.

    52 53

    Complete the equivalent fraction pairs.

    13

    =

    26

    1

    2

    3

    4

    5

    6

    7

    8 34

    = 8

    9 4 =

    28

    10 15

    = 10

    11 4

    =

    810

    12 48

    = 6

    13 46

    = 3

    0 112

    0 148

    58

    38

    18

    68

    28

    78

    0 124

    14

    34

    1 14

    = 8

    2 12

    = 4

    3 48

    = 4

    4 34

    = 8

    5 12

    = 8

    0 123

    13

    0 1612

    0 136

    56

    16

    26

    46

    6 13

    = 6

    7 36

    = 12

    8 16

    = 12

    9 23

    = 12

    10 46

    = 3

    11 56

    = 12

    A

    26

    B

    35

    C

    34

    D

    12

    E

    210

    F

    14

    G

    13

    H

    23

    I

    68

    J

    15

    K

    24

    L

    46

    M

    28

    N

    610

    0 112

    0 125

    15

    45

    35

    0 1410

    510

    310

    110

    610

    210

    710

    810

    910