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    Publisher JAYS' EDUCATION704 Old Cleveland Rd EastWellington Point Queensland 4160phone 07 3822 [email protected]

    FRACTIONSSELFCHECKINGMATHSPROGRAMADDSUBTRACT

    Author Hana Jay

    Illustrations Dana Sundgren,

    Cover design Dana Sundgren

    Computer compilation Tom Jay

    Graphics Tom Jay

    1stelectronic edition (November 2009)

    Jays Education

    ISBN 978-1-921622-13-7

    Reproduction and communication for educational purposesThe Copyright Act 1968allows a maximum one chapter or 10% of the pages of this work,whichever is the greater, to be reproduced etc. by an educational institution for its ownpurposes provided that the institution has given a notice to CAL Australia (in othercountries to the national Copyright Agency).

    However the publisher is here with granting the right to reproduce 100% of this book tothe original purchaserfor classroom or personal use. Commercial use is prohibited.

    Electronic copying, storage or transmission is permitted only for the use of the originalpurchaser. The pdf file must be left intact and in the original format and content.

    Jays' Education is reserved and must be kept displayed on each sheet copied.

    CAL Copyright Agency LimitedLevel 15233 Castlereagh StreetSydney 2000Phone 02 9394 7600 Fax 02 9394 [email protected]

    Reproduction and communication for other purposes

    Except as permitted by the Copyright Act 1968 (for example a fair dealing for the purposesof study, research, criticism or review) no part of this book may be reproduced, stored in aretrieval system, communicated or transmitted in any form or by any means without priorwritten permission. Direct all inquiries to the publisher, see address at the top of this page.

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    Self Checking Fractions Jays Education

    Using the LUK Self Checking Program

    Open the LUK box* and see that the lid is divided into 24 blank squares. The base is

    divided into 24 numbered squares. Each numbered square has a large number in the

    middle and a smaller number in each corner. The numbers are consecutive.

    The large numbers are suitable for simple computations, the smaller numbers require

    finer visual skills.

    How to use the LUK box

    Step 1.

    Place the 24 tiles in sequence from 1 to 24 into the blank squares on the lid of the

    LUK box.

    Step 2.Choose your page (worksheet).

    Step 3.

    Pick up tile number 1 and place it under the number 1 question. Work out the

    problem and find the answer to that question in the Answer Box. Next to the answer

    is a code number (in the corner).

    Find that number on the base

    of the LUK box and place the tileonto that number.

    If the answer is and the number is 7,

    place tile number 1 on 7.

    Pick up tile number 2 and place it under

    the number 2 question. Work out the problem,

    find the answer and the code number and place the tile number 2 on that number in

    the LUK box.

    Repeat the same procedure until all numbered squares are covered by the tiles.

    1 - 24

    25 - 48

    49 - 72

    73 - 96

    97 - 120

    are the large numbers in the middleare the small numbers in the left hand top corner

    are the small numbers in the right hand top corner

    are the small numbers in the left hand bottom corner

    are the small numbers in the right hand bottom corner

    34

    7eg:

    1 2 3 4 5 6

    8 9 10 11 12

    13 14 15 16 17 18

    19 20 21 22 23 24

    1 2 3 4 5 6

    8 9 10 11 12

    13 14 15 17 18

    19 20 21 22 23 24

    II

    * . 07 3822 1813 (+61 738221813).

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    IIISelf Checking Fractions Jays Education

    Step 4.

    The tiles are in place, the task is accomplished. Close the lid and turn the LUK box over

    sideways. Open the lid and a pattern will appear.

    Step 5

    Match the pattern in the box with the pattern on the bottom of the page. If the

    patterns match, well done! You have not made a single mistake! If the pattern is not

    quite correct, but is recognisable, you have still done a good job. If no pattern is visible,

    there is more work to be done on this particular task. You may need help from your

    teacher or parent.

    There are 3 ways how to use the LUK Self Checking Program

    Use the LUK box as you go. Work out the problems one by one. Look for the

    answers in the answer box, find the code number (next to the answer) and place

    the tile in the LUK box as described in step 3. You dont need to write the

    answers, just place the tiles in the LUK box.

    Work out the problems, write down the answers and thencheck each answer in

    the Answer Box. Look for and use LUK code numbers (next to the answers) to

    place the tiles one by one onto the code numbers in the LUK Box.

    The teacher has the LUK box and the student has the tiles. Tiles are sorted into 3

    or 4 consecutive piles. The student takes the tile number 1 , works out the

    problem and finds the answer and the code number, hands the tile to the teacher,

    calling out the code number. The teacher places the tile into the LUK box. The

    procedure is repeated until all tiles are placed in the LUK box.

    The LUK Self Checking Program is multipurpose.

    A student can work by himself, check his answers and self correct the mistakes.

    The student will experience satisfaction from work well done when viewing the

    completed LUK pattern.

    The student will be motivated to progress to the next page.

    Working on the tasks, page by page, the student will acquire all the necessary

    strategies and skills to add and subtract fractions.

    While learning to work with fractions the student will further develop his visual,

    spatial and sequencing skills. He will gain confidence and self satisfaction.

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    IVSelf Checking Fractions Jays Education

    Contents and Procedures

    Page

    1, 2, 3, 4

    5, 6

    7, 8

    9, 10, 11, 12

    13, 14, 15

    Procedures

    Name the fraction shaded.

    Write the correct fraction to each pattern.Find the fraction matching the pattern in the answer box.

    Which shaded pattern matches the fraction?

    Look for the code number next to the patternand place the tile on that number in the LUK box.

    Addition of two fractions with the same denominator (bottomnumber).

    Add the two numerators (top numbers) and copy the denominator.Write the answer.

    Find the matching fraction and the code number.

    Addition of a whole number and a fraction.

    Copy the whole number and then copy the fraction, regardlesswhether the whole number is in front of the fraction or behind it.

    The answer is a mixed number (whole number and a fraction).

    Addition of a whole number and a mixed number (whole numberand a fraction).

    Add the two whole numbers and copy the fraction.

    The answer is a mixed number.

    58

    +28

    =78

    +34

    6

    = 346

    2+

    3

    5

    =

    2

    3

    5

    5463 +

    46

    =2 5

    4

    72+

    4

    7=

    3

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    VSelf Checking Fractions Jays Education

    Page

    16, 17, 18,

    19, 20

    21, 22,

    23, 24

    25, 26

    27, 28

    Procedures

    Addition of a mixed number and a fraction.

    Copy the whole number.Add the two fractions (same denominators) and write the new

    fraction after the whole number.

    The answer is a mixed number.

    Addition of two mixed numbers (same denominators).

    Add the two whole numbers and add the two fractions.

    The whole number comes first and then the fraction.

    The answer is a mixed number.

    Subtraction of two fractions with the same denominators.

    Take (subtract) the second fraction from the first fraction.Subtract the numerator and copy the denominator.

    The answer is a fraction.

    Subtract a fraction from a mixed number (same denominators).

    Copy the whole number andthen take the second fraction from the first fraction(subtract the numerator and copy the denominator).

    The answer is a mixed number.

    317

    +37

    = 5472

    5610

    +310

    = 59

    10

    18

    + 418

    =428

    59

    39

    =29

    645

    25

    = 625

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    5

    2 3

    5 6

    8 11

    112

    713

    10 19

    17 21

    420

    15 22

    18 23

    9 14

    1624

    1

    2

    46

    24 23

    28

    22

    23

    21

    410

    20

    8

    68

    9

    34

    10

    39

    11

    38

    12

    710

    13

    57

    3

    13

    4

    14

    5

    6

    310

    7

    25

    19

    35

    18

    36

    17

    24

    16

    26

    15

    45

    14

    27

    78

    610

    47

    18

    STARTSTARTSTARTSTART FINISHFINISHFINISHFINISH

    ANSWERS

    Self Checking Fractions Jays Education

    The number next to the pattern is the code number needed to placed the tiles into the LUK box .

    Find and cross the patterns matching the fractions.

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    + =24

    14

    + =26

    16

    + =12

    12

    + =16

    16

    + =2313

    + =2737

    + =13

    13

    + =17

    17

    + =14

    14 + =

    37

    37

    + =15

    25 + =27 27

    + =35

    15

    + =27

    17

    + =15

    15

    + =47

    37

    + =2

    5

    3

    5

    + =2

    8

    3

    8

    + =56

    16

    + =38

    38

    + =36

    26

    + =28

    28

    + =36

    16

    + =48

    48

    9 10 11 12

    58

    88

    25

    36

    27

    45

    46

    1 2 3 4 5 6 7 8

    13 14 15 16

    17 18 19 20 21 22 23 24

    56

    67

    37

    24

    66

    57

    47

    77

    48

    26

    68

    55

    33

    34

    23

    22

    35

    Check and cross the answers.The number in the corner is the code number to look for to place the tile on into the LUK box.

    7

    Self Checking Fractions Jays Education

    34

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    15

    =25

    + 12

    9 10 11 12

    27

    18

    46

    36

    13

    19

    37

    1 2 3 4 5 6 7 8

    13 14 15 16

    17 18 19 20 21 22 23 24

    47

    28

    14

    49

    47

    48

    59

    39

    29

    67

    38

    34

    16

    56

    26

    25

    174

    6

    5

    5

    7

    5

    2

    6

    4

    5

    6

    5

    4

    6

    6

    4

    7

    6

    3

    7

    5

    6

    6

    8

    13

    21

    20

    19

    23

    22

    24

    15

    14

    17

    16

    18

    9

    8

    7

    11

    10

    12

    3

    2

    1

    5

    4

    6

    Self Checking Fractions Jays Education

    =34+ 11

    =26+ 13

    =17

    + 24

    =13

    + 22

    =1

    6+

    23=

    27

    + 14

    =28

    + 33

    =56

    + 31

    =47

    + 32

    =14

    + 24

    =18

    + 23

    =19

    + 33

    =49

    + 23

    =46+ 15

    =37

    + 24

    =48

    + 33

    =3

    6+

    25

    =59

    + 34

    =67

    + 22

    =3

    9

    + 16

    =47+ 35

    =38

    + 14

    =29

    + 33

    253

    Check and cross the answers.The number in the corner is the code number to look for to place the tile on into the LUK box.

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    13

    21

    20

    19

    23

    22

    24

    15

    14

    17

    16

    18

    9

    8

    7

    11

    10

    12

    3

    2

    1

    5

    4

    6

    =25

    25

    +1

    9 10 11 12

    68

    24

    59

    710

    47

    23

    34

    1 2 3 4 5 6 7 8

    13 14 15 16

    17 18 19 20 21 22 23 24

    610

    79

    79

    45

    57

    37

    48

    810

    56

    38

    910

    78

    35

    46

    410

    36

    255

    1

    2

    5

    2

    3

    3

    2

    3

    4

    1

    5

    2

    4

    1

    3

    5

    2

    3

    4

    1

    4

    4

    1

    17

    =39

    29

    +1

    =

    24

    14+

    1

    =37

    27

    +1

    =49

    39

    +1

    =4

    10

    3

    10+

    2

    =36

    16

    +2

    =48

    28

    +2

    =1

    3

    1

    3+2

    =59

    29

    +2

    =14

    14

    +3

    =2

    10

    2

    10

    +3

    =58

    28

    +3

    =17

    37

    +3

    =

    16

    26+

    3

    =15

    25

    +4

    =3

    105

    10+4

    =1

    5

    1

    5+

    4

    =26

    36

    +4

    =27

    17

    +4

    =2

    8

    1

    8+5

    =3

    103

    10+5

    =28

    28

    +5

    =6

    10

    3

    10

    +5

    451

    Check and cross the answers.The number in the corner is the code number to look for to place the tile on into the LUK box.

    Self Checking Fractions Jays Education

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    21

    9 10 11 12

    68

    39

    26

    34

    58

    69

    37

    1 2 3 4 5 6 7 8

    13 14 15 16

    17 18 19 20 21 22 23 24

    46

    24

    28

    57

    35

    47

    410

    67

    23

    48

    79

    56

    36

    38

    510

    27

    255

    4

    2

    4

    4

    5

    3

    3

    2

    4

    4

    2

    5

    3

    3

    4

    3

    4

    5

    3

    3

    4

    4

    4

    13

    21

    20

    19

    23

    22

    24

    15

    14

    17

    16

    18

    9

    8

    7

    11

    10

    12

    3

    2

    1

    5

    4

    6

    =36

    +1 2 26

    =47

    +2 1 27

    =15 +2 2 15

    =26

    +3 1 16

    =14

    +2 1 14

    =1

    3 +

    2 21

    3

    =28

    +1 1 38

    =38

    +1 1 38

    =37

    +2 1 27

    =1

    7

    +3 2 1

    7

    =18

    +2 2 18

    =29

    +3 2 19

    =26

    +1 1 26

    =28

    +3 2 18

    =49 +2 1 29

    =25

    +3 1 15

    =16

    +2 2 16

    =1

    7 +

    2 22

    7

    =14

    +3 1 24

    =37

    +1 2 17

    =1

    8

    +3 2 38

    =4

    10+2 2 110

    =3

    10+2 1 110

    =49

    +3 1 39

    563

    Self Checking Fractions Jays Education

    Check and cross the answers.The number in the corner is the code number to look for to place the tile on into the LUK box.

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    13

    21

    20

    19

    23

    22

    24

    15

    14

    17

    16

    18

    9

    8

    7

    11

    10

    12

    3

    2

    1

    5

    4

    6

    9 10 11 12

    27

    58

    39

    37

    38

    57

    46

    1 2 3 4 5 6 7 8

    13 14 15 16

    17 18 19 20 21 22 23 24

    34

    29

    69

    45

    67

    48

    28

    24

    47

    56

    39

    25

    45

    26

    67

    23

    363

    6

    4

    4

    4

    6

    6

    2

    7

    4

    2

    4

    5

    4

    6

    4

    5

    2

    8

    5

    3

    5

    6

    5

    23

    Self Checking Fractions Jays Education

    =35

    +2 1 15

    =14

    +3 2 14

    =26 +

    1 126

    =25

    +3 1 25

    =16

    +2 1 46

    =1

    7+

    4 2

    3

    7

    =28

    +4 3 18

    =17

    +2 2 17

    =1

    3

    +4 4 1

    3

    =49

    +1 1 29

    =18

    +2 3 18

    =14

    +3 1 24

    =15

    +4 2 15

    =16

    +3 2 16

    =27 +

    1 137

    =37

    +4 1 37

    =29

    +4 2 19

    =1

    6+

    2 3

    2

    6

    =27

    +1 3 17

    =28

    +3 1 28

    =1

    9

    +4 2 1

    9

    =37

    +2 2 37

    =28

    +4 2 38

    =29

    +3 1 39

    453

    Check and cross the answers.The number in the corner is the code number to look for to place the tile on into the LUK box.

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    24

    9 10 11 12

    45

    39

    26

    34

    58

    69

    37

    1 2 3 4 5 6 7 8

    13 14 15 16

    17 18 19 20 21 22 23 24

    46

    24

    28

    57

    35

    47

    410

    67

    23

    48

    79

    56

    36

    38

    510

    27

    255

    4

    3

    4

    4

    5

    3

    3

    2

    4

    4

    2

    5

    3

    3

    4

    3

    4

    5

    3

    3

    4

    4

    4

    13

    21

    20

    19

    23

    22

    24

    15

    14

    17

    16

    18

    9

    8

    7

    11

    10

    12

    3

    2

    1

    5

    4

    6

    =36

    +1 226

    =47 +2 1

    27

    =15 +2 2 15

    =26

    +3 1 16

    =14

    +2 114

    =13 +

    2 21

    3

    =28

    +1 1 38

    =25 +1 2

    25

    =37

    +2 1 27

    =1

    7

    +3 2 17

    =18 +2 2

    18

    =29

    +3 2 19

    =26

    +1 1 26

    =28

    +3 218

    =49 +2 1 29

    =25

    +3 1 15

    =16

    +2 2 16

    =1

    7 +

    2 22

    7

    =14

    +3 1 24

    =37

    +1 2 17

    =1

    8

    +3 2 38

    =4

    10+2 2 110

    =3

    10+2 1 110

    =49

    +3 1 39

    563

    Self Checking Fractions Jays Education

    Check and cross the answers.The number in the corner is the code number to look for to place the tile on into the LUK box.

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    28

    9 10 11 12

    610

    68

    27

    48

    410

    49

    46

    1 2 3 4 5 6 7 8

    13 14 15 16

    17 18 19 20 21 22 23 24

    15

    79

    59

    35

    37

    28

    38

    510

    810

    2

    5

    3

    8

    6

    9

    3

    6

    2

    6

    4

    7

    3

    9

    7

    106

    3

    3

    5

    2

    4

    5

    2

    2

    4

    3

    4

    5

    7

    3

    5

    6

    4

    6

    7

    2

    5

    6

    2

    Self Checking Fractions Jays Education

    =45

    152

    352

    =69

    292

    =78

    382

    =67

    372

    =7

    103

    102

    =

    56

    163

    =89

    193

    =8

    102

    103

    =5

    7

    3

    73

    =35

    254

    =78

    184

    =89

    394

    =56

    264

    =9

    102

    105

    =57175

    =89

    295

    =68

    385

    =

    46

    265

    =45

    256

    =68

    386

    =9

    10

    1

    10

    6

    =59

    296

    =48

    287

    =8

    103

    107

    Check and cross the answers.The number in the corner is the code number to look for to place the tile on into the LUK box.

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    13

    21

    20

    19

    23

    22

    24

    15

    14

    17

    16

    18

    9

    8

    7

    11

    10

    12

    3

    2

    1

    5

    4

    6

    9 10 11 12

    58

    310

    39

    37

    49

    410

    29

    1 2 3 4 5 6 7 8

    13 14 15 16

    17 18 19 20 21 22 23 24

    59

    610

    28

    36

    47

    68

    48

    27

    26

    3

    8

    1

    4

    2

    6

    6

    9

    1

    3

    2

    5

    7

    10

    1

    54

    5

    3

    5

    4

    1

    4

    3

    2

    2

    2

    2

    3

    5

    4

    3

    1

    5

    6

    3

    5

    6

    6

    3

    29

    Self Checking Fractions Jays Education

    =56

    6 261365

    =7

    104 3101

    =67 5 371

    =89

    3 291

    =23

    4 131

    =35 7

    251

    =9

    105 3101

    =78

    4 281

    =5

    9

    62

    91

    =45

    4 251

    =78

    2 381

    =3

    4

    6

    2

    41

    =46

    5 261

    =9

    107 2101

    =69 3 291

    =67

    4 271

    =68

    5 381

    =79 3291

    =48

    6 281

    =78

    5 181

    =5

    7

    43

    71

    =49

    3 291

    =6

    102 3101

    =4

    6

    7

    2

    61

    Check and cross the answers.The number in the corner is the code number to look for to place the tile on into the LUK box.

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    30Self Checking Fractions Jays Education

    =67

    4 372372

    =35

    5 152

    =48

    6 382

    =9

    103 1102

    =34

    6 142

    =46 5

    362

    =89

    4 392

    =45

    6 152

    =5

    9

    3 3

    92

    =47

    5 372

    =78

    4 382

    =7

    105 3102

    =79

    6 192

    =56

    7 362

    =574 172

    =58

    6 382

    =68

    7 382

    =8

    10 53

    102

    =56

    4 162

    =67

    5 172

    =6

    9

    7 3

    9

    2

    =6

    103 3102

    =48

    6 182

    =9

    107 3102

    9 10 11 12

    59

    410

    69

    28

    35

    47

    510

    1 2 3 4 5 6 7 8

    13 14 15 16

    17 18 19 20 21 22 23 24

    48

    24

    17

    26

    310

    16

    25

    810

    37

    18

    2

    938

    46

    5

    738

    39

    6

    104

    4

    2

    1

    4

    3

    5

    2

    4

    2

    3

    2

    3

    3

    4

    4

    3

    3

    5

    1

    5

    5

    2

    1

    Check and cross the answers.The number in the corner is the code number to look for to place the tile on into the LUK box.

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    31

    9 10 11 12

    58

    78

    38

    37

    45

    35

    57

    1 2 3 4 5 6 7 8

    13 14 15 16

    17 18 19 20 21 22 23 24

    46

    810

    25

    89

    610

    310

    39

    36

    16

    510

    25

    79

    48

    67

    49

    710

    274

    3

    3

    4

    1

    8

    3

    6

    7

    2

    8

    6

    3

    4

    4

    7

    4

    9

    4

    3

    6

    2

    4

    6

    =47

    +2 1 27

    =25

    +4 215

    =410 +3 3 210

    =29

    +4 329

    =38

    +2 1 28

    =27 +

    6 23

    7

    =5

    10 +3 13

    10

    =25

    +4 325

    =68

    5 2 38

    =6

    9 +

    3 3

    2

    9

    =58

    +5 3 28

    =36

    +4 2 16

    =1

    5

    +6 3 1

    5

    =9

    107 3

    210

    =89 4 1 19

    =57

    4 3 27

    =8

    106 2

    310

    =68

    5 328

    =45

    7 3 25

    =56

    4 1 26

    =6

    10

    6 2

    3

    10

    =57

    4 2 37

    =46

    5 1 36

    =6

    9

    7 3 3

    9

    673

    Self Checking Fractions Jays Education

    Check and cross the answers.The number in the corner is the code number to look for to place the tile on into the LUK box.

    13

    21

    20

    19

    23

    22

    24

    15

    14

    17

    16

    18

    9

    8

    7

    11

    10

    12

    3

    2

    1

    5

    4

    6

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    32

    9 10 11 12

    35

    89

    25

    47

    78

    13

    23

    1 2 3 4 5 6 7 8

    13 14 15 16

    17 18 19 20 21 22 23 24

    79

    24

    67

    35

    12

    610

    48

    58

    59

    69

    36

    26

    38

    810

    37

    310

    14

    4

    4

    4

    3

    2

    3

    5

    6

    7

    2

    3

    3

    1

    3

    2

    4

    4

    2

    6

    Self Checking Fractions Jays Education

    =13

    +5 2 13 =46

    6 2 16

    =78

    284

    =

    27 + 3

    27

    =25

    + 13

    =13

    +5

    2

    +

    + =48

    38

    =35 4

    =14

    143 +

    =2

    5+

    1 3

    1

    5

    =69

    292 +

    =47

    + 3 27

    + =5

    9

    2

    9

    =910 3103 =12 +4

    =8

    105 3

    =

    58 3 2 18

    =6

    103

    102

    =5

    6

    4 13

    6

    =5

    8

    2

    86

    =59

    4 2

    =34

    24

    =67

    37

    =89

    29

    Check and cross the answers.The number in the corner is the code number to look for to place the tile on into the LUK box.

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    33Self Checking Fractions Jays Education

    Page Pattern Date Page Pattern

    1 12

    2 13

    3 14

    4 15

    5 16

    6 17

    7 18

    8 19

    9 20

    10 21

    11 22

    Comments:

    Date Page

    23

    24

    25

    26

    27

    28

    29

    30

    31

    32

    Pattern Date

    Progress Chart Students name: ....................................................................

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    .

    ,

    .

    .

    ,

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    , .

    50

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    ,

    .

    Dana Sundgren

    VIISelf Checking Fractions Jays Education

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    www.jayseducation.comDownloads and CDs . V i s i t us to in spect the books .

    J a y s J a y s J a y s J a y s EducationEducationEducationEducation

    Numeracy (no LUK)

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    What Time Is It?

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    Fractions 2Fractions 3

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    Still More Pencil Skills

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    Learn to Draw in Few Steps

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