SUBTRACTION by qingyunliuliu

VIEWS: 39 PAGES: 23

									ADDITION: A child working towards Level 1c or below
     The child needs to use real objects for calculations, not just pictures




Practical experiences / models and images:

     Two hoops with sets of objects – combine sets into one
     Introduce the vocabulary of addition in practical „real-life‟ addition problems, e.g. „How many
      biscuits are there altogether?‟ „How many more do we need?‟
     Wave 3 intervention:




     Use balances to work on equivalences (the = sign), e.g. making sets the same as each
      other
     Wave 3 intervention:




Mentally:

     Add 1 to numbers less than 10
     Wave 3 intervention:




Addition policy                      Page 1 of 23                               M. Knight   Sep 2008
Written recording:

     The practical experiences will transfer to pictorial recording where a child will begin to
      record combining sets and adding „one more than‟ in pictorial representation (e.g. using
      cars and a picture of a group of cars at the same time)




     Progress to using the pictures and introducing the symbols associated with addition and the
      symbol which means „is the same as‟




         3        +        2           =            5

     ITP: Counting




Addition policy                      Page 2 of 23                            M. Knight    Sep 2008
ADDITION: A child working towards Level 1b / 1a
     The child may still need to use real objects for calculations
     Use numbers up to 30


Practical experiences / models and images:

     ITP: Counting




     Lines of cubes next to a marked number line will help the child to move from objects to a
      more abstract understanding
     Empty box problems (e.g. 2 +  = 5) should initially be introduced by using cubes and an
      actual box to hide one set
     Wave 3 intervention:




Mentally:


     Count on and back in 1s from any number less than 30
     Wave 3 intervention:




     Count on and back in 10s from numbers up to 100
     Know by heart complements to 10




Addition policy                      Page 3 of 23                           M. Knight   Sep 2008
     ITP: Timed number bonds




     Add one or ten to numbers up to 30




Written recording:


     Record calculations using diagrams:




     Begin to use numbers and symbols
     Add two or three sets of numbers up to 10
     Draw jumps on a prepared number line – find the start number and then count on to work
      out more than
        8+5

                                                  +1 +1 +1 +1    +1



          0       1   2   3   4   5   6   7   8      9   10 11 12 13 14 15
     Wave 3 intervention:




Addition policy                       Page 4 of 23                       M. Knight   Sep 2008
ADDITION: A child working towards Level 2c/2b
     The child should be using numbers between 0 and 50 (level 2c) and then up to 100 (level
      2b)


Practical experiences / models and images:

     Use pictures and marks:
        There are 7 people on the bus. 8 more get on. How many people are on the bus?



     Lines of cubes next to a marked number line will help the child to move from objects to a
      more abstract understanding
     Bead strings or bead bars can be used to illustrate addition including bridging through ten
      by counting on 2 then counting on 3
        8 + 5 = 13



     Number tracks / lines
     ITP: Counting on and back




     ITP: Measuring cylinder




Addition policy                      Page 5 of 23                            M. Knight   Sep 2008
     ITP: Thermometer




     ITP: Beadsticks




     ITP: Place value charts and partitioning tool




     ITP: Place value dots




Mentally:


     „Instant‟ recall of complements to 20




Addition policy                     Page 6 of 23      M. Knight   Sep 2008
      ITP: + and – flash cards




      Wave 3 intervention:




      Complements to 100 (multiples of 10)
      Count on and back in 1s from numbers up to 50
      Count on and back in 10s from numbers up to 100
      Add 1 or 10 to numbers up to 50, using a number line
      ITP: Add/subtract 1, 10, 100, 1000 (Excel)




Written recording:


      Draw an empty number line and count on in tens and ones
        First counting on in tens and ones.
        34 + 23 = 57

                  +10                  +10

                                                     +1 +1 +1

34                        44                        54 55 56 57



Addition policy                      Page 7 of 23                 M. Knight   Sep 2008
      Progress to becoming more efficient by adding the units in one jump (by using the known
       fact 4 + 3 = 7).


        34 + 23 = 57
              +10                         +10
                                                              +3


34                            44                         54          57

      Progress to using larger jumps of multiples of 10 (level 2b)
        34 + 23 = 57

                              +20
                                                              +3


34                                                       54          57



      Bridging through ten can help children become more efficient.
        37 + 15 = 52

             +10
                                    +3        +2


37                            47         50     52

      Jottings, partitioning one or both numbers:
         23 + 12 = 23 + 10 + 2           or        23 + 12 = 20 + 3 + 10 + 2
                   = 33 + 2                               = 30 + 5
                   = 35                                   = 35
      Use pairs totaling 10:
        3 + 8 + 7 = 10 + 8
                    = 18
           10




Addition policy                          Page 8 of 23                          M. Knight   Sep 2008
ADDITION: A child working towards Level 2a
     The child should be using numbers up to 100


Practical experiences / models and images:

     Children will still need support through the use of marked number lines, bead bars, bead
      strings, etc. when new strategies and methods are being taught and practiced
     ITP: Counting on and back




     ITP: Measuring cylinder




     ITP: Thermometer




Addition policy                     Page 9 of 23                           M. Knight   Sep 2008
Mentally:


     „Instant recall‟ of addition facts for all numbers up to 20 and pairs of multiples of 10 up to
      100
     ITP: Number facts




     ITP: Function blocks




     ITP: 4 Numbers (Excel)




     Add pairs of multiples of 10 up to 100 (e.g. 60 + 30)




Addition policy                       Page 10 of 23                             M. Knight    Sep 2008
     ITP: Add/subtract 1, 10, 100, 1000 (Excel)




     TU + U or multiple of 10 (e.g. 36 + 3 and 36 + 40)
     ITP: Counting over boundaries




     ITP: Measuring scales




     ITP: Beadsticks




Addition policy                    Page 11 of 23           M. Knight   Sep 2008
      Begin to bridge through 10s numbers using known facts
        8 + 7:




Written recording (TU + TU / HTU + HTU):


      Continue to use empty number lines with increasingly large numbers, partitioning smaller
       number only:

        Count on from the largest number irrespective of the order of the calculation.


        38 + 86 = 124

                                +30
                                                                 +4          +4


86                                                       116          120         124

      Compensation:


     49 + 73 = 122
                                      +50



                                                                        -1

73                                                                    122 123




      Jottings, partitioning smaller number:
        42 + 27 = 42 + 20 + 7
                  = 62 + 7
                  = 69
      Use pairs totaling 10 or 20
        4 + 8 + 16 + 2 = 20 + 10

                         = 30
          10      20




Addition policy                       Page 12 of 23                             M. Knight   Sep 2008
ADDITION: A child working towards Level 3c/3b
     Begin to use numbers beyond 100


Practical experiences / models and images:

     Children will still need support through the use of marked number lines, bead bars, bead
      strings, etc. when new strategies and methods are being taught and practiced
     ITP: Counting on and back




     ITP: Number line




Mentally:


     Use rounding to estimate totals
     Wave 3 intervention:




     Count back in 1s, 10s and 100s from TU or HTU
     ITP: Add/subtract 1, 10, 100, 1000 (Excel)




Addition policy                    Page 13 of 23                           M. Knight   Sep 2008
     ITP: Beadsticks




     Instant recall of addition facts for each number to 20, multiples of 10 and complements to
      100
     ITP: Complements (Excel)




     ITP: Addition and subtraction facts (Excel)




        ITP: Total 20s




Addition policy                     Page 14 of 23                           M. Knight   Sep 2008
     ITP: Measuring cylinder




     ITP: Add and subtract pyramids




     TU + U, TU + TU
     ITP: Make numbers (Excel)




Addition policy                   Page 15 of 23   M. Knight   Sep 2008
Written recording:


     Develop jottings into a vertical method:
        47 + 76 = 47 + 70 + 6 = 117 + 6 = 123 or          47 + 76 = 40 + 70 + 7 + 6 = 110 + 13 = 123
                  
           47  40  7
          76   70  6
               110  13  123
     Wave 3 intervention:




     Wave 3 intervention:




     Wave 3 intervention:




     When children are confident with this method and have a good understanding of place
      value and partitioning, move to a more compact method:
            47
           76
           110         Begin by adding the most significant digits first (i.e. the tens digits)
            13
           123
     Progress to adding the least significant digits first, discussing how this gives the same
      answer:
            47
           76
            13
           110
           123
        The addition of the tens in the calculation 47 + 76 is described in the words „forty plus
        seventy equals one hundred and ten‟, stressing the link to the related fact „four plus seven
        equals eleven‟.


     This compact form of recording remains reasonably efficient and is one of the methods
      suggested in the guidance accompanying the Primary Framework.
     Wave 3 intervention:




Addition policy                        Page 16 of 23                                    M. Knight   Sep 2008
ADDITION: A child working towards Level 3a/4c
     Begin to use decimals, including money and decimals with up to two decimal places


Practical experiences / models and images:

     Children will still need support through the use of marked number lines, bead bars, bead
      strings, etc. when new strategies and methods are being taught and practiced




Mentally:


     Use addition facts up to 20 when using larger numbers
     ITP: Patterns of calculations (Excel)




     Wave 3 intervention:




     ITP: Addition of 1 digit and 2 digit numbers (Excel)




Addition policy                     Page 17 of 23                          M. Knight   Sep 2008
     ITP: Addition and subtraction number sentences (Excel)




     Use knowledge of place value and addition and subtraction of two digit numbers to derive
      sums and differences and doubles and halves of decimals
     Add strings of up to five numbers
     Decimal complements to 1
     Wave 3 intervention:




     ITP: Complements (Excel)




Addition policy                    Page 18 of 23                          M. Knight   Sep 2008
Written recording:


     Begin to develop vertical method to carrying below the line:
             47            258            366
            76            87           458
            123            345            824
            11             11             11

        When modeling this, make sure you use the value of the digits, e.g. in the first example: “7
        add 6 is 13 so I‟ll carry ten. 40 add 70 add the carried ten is 120 so I need to carry one
        hundred” – do not refer to it as carrying one.
     Extend this method to numbers with at least four digits
                  587                                 3587
             + 475                                +    675
                  1062                                4262
                  1 1                                 1 1 1


     Wave 3 intervention:




     Extend the method to more than two numbers and different numbers of digits:




     Wave 3 intervention:




     Introduce addition of decimals using an empty number line so that the place value of each
      digit is reinforced, then introduce vertical method with decimals
                  5.3
              + 2.1
                   7.4
     Wave 3 intervention:




Addition policy                      Page 19 of 23                            M. Knight    Sep 2008
     Wave 3 intervention:




     Wave 3 intervention:




     Wave 3 intervention:




Addition policy              Page 20 of 23   M. Knight   Sep 2008
    ADDITION: A child working towards Level 4b/4a
     Use decimals with 2 decimal places


Practical experiences / models and images:

     Children may still need support through the use of marked number lines, bead bars, bead
      strings, etc. when new strategies and methods are being taught and practiced


Mentally:


     Add larger strings of numbers
     Decimal complements to 10
     U.t + U.t
     ITP: Counting over boundaries




     ITP: Make numbers (Excel)




Addition policy                    Page 21 of 23                         M. Knight   Sep 2008
     ITP: Decimal addition and subtraction facts




     ITP: Place value charts and partitioning tool




     Add negative numbers
     ITP: Thermometer




Written recording:


     Children should be able to choose the most appropriate method from those that have been
      taught, e.g. mental methods, mental methods with jottings, empty number line, counting up




Addition policy                     Page 22 of 23                         M. Knight   Sep 2008
     Wave 3 intervention:




     Wave 3 intervention:




Addition policy              Page 23 of 23   M. Knight   Sep 2008

								
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