# SUBTRACTION by qingyunliuliu

VIEWS: 39 PAGES: 23

• pg 1
```									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
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: 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

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

 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
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

 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

```
To top