# pbs mathematics + - x . reception: addition practicalmental (jottings) in reception to help us...

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Progression in Calculations:A guide for parentsPBS MATHEMATICS

+-x?

Reception: AdditionPRACTICALMENTAL (Jottings)In Reception to help us with our addition we:Use small equipment to add, such asSkittlesLarge DominoesCountersFingersMultilinkNumber linesNumber FanNumiconCounting on in our headsCounting in 1s, 2s, and 10sOne moreSTANDARDINFORMAL (Workings Out)Number sentences using the + and = symbols and to represent a missing number:

Numbers to 10

2 + 3 =

Using bowls and small equipment

+ =

3 + 2 = 55

Reception: SubtractionPRACTICALMENTALIn Reception to help us with our subtraction we:Use small equipment to add, such asSkittlesLarge DominoesCountersFingersMultilinkNumber linesNumber FanNumicon

Counting on and backCounting in 1s, 2s, and 10sFinding one lessSTANDARDINFORMAL (Workings Out)Number sentences using the -- and = symbols and to represent a missing number:

Numbers to 10

3 - 1 =

Using bowls and small equipment

3 flowers take away one = 2 At this stage it is about the physical process of taking things away 2

Key ObjectiveTo begin to relate subtraction to taking away

+ = 2

+ + + = 4 2 + 2 = 4

+ + + + + = 6

Counting on Counting in 1s, 2s, and 10sCounting 1 moreCounting 5 moreSTANDARDINFORMAL (Workings Out)Number sentences using the X and = symbols and to represent a missing number:

Numbers to 10

3 x 2=

Using setting circles to make groups of small equipment How many altogether?

3 X 2 = 6 3 sets of 2 altogether is .. 61 set of 3 is 3

Doubling numbers to 5 using fingers and mental recallReception: DivisionPRACTICALMENTALPractically sharing objects/ small equipment.Not only in maths lessons but also during continuous provision.

Counting on Counting in 1s, 2s, and 10sCounting 1 moreCounting 5 moreSTANDARDINFORMAL (Workings Out)Number sentences using the and = symbols and to represent a missing number:

10 2 = 5

6 2 = 3

Using small equipment in bowls during snack time practical activities.

10 balls; share between 2 children equally. One for you, one for me, etc.

8 sweets shared by 4 children is 2 sweets each.

Halving numbers to 10 using fingers and mental recall

PRACTICALMENTALUse of number lines, 100 square, fingers, number fans, counters and small equipment.

+ 4 = 9 +

Number bonds to 20Counting in steps of 1s, 2s, 5s, and 10sRecall doubles of all numbers to al least 20Addition facts for totals to at least 20Addition can be done in any orderMultiples of 1s, 2s, 5s, 10sFind the difference (the gap between the numbers)Solve practical word problems, involving additions to 10 and then 20.STANDARDINFORMALNumber sentences to 20

+ 4 = + 7 = 10

+ = 17

Find the missing = 3 + 14 numbers

Jane had 3 balls. She was given 2 more. How many balls does she have now?

+

3 + 2 = 5

Year 1: SubtractionPRACTICALMENTALUse of Number Lines; 100 square, fingers, number fans, counters and small equipment.

Halve numbers to 20Subtraction of a one digit number or two digit number and a multiple of 10 from a two digit numberNumber facts subtraction to at least 5Count back in 1s, 2s, 5s, and 10sNumber bonds to 10STANDARDINFORMALNumber sentences using and = signs

10 = 6

- 3 = 7

10 + 5 =

There are 20 children in our class. Three are away today. How many are here?

20 3 = 17

I I I I I I I I I I I I I I I I I I I I

Using Fingers

Use a hundredSquare to make1 less10 less10 1 =

10 2 = Year 1: MultiplicationPRACTICALMENTALSetting hoops

= 9

Repeated AdditionUnifix towers - make a double

Chanting in steps of 1s, 2s, 3s, 5sx, and 10sQuick recall of all doubles to 20STANDARDINFORMAL 0, 5,__, __, 20

double 2 = 4

2+ 2 = 4

There are three ducks in three different ponds.How many ducks altogether?

+ + + + = 10pxxxxxxxxxUse of 100 square,Number fans,Counters and small equipment

Use fingers

2p2p2p2p2pYear 1: DivisionPRACTICALMENTALSetting hoops

Sharing out counters, cubes and other small equipmentEqual amounts in each groupUse a scarf, fold it in half, then in quarters

Halving numbers up to 20 (the opposite of doubling)STANDARDINFORMALKey ObjectiveTo begin to share objects into equal groups and count how many in each group

Find half of 8

Share 10 strawberries between 2 children

00000000

Year 2: AdditionPRACTICALMENTAL Use of number lines, 100 square, fingers, fans counters and small equipment.

21 + 7 = 28

Number bonds to 20Number bonds to 50 (more able)Counting in 2s, 5s and 10sDoubles to 20 (then to 50 for more able)Number bonds of multiples of 10Knowing to put the largest number first in additionSTANDARDINFORMALNumber sentences to 100 using the + and = signs

+ 15 = 30

15 + = 30

15 + 15 =

30 + 8 = 38Use 100 square to add 10; add 9 and add 11quickly.Use partitioning21 + 17 = 38

21 + 17 =

20 + 10 1 + 7

30 + 8 38

2117201107201017Year 2: SubtractionPRACTICALMENTAL Use of number lines, 100 square, fingers, fans counters and small equipment.

21 - 7 = 14

Counting backwards in 1s, 2s, 5s, and 10sSubtraction facts within 10Subtraction facts within 20 (within 50 for more able children)Halving to 20Subtraction facts of multiples of 10STANDARDINFORMALNumber sentences within 100 using the - and = signs

- 10 = 5

15 - = 5

15 - 10 =

-- --

20 + 3 = 23Quick ways toSubtract 10Subtract 9Subtract 11

Using a 100 square3512305102301052Example shows use of arrow cards to aid withsubtraction calculationsYear 2: MultiplicationPRACTICALMENTAL2 sets of 2 = 4

Making setsUsing equipment to multiply

Counting in 2s, 5s and 10sDoubling to 20 (to 50 for more able)Multiples of 2s, 5s and 10s (and for 3s for more able)Knowing that multiplication is the reverse of divisionSTANDARDINFORMAL2 x 3 = 610 + 10 is the same as 2 x102x, 5x, and 10x tables ( plus 3x for more able)

There are 4 ponds and each pond has 5 ducks. How many ducks altogether?

0 00 0

Children physically do the problem and then draw it out.Year 2: DivisionPRACTICALMENTALPractical dividing using equipment4 dived by 2

Counting in 2s, 5s, and 10sHalvingKnowing that division is the reverse of multiplication.STANDARDINFORMAL60 10 = 6

There are 25 pencils in each classshared equally between 5 pots.Children physically do the problem, then draw it out.Year 3: AdditionPRACTICALMENTAL

100 + 20 + 2 = 122Using a number line

57 + 86

+50 +4 +3

__________________________________________86 136 140 143

STANDARDINFORMAL 176 +48 ------ 100 110 14 ------ 224 83 42 ------- 120 5 ------- 125Start with the larger number, partition the smaller number 57 into tens and units and count on the multiples of 10 firstand then the units. Use apparatusto help withyour calculation100202Line up units with unitsLine up tens with tens(100 + 070 + 406+ 8 Add tens and units:Begin with the most significant digit.Year 3: SubtractionPRACTICALMENTAL

86 - 34 = 52Using a number line

54 -28

+2 +20 +4

28 30 50 54 = 26 STANDARDINFORMAL 54 28 Decomposition

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