Progression Tuesday 11 th February 2014. Counting Knowing the number names in order. Synchronising...

ProgressionTuesday 11th February 2014

Counting

Knowing the number names in order.

Synchronising saying words and pointing or moving objects.

Keeping track of objects counted.

Recognising that the number associated with the last object touched is the total number of objects.

Recognising small numbers of objects without counting them.

Developing counting skills.

Counting

counting things you cannot move or touch or see, or objects that move around.

counting objects of different sizes.

recognising that if a group of objects already counted is re-arranged then the number of them stays the same.

recognising that if objects are added or removed the number changes.

Developing counting skills.. continued

• This focuses on the development of children’s awareness, understanding and use of the language of number.

Addition

+

MENTAL

MATHS

These are a selection of mental strategies: Mental recall of number bonds 6 + 4 = 10 + 3 = 10 25 + 75 = 100 19 + = 20

Use near doubles 6 + 7 = double 6 + 1 = 13

Addition using partitioning and recombining 34 + 45 = (30 + 40) + (4 + 5) = 79

Counting on or back in repeated steps of 1, 10, 100, 1000 86 + 57 = 143 (by counting on in tens and then in ones) 460 - 300 = 160 (by counting back in hundreds)

Add the nearest multiple of 10, 100 and 1000 and adjust 24 + 19 = 24 + 20 – 1 = 43 458 + 71 = 458 + 70 + 1 = 529

Use the relationship between addition and subtraction 36 + 19 = 55 19 + 36 = 55 55 – 19 = 36 55 – 36 = 19

Addition

How can I record?Draw simple pictures and talk about it…

Record ideas in a number sentence….

Practical

Addition

Addition

Addition

Addition

Reordering to start with the largest number.

AdditionNumber line

AdditionNumber line

AdditionPartitioning

AdditionThese are introduced when the children have a sound grasp of place value & of the whole addition process.

AdditionStandard Method Column addition….

364+ 54 418 1

£ . 14.62+ 1.87 56.49 1

238.6121051.05+ 81.0691370.731 1 1 11

Subtraction

-

MENTAL

MATHS

These are a selection of mental strategies:

Mental recall of addition and subtraction facts 4 = 10 – 6 20 - 17 = 3

10 - □ = 2 □ - 8 = 11

Find a small difference by counting up 82 – 79 = 3

Counting on or back in repeated steps of 1, 10, 100, 1000 86 - 52 = 34 (by counting back in tens and then in ones) 460 - 300 = 160 (by counting back in hundreds)

Subtract the nearest multiple of 10, 100 and 1000 and adjust 24 - 19 = 24 - 20 + 1 = 5 458 - 71 = 458 - 70 - 1 = 387

Use the relationship between addition and subtraction 36 + 19 = 55 19 + 36 = 55 55 – 19 = 36 55 – 36 = 19

Subtraction

5

Subtraction

SubtractionNumber line

Subtraction

Subtraction

Subtraction

Subtraction

74 – 27 27 = 20+7

74 – 20 = 54

54 – 7 = 47

Partitioning

Subtraction

Subtraction

Subtraction

New Facts from known ones

Place Value Inverse13+14 = 27 4+3=730+40=70 7-3=40.3+0.4 = 0.7 7-4=330+4=34

Near facts Equivalent4+4=8 2+5=73+3=6 1+6= 7

3 + 4 = 7

Multiplication

x

MENTAL

MATHS

These are a selection of mental strategies:

Doubling and halving Applying the knowledge of doubles and halves to known facts.

Using multiplication facts Year 2 ~ 2x, 5x, 10x Year 3 ~ 2x, 3x, 4x, 5x, 6x, 8x, 10x Year 4 ~ Calculate all multiplication facts up to 12 x 12 Year 5 ~ Quickly recall all facts up to 12 x 12.

Using and applying multiplication facts Use tables knowledge to derive other facts. e.g. If I know 3 x 7 = 21, what else do I know? 30 x 7 = 210, 300 x 7 = 2100, 3000 x 7 = 21 000, 0.3 x 7 = 2.1 etc

Multiplying by 10 or 100 Knowing the effect of multiplying by 10 (shift in the digits one place to the left).

Knowing the effect of multiplying by 100 (shift in the digits two places to the left).

Partitioning 23 x 4 = (20 x 4) + (3 x 4) Use of factors= 80 + 12 8 x 12 = 8 x 4 x 3= 102

MultiplicationChildren are introduced to multiplication by counting on and back in equal steps of ones, twos, fives and tens.

Working practically or drawing a picture helps children to visualise the problem.

4 x 2

MultiplicationFirst recognize that multiplication is repeated addition.

No of lots how many per group total3 x 5 = 15

Is the same as 3 lots of 5 or 5 + 5 +5 = 15Use pictorial cues to represent a x sum.Encourage them to write the sum:

5 + 5 + 5 = 15

MultiplicationChildren use arrays to model a multiplication calculation.

3 x 5

5 x 3

Using repeated addition

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

MultiplicationDots or tally marks are often drawn in groups. This shows 3 groups of 6.

Children can count on in equal steps using an empty number line. This shows 4 jumps of 4.

3 x 6

Multiplication

Multiplication

MultiplicationGrid method of multiplication

38 x 7238 x 72

XX 7070 22

3030 21002100 6060

88 560560 1616

21602160+ 576+ 576 27362736

11

Multiplication

1692

Multiplication

Division

÷

MENTAL

MATHS

These are a selection of mental strategies:

Doubling and halving Knowing that halving is dividing by 2 and doubling is multiplying by 2

Deriving and recalling division facts Recall corresponding division facts linked to tables knowledge.Know 5 x 6 = 30 so ? ÷ 5 = 6

Using and applying division facts Children should be able to utilise their tables knowledge to derive other facts. e.g. If I know 3 x 7 = 21, what else do I know? 21÷ 7 = 3, 21 ÷ 3 = 7, 3000 x 7 = 21 000, 0.3 x 7 = 2.1 etc

Dividing by 10 or 100 Knowing the effect of dividing by 10 (shift in the digits one place to the right). Knowing the effect of dividing by 100 (shift in the digits two place to the right).

Use related facts Given that 1.4 x 1.1 = 1.54 What is 1.54 ÷ 1.4, or 1.54 ÷ 1.1?

Working practically or drawing a picture helps children to visualise the problem.

DivisionSharing is a skill children come to school with.

‘One for me one for you’ is repeated subtraction.

12 ÷ 2 = 6

DivisionChildren progress to removing ‘groups’ of a number.

There are 12 sweets and each party bag needs three sweets. How many party bags can be made?

In this example children put ‘groups of three sweets’ into the party bags until they have no sweets left.

Division

DivisionChildren can count on in equal steps using an empty number line to work out how many groups of there are.

This shows you need 4 jumps of 7 to reach 28.

Children begin to jump in ‘chunks’ of the number they are dividing by, in this example ‘chunks of 4’ are used. A jump of 10 groups of 4 takes you to 40. Then you need another 5 groups of 4 to reach 60, leaving a remainder of 3. Answer is 16 tables.

DivisionShort Division

6 1 3 2

221 1

DivisionShort Division with remainders and decimals.

WOW!!After all that you deserve a cuppa!

When your child can do all of this, they will

learn even more FUN Maths.

A Numberless WorldIf all the numbers in the world were rubbed out, removed, taken away:

I wouldn’t know how old I was, I wouldn’t know the time of day, I wouldn’t know which bus to catch, I wouldn’t know the number of goals I’d scored.

I wouldn’t know how many scoops of ice-cream I had, I wouldn’t know the page on my reading book, I wouldn’t know how tall I was, I wouldn’t know how much I weighted.

I wouldn’t know how many sides there are in a hexagon, I wouldn’t know how many days are in the month, I wouldn’t be able to work my calculator. And I wouldn’t be able to play hide-and-seek!

But I would know As far as my mum was concerned, I was still her NUMBER ONE!

Ian Souter