What is the National Curriculum anyway? A new version was introduced in September 2014. Academies,...

What is the National Curriculum anyway?

A new version was introduced in September 2014.

Academies, free schools and independent schools do not have to

follow the curriculum.

Why the changes?

“[The new curriculum] combines the best elements of what is taught in the world's most successful school systems, including Hong Kong, Massachusetts, Singapore and Finland, with some of the most impressive [existing] practice from schools in England."

•The idea - somewhat controversially - is for children to "go further...at an earlier age"

So what's all this about fractions at five then?

•This is about very simple fraction work initially, such as understanding what a half or a quarter of a cake or biscuit is. Oh and calculators will not be allowed until secondary school!

•pupils being expected to be taught times tables to 12 by age 9 and converting fractions to decimals in year 4.

Will the 2014 primary curriculum involve any new tests?

•The Department for Education is currently in the process of reforming KS2 tests, but details have not yet been published.

Could it all be too much for some children?

•‘We make no apologies for having high expectations for our children,’

•‘We believe they can achieve more, and we will not stand by and allow pupils to lose ground with their peers in countries across the world.’

•For most children, these changes will take effect from September 2014, but children in Years 2 and 6 will follow the existing programmes of study until September 2015 in English, maths and science.

Middleton Tyas and Eppleby Forcett

C of E Primary Schools.

New Curriculum2014

Maths Workshop Calculation Strategies

New Curriculum 2014• The new curriculum represents a substantial increase

in both the amount of Maths being taught and the expectations of children at each age range. In general, much of what was traditionally taught in Y5/Y6 (3-digit multiplication using formal written methods, formal column addition and subtraction of 4-digit numbers as well as amounts of money, time intervals involving 24 hour clock, two-place decimals ...) now has to be completed and may be assessed by the end of Y4.

Year 6

• By the end of Y6, the children may be assessed on addition/subtraction of fractions including mixed numbers, multiplication and division of fractions by integers, formal algorithms for multiplication and division of four-digit by two-digit numbers, as well as more advanced calculations involving decimals and percentages, for example using the fact that 3/8 is 0.375.

Calculation Strategies

• To be able to choose an appropriate method for calculation e.g mental, mental with jottings, expanded written, formal written, calculator.

• To develop efficient methods of calculation with all four operations.

• To develop a mathematical understanding, a feel for the value of number rather than just learning a mechanical method that can be prone to error.

We want pupils:

To develop learners for life

AimsTo develop an understanding of the expanded and formal

(traditional) methods we teach at school for addition, subtraction, multiplication and division.

Calculation

At school we want the children to have:

• To be able to count efficiently• Good understanding of Place Value• To use images and models• To use memorised number facts• To Double/Halve

1. Place Value

Common errors:• Write 101 in figures (1001)• 3.4 x 10 (3.40)• Write one pound and 5p as a decimal (1.5)• 0.2 x 0.2 (0.4)It is so important that children at KS1 have sound understanding of place value to be able to use written calculation methods at KS2 (examples on next slides)

Addition

Partitioning:47 + 35=

40 30 70

7 5 12

82

Addition

Partitioning:374 + 248=300 70 4

200 40 8

500 110 12

600 20 2

622

Addition

Partitioning:£48.56 + £23.70 =40.00 8.00 0.50 0.0620.00 3.00 0.70 0.00

£60.00

£11.00

£1.20 £0.06

£70.00 £2.00 £0.20 £0.06

£72.26

Addition

Expanded Vertical Method:374 + 248=

12110

500

374 248+

+

622

Addition

Expanded Vertical Method:£48.56 + £23.70=

0.06 1.20

60.0011.00

£48.56 £23.70+

+

£72.26

Addition

Compact Vertical Method:374 + 248 = 374

248+

21

216

Addition

Compact Vertical Method:£48.56 + £23.70= £48.56

£23.70+

£7 .261

21

Subtraction

Partitioning:This method links to counting back on a number line.

74 - 27 =

74 - 20 = 54

54 - 7 = 47

Subtraction

Expanded Method – No adjustment or decomposition needed:

563 - 241=

500 + 60 + 3200 + 40 + 1

_

300 + 20+ 2 = 322

Subtraction

Expanded Method – Adjustment from the tens to the units:

563 - 246=

500 + 60 + 3200 + 40 + 6

_

300 + 10+ 7 = 317

1350

Subtraction

Compact Method – Adjustment from the tens to the units:

563 + 246=

563-246

51

713

Multiplication

Compact Grid Method47 x 36 = X 40 7

30 1200 210 1410

6 240 42 282

1692

Division

Grouping Expanded196 ÷ 6 = 32 R 4

6 ) 196(6 x 10)

(6 x 10)

(6 x 10)

(6 x 2)

-60

-60

-60

-12

136

76

16

4

Division

Grouping Efficiently346 ÷ 8 = 43 R 2

8 ) 346(8 x 40)

(8 x 3)

-320

-2426

2

2. Use of Images and ModelsAddition

Pictures and Symbols:I buy 2 cakes and my friend buys 3 cakes. How many cakes did we buy altogether?May be recorded as: 2 + 3 = 5

Addition

Pictures and Symbols:18 + 5 = 23

Addition

Number Line:18 + 5 =

+1+1

18 20 23

+1+1+1

19 21 22

Addition

Number Line - Efficient Jumps:47 + 35 =

+3 +2+30

47 77 80 82

Addition

Number Line - Efficient Jumps:374 + 248 =

+40 +8+200

374 574 614 622

Addition

Number Line - Efficient Jumps:£48.56 + £23.70 =

+70p+£3+£20

£48.56 £68.56 £72.26£71.56

Subtraction

Pictures and Symbols:I have five cakes I eat two of them. How many do I have left?May be recorded as: 5 - 2 = 3

X X

SubtractionStage 1

Pictures and Symbols:13 - 5 = 8

Subtraction Stage 2

Number Line - Counting Back:13 - 5 =

-1-1

8 10 13

-1-1-1

9 11 12

Subtraction

Number Line – Counting Back Efficient Jumps:74 - 27 =

-4-3

47 54 74

-20

50

Subtraction

Number Line – Counting On Efficient Jumps:74 - 27 =

+40 +4+3

27 30 70 74

40 + 4 + 3 = 47

Multiplication

Pictures and Symbols:There are three sweets in one bag.How many sweets are there in five bags?

Multiplication

Number Line – Repeated Addition:5 x 3 or 3 x 5

0 3 6 9 12 15

0 5 10 15

Multiplication

Arrays5 x 3 or 3 x 5

Multiplication

Expanded Grid Method13 x 4 =

X 10 3

4

10 x 4 = 40 3 x 4 = 12

40 + 12 = 52

Multiplication

Compact Grid Method13 x 4 =

X 10 3

4 40 12

40 + 12 = 52

Division

Pictures and Symbols:How many apples in each bowl if I share 12 apples between 3 bowls?

Division

Number Line:15 ÷ 3 = 5

0

+3 +3 +3+3+3

3 6 9 12 15

15

-3 -3-3 -3-3

129630

Division

Number Line: Chunking.96 ÷ 6 = 16

0 60 96

10 x 6 = 60 6 x 6 = 36

Division

Number Line: Counting Back by Chunking.200 ÷ 6 = 33 R 2

2002 20

30 x 6 = 1803 x 6 = 18

0

3. Memorised Number Facts

• Fewer children come to school knowing rhymes/numbers etc.

• Memorisation is the grounds on which we build maths. 78+5= by year 3 children should not be counting on in ones but know that 2 more is 80 plus another 3.

• If children don’t know their number facts, they can’t do maths.

4. Double and Halve

• Why is doubling and halving important?• It is the simplest maths function we teach. We

do this and then it is reversed.

• 1 million divide by 8 How would you do it? Halve, Halve, Halve it

• 13 divided by 5 How? Divide by 10 and double it.