The New Curriculum and calculation

methods in KS2

Tuesday 17th November 2015

The New Curriculum

•Five-year-olds will be expected to learn to count up to 100 (compared to 20 under the old curriculum) and learn number bonds to 20 (old was up to 10)•Fractions (1/4 and 1/2) will be taught from KS1, and by the end of primary school, children should be able to convert decimal fractions to simple fractions (e.g. 0.375 = 3/8)•By the age of nine, children will be expected to know times tables up to 12×12 (old curriculum 10×10 by the end of primary school)•Calculators will not be introduced until near the end of KS2, to encourage mental arithmetic.

A child working confidently in mathematics:

• Has a sense of the size of a number• Knows where numbers fit in the number system• Knows number facts• Knows how to use what they know to work out new

information• Uses a range of methods of calculating in their head and

on paper• Makes sense of a problem and knows how to start to

solve it• Checks their answers• Knows if their answers are reasonable• Talks about how they work things out• Suggests suitable units for measuring• Justifies and proves answers• Can explain and make predictions from data in graphs

tables and charts

Addition

Resources to help children with addition

                         

Stages in addition

1) Informal counting strategies e.g. counting songs, rhymes and games

2) Practical and pictorial addition – (a) count all

(b) count on

3) Use of number lines to count on from one number to another

4) Blank number lines: 8 + 6 = 14 (counting on in ones)

5) Blank number lines: 8 + 6 = 14 (chunking)

Progressing:

6) Partitioning

Horizontal expansion

T U + T U =

76 + 4 7 =

70 + 40 = 110

6 + 7 = 13

110 + 13 = 123

4 7 = 40 + 7

7 6 = 70 + 6 110 + 13 = 123

Vertical layout

7 6

+ 4 7

1 3

+ 1 1 0

1 2 3

Compacted Method

or

leading to

9

7) Vertical layout

Contracting the working out into a compact efficient form:

T U H T U

7 6 3 4 6

+ 1 4 7 + 1 1 9 3

1 2 3 5 3 9

                                                 

Decimals

3.6 + 4.8 = 8.4

5.34 + 12.77 = 18.11

0.07 + 0.04 = 0.11 6 . 8 90.7 + 0.3 = 1.0 1 . 5 612 + 5 = 17.00 8 . 4 5

1 10.11 + 1.0 + 17.0 = 18.11

+ 3.0 + 0.6

4.8 7.8 8.4

Subtraction

Resources to help children with subtraction

                         

1.

Stages in subtraction

1) Informal counting strategies e.g. counting songs, rhymes and games

2) Practical and pictorial subtraction

3) Use of number lines to count back or on from one

number to another

4) Finding the difference between groups of objects

or numbers

5) Using an empty number line to count up

1.

                                                 

6) Stages in subtraction by decomposition

67 - 32 = 35 60 - 30 = 30 7 - 2 = 530 + 5 = 35

61 - 27 = 3450 – 20 = 30 11 – 7 = 430 + 4 = 34

7) Expanded layout

563 – 241 = 863 – 346 =

50 13

500 + 60 + 3 800 + 60 + 3- 200 + 40 + 1 - 300 + 40 + 6 300 + 20 + 2 = 322 500 + 10 + 7 = 517

leading to

or

Compacted method

17

26 12 6 12

                                                 

8) Compact Method 563 – 271 = H T U 4 1

5 6 3- 2 7 1 2 9 2

Decimals

5.3 – 3.9 =

0.1 + 1 + 0.3 = 1.4

4 1 5 . 3 3 . 91 4

0.1 1 0.3

3.9 4 5 5.3

Multiplication

Resources to help children with multiplication

                         

10 20 30 40 50

5

50

60

55

45

3540 30

25

20

15

10

24 6

1) Counting groups of objects

2) Grouping objects

Repeated addition 3 x 2 2 + 2 + 2 = 6

3) Arrays in real life

5 x 3 or 3 x 5

6 x 4 or 4 x 6

7 x 6 or 6 x 7

4 x 6 or 6 x 4

4 x 3 or 3 x 4

Solving multiplication problems

How many legs on 6 spiders? Notation: 8 x 6 =

Repeated addition: 8 + 8 + 8 + 8 + 8 + 8 = 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 =

Array:

Using known facts: I know that 5 x 8 = 40, so 6 x 8 = 48

Jottings: 8 16 24 32 40 48

4) Number line

+ 70 +21

10 x 7 3 x 7

0 70 91

13 x 7 = 91

5) Grid Method

13 x 7

X 10 3

7 70 21

70 + 21 = 91

Grid Method

123 x 13 = X 100 20 3

10 1000 200 30

3 300 60 9

1230 + 369 = 1000 + 200 + 300 + 30 + 60 + 9 = 1000 + 500 + 90 + 9 =

1230

369

Grid Method Decimals

7 x 3.3 =

X 3 0.3

7 21 2.1

21 + 2.1 = 23.1

6) Expanded Short Multiplication

38 x 7 = 266

30 + 8 x 7 5 6 (8 X 7) 2 1 0 (30 X 7) 2 6 6

56 x 27 = 1512

50 + 6 20 + 7 4 2 (6 X 7) 3 5 0 (50 X 7) 1 2 0 (6 X 20) 1 0 0 0 (50 X 20) 1 5 1 2

7) Compact Multiplication

2 3 x 1 2 4 6 (2 x 23) 2 3 0 (10 x 23)

2 7 6

1 2 3 1 2 2 4 6 ( 2 x 123) 1 2 3 0 (10 x 123)

1 4 7 6

Division

Resources to help children with division

                         

½ ½

1) Sharing objects

Share these six biscuits between three teddies.

How many biscuits does each teddy get each?

2) Linking with halving and quartering shapes

Splitting into equal groups/parts

½ ½

¼ ¼

¼ ¼

3) Using tens and units to solve division problems

48

48 ÷ 2 = 24

12 ÷ 4 = 3

15 ÷ 3 = 5

4) Division as grouping – Repeated Addition

15 ÷ 3 = 5

+ 3 + 3 + 3 + 3 + 3

0 3 6 9 12 15

5) Arrays to find answers with a remainder

13 ÷ 4 = 3r1

13 ÷ 4 = 3r1

+ 4 + 4 + 4 +1

0 4 8 12 13

Finding remainders

39

7 and two fifths!

7 r2

Solving division problems

How many boxes of 6 eggs do I have if I have 36 eggs altogether?

Notation: 36 ÷ 6 =

Array:

Using known facts (grouping) : I know that 6 x 6 = 36, so 36 ÷ 6 = 6

Jottings:

6 12 18 24 30 36

6) Long Division

560 ÷ 24 =

How many packs of 24 biscuits can we make with 560 cookies?

23 r 8 24 5 6 0 4 8 0 (20 packs 20 x 24) 8 0 7 2 (3 packs 3 x 24) 8

7) Counting on by chunking

100 ÷ 7 = 14r2

8) Compact Bus Stop when dividing by a single digit

10x7 = 70 4x7 = 28 r 2 10 4

0 70 98 100

2 3 1 3 6 9 3

3 1 2 r1 3 9 3 7

Any questions?

If you have any questions please feel free to ask.

Fractions

Fraction of shape: Total number of equal parts (denominator). How many of those parts are coloured / shaded / eaten (numerator)

Fraction of number using sharing/division

Fraction of number using grouping/division

1. 2/5 of 25 How many parts can be made from denominator

2. 25÷5 (this gives the value of each part)3. 5 x 2 = 10 (value times numerator)

Simplification: thinking about the common factor between the numerator and the denominator and dividing each.

3/12 - ¼ 5/10 - ½

DecimalsIntroduced in terms of money and half (0.5)

£1.21 13.5cm

Number line to show decimals between whole numbers.

1 1.25 1.5 1.75 2

Place Value and Fractions

H T U 1/10 1/100 1/1000

8 3 1 . 2 7 4

Measure (converting measures)

E.g. 1534g = 1.534kg 250ml = 0.25l

Percentages and their equivalents

% per hundred

Ten and a unit value (upper KS2)For example 16%

100% 50% 25% 75% 10%

Whole ½ ¼ ¾ 1/10

1 0.5 0.25 0.75 0.1

Knowing halves

Halve and halve again

Halve and a quarter

Whole less a quarter

Divide by 10

Equivalence

(Beg KS2) knowing basic equivalents:0.25 = ¼= 25%0.5 = ½ = 50%0.75 = ¾ = 75%

(Later KS2) Progress in ks2

Using calculation to go from fraction to decimals etc

e.g. 4/5 = 4÷5 = 0.8

Percentages to fractions

e.g. 32% = 32/100 = 16/50 = 8/25

Any questions?

If you have any questions please feel free to ask.

Word Problems

Simple 1 step problems

These often involve 1 operation

+ - x ÷add take away times shareTotal subtract multiply dividePlus minus product groups ofAltogether how many more than lots of eachMore than differenceSum of left

Word Problems

Multi-Step problems

These often involve 2 or more operations

Word Problems

Advanced Multi-Step problems

Involve percentages/fractions/decimals/Unit conversion

Jennifer earns £624 per month. She pays 6% to her mum. How much does she have left.

There were 300 children at Hogwarts school of Witchcraft and Wizardry. 1/10 had a toad at their pet, ½ had an owl and 4/10 had a cat. How many of each pet were in the school.

Laura had spent 2 and a half hours reading her book. She read 10 pages every 5 minutes. How many pages did she read?

Cows travel at 15m per minute. How far in km will it travel in 2 hours.

Jenna has a bag of flour that weighs 1.5kg and some butter that weights 250g and some sugar that weights 1.07kg. How much her ingredients weight altogether in grams.

Finding all possibilities

•Have a system for finding all possibilities E.g. Start with the smallest number, keeping something the same.

•Check for repeats

•Know and reason when all possibilities have been found.

•Organise results in an ordered list, tables or sections

Logic Problems

•Identify given facts and prioritise them.

•Look for relationships and patterns.

•Use one piece of information in the problem and see what effect it has.

•Choose a recording system to organise given information.

•Check the answer fits the criteria.

Diagram and visual puzzles

•Use a systematic approach to solve and record problem.

•Use drawings and annotations.

•Try possibilities to check the solution.

•Visualise problem using familiar shapes and patterns.

Vocabulary

Add, addition, plus, more, increase

Score, total, altogether, equals

Sum

Number sentence

Record, draw, show me, jottings

Place Value (Thousands, Hundreds, Tens and units)

Count on, jump on

Vocabulary

Subtract, subtraction, minus, take away, less, leave, fewer, decrease, left, difference, grouping and re-grouping

Equals

Number sentence

Record, draw, show me, jottings

Sum! Count on/count back

Place Value - Thousands, Hundreds, Tens and Units

                  

Vocabulary

Lots of, groups of, ‘x ’, times, multiply, multiplied byMultiple ofOnce, twice, three times… ten times…Times as (big, long, wide… and so on)Repeated additionArray, row, columnDoubleOne each, two each, three each…Group in pairs, threes… tens

Number sentence

Record, draw, show me, jottings

Vocabulary

Share, share equallyOne each, two each, three each…Group in pairs, threes… tensEqual groups÷, divide, division, divided by, divided intoHalve, quarter, ½, ¼, One each, two each, three each…Group in pairs, threes… tensLeft, left over, remainderGrouping and chunking

Number sentence

Record, draw, show me, jottings