Numeracy WorkshopYear One and Year

TwoApril 2015

St Patrick’s Catholic Primary School 

St Patrick’s Catholic Primary SchoolWritten Calculation Policy

 (Updated with the 2014 National Curriculum)

This workshop is based on our school calculation policy with has been written in line with the new National Curriculum for Mathematics.

It provides guidance on progression and is set out in yearly blocks for the four operations addition, subtraction, multiplication and division.

Use of ResourcesAs a school we will:

Use suitable resources, models and images to support children’s understanding of calculation and place value.

Each year group will use the following practical resources, as appropriate:

Reception: Numicon, other equipment to support counting (i.e toys, beads, cubes etc)

Year 1: Numicon, bead strings, straws, base 10 rods, money, other equipment to support counting (i.e toys, beads, cubes etc)

Year 2: Numicon, straws, base 10 rods, cuisenaire rods, money

KS2: Numicon, base 10 rods, cuisenaire rods , chips, money

Addition

Addition - Year One

G iven a num ber, iden tify one m ore R ead, w rite and in terpret m athem atica l s tatem ents invo lv ing add ition (+)

and the equals (=) s ign Add one- d ig it and tw o-d ig it num bers w ith in 20 , includ ing zero So lve m issing num ber prob lem s eg 10 + = 16

NB Ensure that children are confident with the methods outlined in the previous year’s guidance before moving on.

Children will continue to practise counting on from any number e.g.‘Put five in your head and count on four.’

Then progress to a marked number line (Progress to other manipulative resources as outlined in Introduction):

6 + 6 = 12

‘Put your finger on number six and count on six.’

8 + 7 = 15 ‘Put your finger on number eight and count on seven.’

+1 +1 +1 +1 +1 +1 +1

8 9 10 11 12 13 14 15

Ensure children are confident with using a marked number line before moving on to an empty number line (see year two guidance).

Continue to practise counting on from the largest number for addition with totals within 20.

Partitioning 2 digit numbers

Number bonds 10 and 20

Addition - Year Two

Add numbers using concrete objects, pictorial representations, and mentally, including:

A two digit number and ones

A two digit number and tens

Two two-digit numbers

Three one-digit numbers

NB Ensure that children are confident with the methods outlined in the previous year’s guidance before moving on.

Counting on in ones using an empty number line, within 100…

28 + 6 = 34

+1 +1 +1 +1 +1 +1

28 29 30 31 32 33 34

…and in tens

28 + 30 = 58

28 38 48 58 Use in conjunction with a 100 square to show jumps of tens. (Progress to other manipulative resources as outlined in Introduction)

+10 +10 +10

48 + 36 = 84

‘Put the biggest number first (48), and then partition the smaller number (36 = 30 + 6) and count on: 48 + 30 + 6.’

+10 +10 +10 +1 +1 +1 +1 +1 +1

48 58 68 78 79 80 81 82 83 84

Use in conjunction with a 100 square to show jumps of tens and ones.

Also use the partitioning method to add two two-digit numbers:

43 + 25 = 68

40 + 20 = 60 3 + 5 = 8

60 + 8 = 68 ‘Partition the numbers into tens and ones/units. Add the tens together and then add the ones/units together. Recombine to give the answer’.

40 3 20 5

Then move on to calculations that bridge the tens:

48 + 36 = 40 + 8 + 30 + 6

40 + 30 = 70 8 + 6 = 14

70 + 14 = 84

48 + 36 = 84

This is an alternative way of recording the partitioning method.

YOUR TURN!

Use a 100 square to add groups of 10 eg 32 + 10, 45 + 20, 57 + 30

Partition a number into tens and units eg 76= 70 + 6.

Try 37, 92.

Draw a blank number line and work out 45 + 23

Work out 25 + 32 using partitioning. Can you use the diennes to support your learning? Can you write it out, showing your workings?

Subtraction

Subtraction - Year One

G iven a num ber, iden tify one less R ead, w rite and in terpret m athem atical s tatem ents invo lv ing subtraction

(-) and the equals (=) s ign Subtract one- d ig it and tw o-d ig it num bers w ith in 20, includ ing zero

Solve m issing num ber prob lem s eg 20 - = 15

NB Ensure that children are confident with the methods outlined in the previous year’s guidance before moving on.

Children will continue to practise counting back from a given number.

Then progress to a marked number line:

12 - 6 = 6

‘Put your finger on number twelve and count back six.’

14 – 5 = 9

9 10 11 12 13 14

‘Put your finger on number 14 and count back five.’ NB Ensure children are confident with using a marked number line before moving on to an empty number line (see year two guidance).

C ounting on to find a sm all difference : Introduce complementary addition to find differences (only use for small differences). The use of models is extremely important here to understand the idea of “difference”.

Count up from the smallest number to the largest to find the difference using resources (Progress to other manipulative resources as outlined in Introduction)

11 – 9 = 2

The difference between nine and eleven is two.

NB If, at any time, children are making significant errors, return to the previous stage in calculation.

Subtraction - Year Two

Subtract num bers us ing concrete ob jects , p icto rial representations, and m entally , includ ing:

o A tw o d ig it num ber and ones o A tw o d ig it num ber and tens o Tw o tw o-d ig it num bers

NB Ensure that children are confident with the methods outlined in the previous year’s guidance before moving on.

Counting back using an empty number line within 100, in ones…

34 - 6 = 28

- 1 -1 -1 -1 -1 -1

28 29 30 31 32 33 34

…and in tens:

58 - 30 = 28

28 38 48 58

Use in conjunction with a 100 square to show jumps of tens.

-10 -10 -10

Subtraction , using partitioning , on an em pty num ber line:

76 – 45 = 31

-1 -1 -1 -1 -1 -10 -10 -10 -10

31 32 33 34 35 36 46 56 66 76

Use in conjunction with a 100 square to show jumps of tens and ones.

If children are confident, use more efficient jumps:

76 – 45 = 31

- 40 -5

31 36 76

76 – 40 – 5 = 31 Use in conjunction with a 100 square to show jumps of tens and ones.

Counting on to find a sm all difference: Introduce complementary addition to find differences (only use for small differences). The use of models is extremely important here to understand the idea of “difference” (see Y1 guidance).

Count up from the smallest number to the largest to find the difference.

12 - 8 = 4

+1 +1 +1 +1

8 9 10 11 12

‘The difference between 8 and 12 is 4.’

32- 28 = 4

+1 +1 +1 +1

28 2 9 30 31 32

‘The difference between 28 and 32 is 4.’

If ch ild ren are confident, further develop th is m ethod:

76 – 58 = 18

+2 +10 +6

58 60 70 76

‘The difference between 58 and 76 is 18.’

Now it’s your go….

Count back using a hundred square or with a blank number line

in 1s, in 10s

Eg 45 – 6 74-20

Count back using a hundred square (using partitioning). Try it with a blank number line.

Eg 85 – 13 67-42

Multiplication

Multiplication – Year One

Solve one-step problem s involving m ultip lication by calcu lating the answ er using concrete objects , p ic toria l representations and arrays w ith the support o f the teacher

Count in multiples of twos, fives and tens (to the 10th multiple)

Children will count repeated groups of the same size in practical contexts. They will use the vocabulary associated with multiplication in practical contexts. They will solve practical problems that involve combining groups of 2, 5 or 10. e.g . socks, fingers and cubes.

‘Six pairs of socks. How many socks altogether? 2, 4, 6, 8, 10, 12’ Use language of repeated addition to support understanding of the concept ‘2+2+2+2+2+2 = 12’

Use arrays to support early multiplication

‘Five groups of two faces. How many faces altogether? 2, 4, 6, 8, 10’ Two groups of five faces. How many faces altogether? 5, 10’

‘2 groups of 5’

‘How many altogether?’

‘5 + 5 = 10’

Double five is ten

Continue to solve problems in practical contexts and develop the language of early multiplication, with appropriate resources, throughout Y1.

Multiplication - Year Two

R ecall and use m ultip lication facts for the 2 , 5

and 10 m ultip lication tables and m ake explicit

links w ith m oney

Calculate m athem atical statem ents for m ultiplication w ithin the

m ultiplication tab les and w rite them using the m ultip lication (× )

and equals (=) signs

solve problem s involving m ultip lication, using m ateria ls, arrays,

repeated addition, m enta l m ethods, and m ultip lication facts,

includ ing problem s in contexts

show that m ultip lication of tw o num bers can be done in any

order (com m utative)

NB Ensure that children are confident with the methods outlined in the previous year’s guidance before moving on.

Children will use a range of vocabulary to describe multiplication and use practical resources, pictures, diagrams and the x sign to record.

Com bining Groups (repeated addition):

‘3 groups of 10 crayons’

‘How many crayons

altogether?’ ‘10 + 10 + 10

= 30’

‘3 groups of 10’ ‘3 times 10’ ‘3 lots of 10’

‘3 x 10 = 30’ ’10 x 3 = 30’

‘5 groups of 3’ ‘5 lots of 3’ ‘3 + 3 + 3 + 3 +3 = 15’

5 times 3’ ‘3 multiplied by 5’ ‘5 x 3 = 15’ ‘3 x 5 = 15’

‘5 + 5 + 5 + 5 + 5 + 5 = 30 ‘

‘6 rows of 5’

‘6 groups of 5’

‘5 groups of 6’

‘5 x 6 = 30’

‘6 x 5 = 30’

U sing arrays to support m ultip lication:

6 x 5 = 30

U sing an em pty num ber line :

6 x 5 = 30

1 x 5 2 x 5 3 x5 4 x5 5 x 5 6 x 5

0 5 10 15 20 25 30

Make the link to repeated addition.

NB If, at any time, children are making significant errors, return to the previous stage in calculation.

Have a go!

Show an array for 6 x 3

Use repeated adding on a blank number line to work out 4 x 5

(5 +5 + 5+5)

Use the counting stick

Division

Division - Year One

So lve one-step prob lem s involving d iv is ion by calcu la ting the answ er using concrete ob jects , p icto ria l representations and arrays w ith the support o f the teacher

Count in multiples of twos, fives and tens (to the 10th multiple)

Children will start with practical sharing using a variety of resources. They will share objects into equal groups in a variety of situations. They will begin to use the vocabulary associated with division in practical contexts.

‘Share these eight apples equally between two children. How many apples will each child have?’

‘Share 20 crayons between 2 pots.’

‘How many crayons are in each pot?’

Children will move from sharing to grouping in a practical way

‘Put 20 crayons into groups of 10. How many pots do we need?’

Use arrays to support early division

‘How many faces altogether? How many groups of two?’

‘Five groups of two’

‘How many groups of 5?’ ‘10 shared equally between 2 people’ ‘Half of ten is five’

Continue to solve problems in practical contexts throughout Y1, and develop the language of early division, with appropriate resources.

Division - Year Two

R ecall and use m ultip lication and d ivis ion facts for the 2, 5 and

10 m ultip lication tab les

Calculate m athem atical statem ents for division w ithin the

m ultiplication tab les they know and w rite them using the division

(÷) and equals (=) signs

Solve problem s involving division , using m aterials, arrays,

repeated subtraction , m enta l m ethods, and m ultiplication and

d ivision facts, including problem s in contexts

NB Ensure that children are confident with the methods outlined in the previous year’s guidance before moving on.

Children will use a range of vocabulary to describe division and use practical resources, pictures, diagrams and the ÷sign to record, using multiples that they know.

Sharing and grouping :

‘30 crayons shared equally between three pots.’ (Sharing) ‘We have 30 crayons and put ten crayons in each pot. How many pots do we need?’ (Grouping)

30 ÷ 10 = 3 30 ÷ 3 = 10

‘How many groups of 5?’ ‘15 shared equally between 3 people is…?’

‘15 divided by 3 equals 5’ ‘15 divided by 5 equals 3’

15 ÷ 5 = 3 15 ÷ 3 = 5 Link with multiplication fact 3 x 5 = 15, 5 x 3 = 15

If appropria te w hen sharing/group , in troduce the idea of rem ainders ‘W e’ve got one le ft over/rem ain ing/spare ’

U sing arrays to support d iv is ion

15 ÷ 5 = 3 15 ÷ 3= 5

How many groups of 3? How many groups of 5? 15 shared between 3 people is…? 15 shared between 5 people is…?

15 divided by 5 = 3 15 divided by 3 = 5

W hen children are ready, use an em pty num ber line to count forwards :

30 ÷ 5 = 6

‘How many jumps of five make thirty?’

1

jum p of 5

2 jum ps of 5

3 jum ps of 5

4 jum ps of 5

5 jum ps of 5

6 jum ps of 5

0 5 10 15 20 25 30 A lso jum p back to m ake the link w ith repeated subtraction:

30 ÷ 5 = 6

‘How many groups of five?’

- 5 - 5 - 5 - 5 - 5 - 5

0 5 10 15 20 25 30

NB If, at any time, children are making significant errors, return to the previous stage in calculation.

One last turn…

Put 15 counters into groups of 5. 15 divided by 5 =

Draw an array to work out 12 divided by 4 =

( draw 4 dots in each row until you get to 12 dots in total. How many rows of 4 make 12?)

Finally…

Children need to know

The maths vocabulary associated with the four different operations eg add/plus/total/altogether/more than for addition.

The symbol for each operation

Recognise when to use and apply eg when solving word problems.

Recognising the maths in our everyday lives, playing games and talking ‘maths’ is really important. There are also lots of games online that your child can play to support their learning.

Any Questions?

Thank you for coming.

Please remember if you have any questions about your child’s learning, do come in and talk to

the class teacher.