Cardinal Road Infant and Nursery School Calculation Evening, January 2016.

Cardinal Road Infant and Nursery School

Calculation Evening,January 2016

Objectives for the evening:

•To share how we teach maths at Cardinal Road.•To give an understanding of progression in maths.

The Four RulesUnderstanding Mental

calculations

Rapid recall

Efficient written methods

Models, images & concrete materials

Stories / rhymesProblem solving and role play

Use of ICT

Foundation Stage

• Children need to leave the Foundation Stage (the end of Reception) with a solid understanding of numbers and their value.

• This is the first stage in being able to calculate – if you cannot count you cannot progress.

Foundation Stage22-36 months (pre Nursery)

• Children begin to be aware of numbers in the environment.• They can say a few numbers in order and experiment using

them in their everyday play.• They are able to ‘give me one’ ‘give me two’• Children begin to be aware that if you add another object to

a group it will become more and if you take away from a group it will become less.

Foundation Stage30-50 months (Nursery)

• Children will learn number names through songs and rhymes.• They will learn to recite numbers to 10 and beyond in order.• They will recognise numbers of personal significance.• They will begin to link the abstract numeral to the quantity.• Children will have a short carpet time focusing on Maths and will be

provided with plenty of opportunity to experiment with number and counting throughout the nursery environment during play.

Foundation Stage40-60 months (Reception)

• Children now explicitly make the link that numbers identify how many objects are in a set and match numeral to quantity .• Children use their fingers, marks on paper or pictures to show numbers.• Children compare two groups of objects, saying when they have more and less and the same number.• They separate groups of three or four objects in different ways,beginning to recognise that the total is still the same.• Shows an interest in representing numbers.• Realise that not only objects, but anything can be counted,including steps, claps or jumps.

Foundation StageEarly Learning Goal (ELG) End of Reception Expectation• Children count reliably with numbers from 1 to 20.• They can count backwards and forwards from any given number

from 1-20.• They can place them in order and say which number is one moreor one less than a given number.• Children understand that as you move forwards the number

value increases and decreases when I move backwards• Using quantities and objects, they add and subtract two single-

digit numbers by counting on or back to find the answer. • They solve problems, including doubling, halving and sharing.

ADDITION AND SUBTRACTION

PROGRESSION FOR ADDITION AND SUBTRACTION

• Counting

• One more / less

• Addition as combining two groups, then counting on

• Subtraction as take away or difference (eg how many more is … than …?)

• Ten more/less

• Recall of addition/subtraction facts to 10, 20 and beyond

• Understand that subtraction and addition are inverses

ADDITION

Year 1

A 2 digit and a 1 digit number

10 + 3 =I buy 10 cakes and my friend buys 3 cakes.How many cakes did we buy altogether?

Addition

An understanding of place Value

8

25 47

So that in Year 2……

74 + 48

Addition by partitioning

70 + 40 = 110 4 + 8 = 12

122

Year 2

374 + 248

Addition by partitioning

70 + 40 = 110 4 + 8 = 12

300 + 200 = 500

622

300 + 70 + 4301 + 40 + 8

500 + 110 + 12

1

COLUMN ADDITION

Extended to:

1247 + 367 £2.36 + £6.48 3.5 + 4.8 7.48 + 2.6 12.5 km + 6.08 km

1

+ 248374

622MORE TRADITIONAL METHODS ARE STILL

USED!

SUBTRACTION

Earlier work involves taking away objects from groups, counting back on a number line or using number beads.

Counting on fingers etc

Year 1 (2 digit and 1 digit number)Taking away – jumps of 1(modelled using bead strings) 13 – 5 = 8

8 9 10 11 12 13

-1 -1 -1 -1 -1

74 48 50 54

− 2− 4

− 20

Number lines - taking away 74 – 26 = 48

Year 2

MULTIPLICATION AND DIVISION

• Counting• Doubling and halving

• Multiplication as repeated addition and describing an array • Division as grouping and sharing• Understand that multiplication and division are inverses (Year 2)• Recall of multiplication and division facts

• Multiply two / three-digit numbers by 10 / 100

Progression for multiplication and division

context

COUNTING IN CONTEXTHow many 10p coins are here?

How much money is that?

How many toes are there on 2 feet?

How many gloves in 3 pairs?

If Sarah counts in 2s and Nigel counts in 5s, when will they reach the same number?

How many lengths of 10m can you cut from 80m of rope?

DOUBLING AND HALVING IN CONTEXT

There are 8 raisins. Take half of them.How many have you taken?

One snake is 20cm long. Another snake is double that length.How long is the longer snake?

I double a number and then double the answer. I now have the number 32. What number did I start with?

2 x 3 or 3 x 23 plates, 2 cakes on each plate

(Children could draw a picture to help them work out the answer)

2 x 3 or 3 x 23 plates, 2 cakes on each plate

(Children could use dots or tally marks to represent objects – quicker than drawing a picture)

Multiplication

pictures

symbols

Number tracks and number lines(modelled using bead strings)

2 x 3 or 3 x 2

[two, three times] or [three groups of two]

Arrays

5 x 3 or 3 x 5

14 x 2 = 28

x 10 42 20 8

Array creator

43x 6

258

1

40 x 6 = 240

3 x 6 = 18X 40 3

6 240 18

43 x 6

Arrays then can lead into what we call grid multiplication- partitioning numbers for multiplication

DIVISION

6 ÷ 2 6 cakes shared between 2

6 cakes put into groups of 2

(Children could draw a picture to help them work out the answer)

pictures

Division

6 ÷ 2 6 cakes shared between 2

6 cakes put into groups of 2

(Children could use dots or tally marks to represent objects – quicker than drawing a picture)

symbols

Number tracks and number lines - grouping(modelled using bead strings)

8 ÷ 2 = 4

6 ÷ 2 = 3

0 2 4 6

Number lines / Arrays

15 ÷ 5 = 3

0 5 10 15

Sharing equally

8 sweets are shared between 2 people. How many do they each receive?

GROUPING OR REPEATED SUBTRACTION-

ASKING IN A DIFFERENT WAY!

There are 8 sweets. How many people can have two sweets each?

As children progress in division, they will continue to use:

repeated subtraction using a number line. They may use an empty number line or a hand drawn jumping line. e.g. 24 ÷ 4 = 6 - children will start at 0 and jump forwards in 4’s to find how many 4’s go into 24 or they may do a multiplication (repeated addition from earlier)

Children will also move onto remainders e.g. 13 ÷ 4 = 3 r 1

0 4 8 12 16 20 24

24 ÷ 4 = 6

• Transum http://www.transum.org/Software/ - provides a mathematics challenge for every day of the year! • Nrich http://nrich.maths.org/public/ - thousands of FREE mathematics enrichment materials for ages 5 to 19 years. The resources are designed to develop problem-solving and mathematical thinking skills.•Woodlands http://resources.woodlands-junior.kent.sch.uk/maths/ - interactive maths games and activities for both KS1 and 2

• I Love Maths Games – games, puzzles and investigations http://www.ilovemathsgames.com/• Professor Kageyama’s maths training for DS consoles

Useful websites and resources

Maths for mums and dads – Rob EastawayRob Eastaway has been Director of Maths Inspiration since it began in 2004. He is an author whose books on everyday maths include the bestselling Why Do Buses Come In Threes? and The Hidden Maths of Sport. He appears regularly on BBC Radio 4 and 5 Live to talk about the maths of everyday life and has given maths talks across the world to audiences of all ageshttp://www.bbc.co.uk/news/11260872