Berkeley Primary School

Calculation Evening,May 2013

Please sit anywhere for the moment

Objectives for the evening:

•To share how we teach calculation at Berkeley.•To give an understanding of progression in calculation.•To let adults experience what their children experience.•To have FUN!•Don’t be shy – get stuck in

Our children...

are all different (believe it or not). They are not widgets at exactly the same point on the ‘production line’.

That’s why we teach them as individuals and tailor maths to suit them. They are all on individual journeys and at varying stages in their progression.

The Four RulesUnderstanding Mental

calculations

Rapid recall

Efficient written methods

Models, images & concrete materials

Stories / rhymesProblem solving and role play

Use of ICT

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

2 + 3 =I buy 2 cakes and my friend buys 3 cakes.How many cakes did we buy altogether?

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

8 + 5 = 8 people are on the bus. 5 more get on at the next stop. How many people are on the bus now?

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

Addition

pictures

symbols

Counting on – jumps of 1(modelled using bead strings) 18 + 5 = 23

18 19 20 21 22 23 24

+1 +1 +1 +1 +1

47 77 80 82

(+ 2)(+ 3)(+ 30)

35 + 47 = 47 + 30 + 5= 77 + (3 + 2)

= 82

35 + 47 = 82

No number line

74 + 48

Addition by partitioning

70 + 40 = 110 4 + 8 = 12

122

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

622

MORE 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

5 – 2 =I have five cakes. I eat two of them. How many do I have left?

A teddy bear costs £5 and a doll costs £2. How much more does the bear cost?

(Take away)

(Find the difference)

13 – 5 =Mum baked 13 biscuits. I ate 5. How many were left?

Lisa has 13 felt tip pens and Tom has 5. How many more does Lisa have?

Drawing a picture helps children to visualise the problem

Using dots or tally marks is quicker than drawing a detailed picture

(Take away)

(Find the difference)

Subtraction

Taking away – jumps of 1(modelled using bead strings) 13 – 5 = 8

8 9 10 11 12 13

-1 -1 -1 -1 -1

Counting on – jumps of 1(modelled using bead strings) 11 – 8 = 3

0 1 2 3 4 5 6 7 8 9 10 11

+1 +1 +1

74 48 50 54

− 2− 4

− 20

Number lines - taking away

74 – 26 = 48

Number lines - counting on

74 – 26 = 48

0 26 30 70 74

+ 4 + 4

+ 40

89 = 80 + 9 - 57 50 + 7

30 + 2 = 32

As they move up into KS2, the children will begin to use partitioning to subtract too- breaking down the numbers into Hundreds, Ten’s, Units etc

We then move onto the RED ALERT questions (or decomposition) where borrowing is introduced:

352 = 300 50 40 12 - 136 = 100 30 6 200 10 6 = 216

7 1

6867 - 2684 4183

MORE TRADITIONAL

METHODS ARE STILL USED!

Does this look more familiar?!

Our children are always encouraged to have a go and to not be afraid of making mistakes. That’s how we learn.

OK…

If you’re still awake, time to head for a maths group and try an activity or two.

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

• Recall of multiplication and division facts

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

Progression for multiplication and division

context

Dice race game

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

4 620

[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

TU x TU(Short multiplication - multiplication by more than a single digit)

64 x 34

HTU x TU(Short multiplication - multiplication by more than a single digit)

372 x 24

X 60 4

30 1800 120

4 240 16

1800 240

120+ 1 6 2176

X 300 70 2

20 6000 1400 40

4 1200 280 8

6000 1400 40 1200 280 8 8928

HTU x TU(Standard Method for long multiplication)

372 x 24

372 24 24x

8 280

120040

140060008928

372 x

1488+ 74408928

Multiplying 4 x 2 then 4 x 70 then 4 x 300

etc

( 372 x 20)

( 372 x 4)

1

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

As children continue with their progress, they will learn methods such as chunking!

This is chunking! http://www.bbc.co.uk/news/11260872

97 ÷ 9 = 10 r 7

EFFICIENT METHODS . . . .

 

   

 

Answer = 125 r 4

Approximation: Answer lies between 100 (600 ÷ 6) and 150 (900 ÷ 6)

754

- 600 (6 x 100)

154

- 120 (6 x 20)

34

- 30 (6 x 5)

4

Extend to U.t ÷ U and HTU ÷ TU

754 ÷ 6

Efficient methods . . . . Short division

291 ÷ 3 = 97

Estimation: 270 ÷ 3 = 90 3 291

972

7 43.4

6.21

43.4 ÷ 7 = 6.2

Estimation: 42 ÷ 7 = 6

2

4

OK…

Time to try some multiplication and division activities.

• 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

• BBC Bitesize http://www.bbc.co.uk/bitesize/ - useful summary of KS1/KS2 content with interactive activities [also has KS3/KS4 materials]

• 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

31 14 20 1624 6 5 2530 29 18 3611 7 13 1

14 20 21 34 39 45 50Three in a row

Choose two numbers from the row of numbers above the grid.

Find the difference between these numbers.

If the answer is on the grid, cover that number with a counter.

A Square of Numbershttp://nrich.maths.org/public/viewer.php?obj_id=2005

Y3