Workshop 2

SUBTRACTION _

Coffee and Calculations

Aims of session To help you:

Develop your knowledge of the subtraction methods that children use in school

Understand the progression in methods used as children move up through the school

Support your child’s learning at home

Maths - The Revised curriculum (September 2013) Year 1 – Be able to;

Read, write and interpret mathematical statements that involve addition (+), subtraction (-) and equal (=) signs

Represent and use number bonds and related subtraction facts within 20,

e.g. 14+6= 20, 20-14=6

Add and subtract numbers to 20

Solve simple problems that involve addition and subtraction

(use concrete objects and pictures)

Year 2 – Be able to; Solve problems involving addition and subtraction – apply increasing knowledge of

mental and written methods

Recall and use addition and subtraction facts to 20 fluently and derive and use related facts up to 100, e.g. 3+7=10, 30+70=100, 10-7=3, 100-70=30

Add and subtract numbers to 100 using objects, pictures and mentally

Understand that addition can be done in any order, but subtraction cannot

Recognise and use the inverse (opposite) relationship between addition and subtraction and use this to check calculations

Year 3 – Be able to; Add and subtract numbers mentally

Add and subtract numbers up to 3-digits using formal written methods of column addition and subtraction

Use inverse

Practise using column addition and subtraction with large 3-digit numbers- become fluent

Year 4 – Be able to; Use the formal written column method for addition and subtraction with up to 4

digit numbers

Year 5 – Be able to; Add and subtract whole numbers with more than 4 digits using column method

Calculate mentally with larger numbers

Year 6 – Be able to; Consolidate year 5 and be fluent and secure in both column addition and

subtraction with large numbers and those with decimals.

Key differences today Interactive teaching

Emphasis on mental calculation

Different approach to written calculation

Maths through problem solving

Maths is fun!

At Gillespie We want children to be able to do

mathematics in their heads, and if the numbers are too large, to use pencil and paper.

also

We want children to learn quick and efficient mental and written methods.

We want children to ask themselves

Can I do this in my head?

Can I use drawings or jottings to help me?

Do I need to use a written method? (pencil and paper)

Do I need a calculator?

Finally – Is my answer sensible?

Head, written or calculator

(13 x 12) - ( 234 ÷ 9)

46 - 37

2,254 - 1,306

1463 -102

26.52 - 8.07 89 - 9

Mental strategies for subtraction

Secure mental subtraction requires the ability to:

recall key subtraction facts instantly (inverse of number pairs to 10, 20 & 100, halves etc) and to apply these to similar calculations

mentally subtract combinations of one and two digit numbers

understand that subtraction is the inverse of addition and recognise that subtraction unlike addition can’t be done in any order (it has to start with the larger number)

understand the language of subtraction

Vocabulary of subtraction

Children are taught to understand subtraction as taking away (counting back) and finding the difference (counting up)

Progression in written methods for subtraction

5 – 2 =

I had five balloons. Two burst. How many did I have left?

Take away

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

Find the difference

7 – 3 =

Mum baked 7 biscuits. I ate 3. How many were left?

Take away

Lisa has 7 felt tip pens and Tim has 3. How many more does Lisa have?

Find the difference

84 – 27 = I cut 27cm off a ribbon measuring

84cm. How much is left?

Counting back on an empty number line

57 64 84

-20 -7

57 64 84 60 -20 -4 -3

54 - 38 = There are 54 children in a school music show.

38 turn up late. How many are on time? Children can partition (split) the smaller number into tens and units.

54 – 38

30 8

54 – 30 = 24

24 – 8 = 16

Exchange one long for 10 units. Then there will be 4 longs and 14 units. Then 38 can easily be subtracted.

834 – 378 = The library has 834 books. 378 are out on loan.

How many books are left on the shelves?

378 400 800 834

+22 +400 +34

22 (400) + 400 (800) 34 (834) 456

Counting up from the smallest number to the biggest, using an empty number line. It is easiest to count up to a multiple of 10 or 100. The steps can also be recorded vertically – this works also for decimals!

FINDING THE DIFFERENCE

8.23 – 4.55 =

4.55 5.00 8.00 8.23

+0.45

+3

+0.23

0.45 + 3.00 0.23 3.68

Counting up from the smallest decimal number to the biggest using the empty number line.

AGAIN, FINDING THE DIFFERENCE!

Column subtraction Expanded column subtraction (firstly without borrowing)

55 – 22 T U

50 5 - 20 2 30 3 = 33

Children should always ensure that the largest number is at the top of the calculation and should start their

calculation with the units column

Then with borrowing! (first using the expanded method)

71 -56 = 15

T U

- 70 1 50 6 10 5

60 1

If you read the units column as ‘1 take away 6’, this can’t be done (unless you want a negative answer), so we have to take a ten from the 70 and add it to the 1 so that the calculation would read ’11 take away 6’

T U 7 1 5 6 1 5 Move towards the standard column method for subtraction called ‘decomposition’

1 6

Development of subtraction...

Subtraction of decimal numbers

Subtraction of 3, 4 and 5 digit numbers and beyond

Subtraction of mixed decimal e.g. £1.34 – 75p

Over to you!

Mistakes – Year 2 Learning Objectives Mistakes seen where;

Understand that subtraction is the inverse of addition and be able to state the subtraction corresponding to a given addition

Know by heart all subtraction facts for each number to at least 10

Children believe that it is

possible to change any addition and subtraction calculation around, e.g. 9+3=12

9-12= 3

(instead of 12-9=3)

Mistakes – Year 4 Learning Objectives Mistakes seen where;

Use known number facts and place value to subtract mentally, including any pair of two digit whole numbers.

Carry out column subtraction of two whole numbers less than 1000.

Children sometimes begin

subtracting with the left hand column first (hundreds or tens)

In vertical subtraction

calculations, children sometimes take the smaller unit number from the larger, regardless of whether it is part of the largest or smallest number in the calculation.

e.g. 45 - 37

Mistakes – Year 6 Learning Objectives

Mistakes seen where;

Carry out column subtraction of numbers including involving decimals.

Children have insufficient understanding of place value & exchanging

leading to –

Children believing that subtractions involving zeros can’t be done,

e.g. 200 -146

Calculations like, 34 can’t be done -27

Errors in column subtraction can easily be dismissed as children just making careless mistakes when in fact there is a Fundamental weakness in understanding - often highlighted when working with

decimals & a decimal point

Any questions?