Blessed Robert Widmerpool Catholic Voluntary Academy

Calculations Policy

This policy outlines how mental and written calculations in all four operations are taught throughout the school, based on the National Curriculum in England 2014. It is a working, adaptable guide that is regularly evaluated and reviewed; a product of a whole school approach using consultation and discussion between all teaching staff and management. Any changes are thus rolled out to Teaching Assistants by class teachers. This establishes continuity, consistency and progression in calculations through the school. Teachers should be aware that this policy is to be used alongside the National Curriculum Programme of Study and the schools’ Scheme of Work to ensure that children are given the opportunities to meet and exceed statutory requirements. Please note that early learning in calculation in Foundation Stage follows the ‘Development Matters EYFS 2012’ document, and this calculation policy is designed to build on progressively from the content and methods established in the Early Years Foundation Stage. AIMS The purpose of this policy is to ensure that calculations in mathematics at BRW builds learning power in pupils, ultimately creating a ‘mastery’ of maths, enabling them to become confident in selecting strategies to solve unfamiliar problems. To achieve this, the school and its calculations policy place great emphasis on the importance of:

fluency in both mental and written calculations, with the understanding that mental fluency is at the heart of successful calculation.

mathematical talk and reasoning

relational understanding, making connections and generalisations between the concrete and the abstract; images, words, symbols and action objects.

the 5 Rs in maths: resilience, resourcefulness, reflectiveness, responsibility and relationships.

learning in a problem solving context. EXPECTATIONS There is an expectation of all pupils that they should firstly consider if calculation can be completed successfully with mental approach. Paper and pen procedures should be used second to mental calculation. The first two questions any child should consider is: what is the best method to use for this problem? Why?

At all stages, children should be encouraged and expected to approximate the size of their answers, calculate and then check. This should become a natural step in any calculation.

The majority of pupils will progress through the calculation methods at broadly the same pace, but pupils should be given enough chances to master fluency in their own time. The decision about when to move on to new methods will depend on the security of pupils’ understanding. If understanding of a calculation is grasped in depth (conceptual and proceduralfluency) then the expectation is that pupils are challenged with rich, open problem-solving opportunities within that concept to allow a broadening and deepening of content, before being accelerated onto the new content. For pupils who are not sufficiently fluent in a stage of calculation, the expectation is that they are given opportunities to master concepts at their pace through further practise, before progressing. The question of when to ‘progress’ pupils ultimately rests upon the assessment of the teacher.

All of this should be undertaken in a rich and sophisticated problem-solving environment.

Key Stage One

By the end of Key Stage One, pupils are expected to have developed mental calculation fluency and early written calculation procedures with whole numbers, counting and place value, using numerals, words and all four operations supported by practical apparatus, images and digital technology. They should know all number bonds to 20 and show precise understanding of place value as well as use regular practise with mental calculations and objects to help them

achieve this. Multiplication facts and their corresponding division facts for the 2s, 5s and 10s should be understood conceptually and memorised to enable rapid recall.

Lower Key Stage Two By the end of lower Key Stage Two, pupils are expected to have become increasingly fluent in calculation methods involving whole numbers and the four operations. Secure knowledge and understanding of number facts and place value is a key part of this. Pupils should develop efficient formal and informal written and mental methods to perform calculation accurately with increasingly large whole numbers, as well as simple fractions and decimals. Mental methods should still take priority and be honed first before exclusive use of written methods, though both types of calculation should be seen as complementary. Pupils should still be supported by practical apparatus, images and digital technology. Multiplication facts and their corresponding division facts to at least 12x12 and number bonds to 100 should be understood conceptually and memorised to enable rapid recall.

Upper Key Stage Two By the end of upper Key Stage Two, pupils should have extended their understanding of calculations in the number system as well as place value to include larger integers. Connections between multiplication and division calculations should be made, including fractions, decimals, percentage and ratio. They develop efficient mental and written calculation methods to solve a range of more demanding problems. Mental methods should still take priority and be honed first before exclusive use of written methods. When faced with problems, children should consider the value of mental calculations before written, however, they should also be seen as complementary. Algebraic calculations should also be developed in pupils. Pupils should still be supported by practical apparatus, images and digital technology. Ultimately, children should leave with fluency in all four operations in terms of mental and written calculations. This includes long multiplication and division as well as fractions, decimals and percentages.

Policy to be reviewed April 2020

Heuristics are strategies that help us to reason and problem-solve efficiently (fluently) in maths. They are a range of

approaches that help children to become successful mathematicians!

We would like to share with you a list of the heuristics used at BRW. Your child will be deepening their

understanding of these over the year, and using them at home as well as at school will support further in their

understanding of maths.

Read on to find out what each heuristic means and to demonstrate what they may look like in practice:

HEURISTICS

(Don’t forget: heuristics don’t have to be used one at a time. Often, two or more can be used to solve a problem)

MEANING

Draw the problem out using jottings, the bar model and any other pictures that will help!

YR 2 EXAMPLE

1) The 24 hours are

showed as the ‘whole’

bar at the top.

2) The ‘whole’ is split

into four equal parts

(quarters),

proportionate to the

whole (24 ÷ 4 = 6).

3) Three equal parts out of

four can be seen visually

3 x 6 or 6 + 6 +6 = 18.

So ¾ of 24 = 18

MEANING

Make a list to and extend it until you reach the answer / all answers. List possibilities, sequences and identify

patterns. Start from the simplest / first possibility and continue from there so you don’t miss any!

YR 3 EXAMPLE

Dodgy digital clock

Ahmed’s bedside digital clock is not working properly. One segment of the display doesn’t light

up.

Which numbers won’t display properly?

Work out how many times between 10:00 and 11:00 won’t display properly.

2) Start at the earliest possibility,

and work ‘in order’

(systematically) through the

subsequent possibilities. Record

which ones fit the criteria.

1) Initial list is made ruling

our digits that won’t display.

MEANING

Once known as ‘trial and error’, this involves narrowing a problem down until you get you to the right answer!

YR 4 EXAMPLE

1) Possibilities for possible

four digit number

combinations are guessed,

checked to see how close

the total is then improved

by playing with other

number options.

MEANING

Looking at how a sequence or diagram changes, and identify what is changing each time. Identify patterns a rules

from this. Pattern is one of the foundations of maths!

FS 1 EXAMPLE

1) Children begin by

noticing patterns in actions

(e.g. ‘Head, Shoulders,

Knees and Toes’); in music;

and in the environment.

2) They move onto making

their own patterns from a

selection of objects.

3) The next step is to

record patterns, and

progress onto verbalising

what’s happening e.g.

what’s the same? What’s

different? What changes?

MEANING

Make suggestions / predictions / conjectures about a problem before you know the answer. What might be

happening? What’s the rule? What’s true? How can you prove this?

YR 6 EXAMPLE

1) A ‘supposition’ or

prediction is made before

the answer is actually

known.

2) Examples 0r ‘proofs’ are tried and tested e.g.

adding three numbers, four numbers, five

numbers etc. to see if their totals are divisible

by the amount of numbers added.

3) A conclusion is made

based on the evidence

they have gathered.

MEANING

Using objects and movement to work through a problem. Popular resources are 10s frames, cubes, counters,

Numicon or images produced to match the problem. Children can then move these resources around / act

out a problem in order to solve their task.

YR 1 EXAMPLE

Peter Rabbit was looking for treasure in his vegetable patch.

His friends decided to come and help. Follow the instructions

to place Peter’s friends:

Dinosaur was under Peter.

Paddington was two squares left of Dinosaur.

Monkey was next to Peter on the left.

Which squares could the other helpers go in?

How many ways can you organise Peter’s friends?

Give your partner instructions on where to place Peter’s

friends.

1) Children were given Peter

Rabbit and his friends to

organise on a vegetable patch.

The children used soft toys

manipulate and organise in

order to solve the problem.

2) They were able to move the

objects easily and reason their

thinking.

MEANING

Start at the answer and ‘undo’ or perform the inverse in order to work out what’s missing.

YR 6 EXAMPLE

1) The problem starts with an

unknown number. Children

analyse the problem and identify

what operations have been

performed to create the answer.

2) Children write the operations

into a number machine, then

‘invert’ or ‘undo’ each operation in

order.

3) 4.5 x 3 = 13.5

13.5 – 6 = 7.5

7.5 x 2 = 15

Children then check that there answer works by starting with

15 and performing the operations that Lara did.

MEANING

Compare problems and ask: what’s the same? What’s different? Identify patterns or rules from this.

YR 6 EXAMPLE

1) The problem is

presented like this to

begin with.

2) The diagram is rearranged. The ‘after’ picture

now shows which segments are equivalent to 34:

18 + 9 + w = 34

27 + w = 34

w = 7

MEANING

Translate / represent the problem into child-friendly language e.g. different words, pictures or symbols.

FS2 EXAMPLE

2) The problem is then represented

in concrete resources – pictures of

the basket, bags and beans

arranged in a large, interactive

part-part whole model, which then

progress to counters.

1) The problem is said in words –

‘Jack has 10 magic beans in his

basket. He needs to share them

between the 2 bags. How many

different ways can he share them?

3) The problem is then represented

using more abstract numerals. All

concrete, pictorial and abstract

representations enable children to

make important mathematical

connections.

MEANING

Break the problem down into steps. What don’t you know? What do you need to know the solve this?

YR 5 EXAMPLE

1) The important information

is identified. This helps to

distinguish what information

they need and what

information they don’t need,

thus simplifying the problem.

2) The problem is further

simplified by drawing a number

line to visually represent

rounding up or down.

MEANING

Solve any sections of the problem that you can or that you know how to. This could lead you onto solving the rest of

the challenge!

YR 6 EXAMPLE

Thank you for taking the time to read about our exciting use of heuristics at BRW, and thank you more so for your

support in encouraging your child to use them in their problem-solving!

Best wishes

Miss Lee

1) This first part of the problem (the column) is

identified as the best way to start, due to all

symbols being the same (triangles), and so

representing equal parts.

2) Once the first part of the

problem is solved, this diagram is

labelled with this new

knowledge.

2) The next and final

part of the problem

(the row) can now be

solved.