BSN Calculation Policy

The British School in The Netherlands

Calculation policy

Internationally British

Compiled by Katie Zwinkels (Maths Lead Teacher Junior School Leidschenveen) in consultation with other BSN Lead Teachers.

Contents

Calculations in mathematics 3

The mathematical aim 3

Numeracy – the foundations 4 Counting 4

Mental maths 5

Supporting your child at home 5 Addition 7 Subtraction 12 Multiplication 16 Division 20 RMeasimaths 26

Useful websites 26 Glossary 27

Introduction

Calculations in mathematics The aim of this policy is to provide a progressive overview of the calculation methods taught at The British School in The Netherlands from the Foundation Stage to Year 6. This can be used as a reference by all teaching staff when planning next steps for their children.

The booklet is not age-group specific as children learn at different speeds and each child will progress through the methods at their own pace. This booklet should also provide parents with the information required, to ensure that they can provide appropriate support with their children’s mathematics at home.

The progression through calculation categories is: ● Mental ● Mental with jottings ● Expanded written ● Formal written When faced with a calculation problem, we want the children to ask themselves: ● Can I do this in my head? ● Could I do this in my head using drawings or jottings to help me? ● Do I need to use a written method? ● Should I use a calculator?

We also want the children to be confident to estimate and then check the answer.

We encourage them to ask: ● ‘Is the answer reasonable/sensible?’

The mathematical aim At the BSN we want to nurture enthusiastic mathematicians, who display a growth mind-set in their maths thinking. If they can’t do something they understand that it is not that they can’t, but that they can’t yet. We understand that to be numerate, children need a solid foundation of number knowledge and understanding, with an ability to see patterns and relationships between numbers, so that they are confident to tackle more complex concepts. We understand that the most effective learning happens when lessons involve action, imagery and conversation.

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Numeracy – the foundations In the Foundation Stage the focus is on developing a number sense by exploring the ‘ness’ of a number, e.g. the sixness of six.

This number sense develops gradually as children explore numbers; their nominality, cardinality and ordinality, notice patterns and start to reason about number through their play. Many of the activities carried out are in a practical context and involve multisensory learning. ● Children learn to sing songs, chant, recognise and write numbers. ● They develop the pre-numeracy skills of one to one correspondence for counting and matching. ● They begin to recognise patterns in number. ● They sort objects into groups saying why they ‘go together’. ● As they develop more confidence with practical activities and language use, they are encouraged to record their work in a variety of ways. This may involve drawing pictures or writing numbers and they will be expected to explain what they have done and why. https://www.gov.uk/government/ publications/early-years-foundation-stageframework--2

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Counting In the early stages, children are given opportunities to count objects arranged in random sets and standardised patterns. This could be achieved when children: ● Look for numerals in the environment. ● Point at each object while they count or move each object while saying a number. ● Count objects that they can’t touch or move. ● Recite numbers up and down by rote, starting from different numbers and begin to understand what 1 more and 1 less than a number means. ● Play games that involve counting e.g. snakes and ladders, dice games, games that involve collecting objects. ● Spot the missing number when listening to a pattern of numbers. ● Are asked questions to extend their thinking, e.g. how many more would you need to make 8? ● Use Numicon to gain a visual image of a number, count and order numbers. ● Use number lines for matching and counting up and down. ● Begin to combine 2 sets of objects together and count how many altogether. ● Compare 2 sets and say which has more, less or if they are equal. ● Talk about subtraction as less than and count backwards while removing items. ● Order numbers.

Introduction

Mental maths Once the children have a good foundation of number knowledge they start to spot number facts and begin to develop a bank of mental maths facts for rapid recall.

Key facts focused on are: ● Number bonds for numbers up to and including 10. ● Doubles of numbers up to 10 and their related halves. ● Counting in steps of 2, 5 and 10. ● Multiplication Facts.

Supporting your child at home Counting ideas ● Practise chanting the number names.

Encourage your child to join in with you.

When they are confident, try starting from different numbers– 4,5,6…

● Sing number rhymes together (there are lots of commercial CDs available). ● Give your child the opportunity to count a range of objects (coins, shapes, buttons, etc). Encourage them to touch and move each object as they count. ● Count things you cannot touch or see.

Try lights on the ceiling, window-panes, jumps, claps or oranges in a bag. ● Play games that involve counting e.g. snakes and ladders, dice games, games that involve collecting objects. ● Look for numerals in the environment.

You can spot numerals at home, in the street or when out shopping. ● Cut out numerals from newspapers, magazines or birthday cards, then help your child to put the numbers in order. ● Make mistakes when chanting, counting or ordering numbers. Can your child spot what you have done wrong? ● Choose a number of the week e.g. 5.

Practise counting to 5 and on from 5.

Count out groups of 5 objects (5 dolls, 5 bricks, 5 pens). See how many places you can spot the number 5.

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Real-life problems

Practising number facts

● Go shopping with your child to buy two or three items. Ask them to work out the total amount spent and how much change you will get. ● Buy some items with a percentage extra free. Help your child to calculate how much of the product is free. ● Plan an outing during the holidays. Ask your child to think about what time you will need to set off and how much the entrance costs will be to an attraction. ● Use a TV guide. Ask your child to work out the length of their favourite TV programme. Can they calculate how long they spend watching TV each day?

Each week? ● Use a bus or train timetable. Ask your child to work out how long a journey between two places should take. Go on the journey. Do you arrive earlier or later than expected? How much earlier/later? ● Help your child to scale a recipe up or down to feed the right number of people. ● Work together to plan a party or a meal on a budget.

● Find out which number facts your child is learning at school (addition facts to 10, times tables, doubles etc). Try to practise for a few minutes each day using a range of vocabulary. ● Play ‘Ping Pong’ to practise complements with your child. You say a number. They reply with how much more is needed to make 10. You can also play this game with numbers totalling 20, 100 or 1000.

Encourage your child to answer quickly, without counting or using fingers. ● Throw 2 dice. Ask your child to find the total of the numbers (+), the difference between them (-) or the product (x). Can they do this without counting? ● Use a set of playing cards (no pictures).

Turn over 2 cards and ask your child to add or multiply the numbers. If they answer correctly, they keep the cards.

How many cards can they collect in 2 minutes? ● Play Bingo. Each player chooses 5 answers (e.g. numbers to 10 to practise simple addition, multiples of 5 to practise the 5 times table). Ask a question and if the player has the correct answer, they can cross it off. The winner is the first player to cross off all their answers. ● Give your child an answer. Ask them to write as many addition sentences/ equations as possible with this answer.

Then try with another operation e.g. subtraction. ● Give your child a number fact (e.g. 5 + 3 = 8). Ask them what else they can find out from this fact (e.g. 3 + 5 = 8, 8 - 5 = 3, 8 - 3 = 5, 50 + 30 = 80, 500 + 300 = 800).

Add to the list over a few days. Try starting with a multiplication fact as well.

These are just a few ideas to give you a starting point.

Try to involve your child in as many problem-solving activities as possible.

The more ‘real’ a problem is, the more motivated they will be when trying to solve it.

Addition

Addition Throughout the Foundation Stage and Key Stage One addition should be supported by practical models and images. Children begin to record in the context of play or practical activities and problems when appropriate.

Begin to relate addition to combining two groups of objects and counting them

1, 2… 3, 4, 5 There are 5 altogether.

Finding one more than a given number There are 3 necklaces in the treasure chest. How many will there be if I put in one more?

Addition with pictures (visual aid) Use pictures (a) or Numicon (b) to help them with their calculations.

(a) 2 + 3 = 5

(a)

(b)

At a party, Tom eats 2 cakes and Ben eats 3.

How many cakes did they eat altogether?

(b) 4 + 5 = 9 Number track Number tracks are used to help the children count on. A counter or similar object is put on the first number and then moved along the track corresponding to the amount being added. added.

3+4= 7

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6

Counting on Children add single digit numbers by storing the biggest number in their brain and counting on.

6+3 Start with 6, add the three by counting on from 6 (7, 8, 9) = 9

Addition using marks on a page

7 + 4 = 11

Children move on to using marks on a page, e.g. dots or crosses to represent objects as this is quicker than drawing a picture.

E.g. 7 people are on the bus. 4 more get on at the next stop. How many people are on the bus now?

Equivalence Using Numicon to explore number bonds for numbers within 10. Children can build number towers or use balances to find ways to make different numbers.

What is equal to 5?

Structured number lines As numbers get bigger children are encouraged to use structured number lines to help with their calculations.

E.g. 3 + 1 = 4 The steps are drawn above the line when adding.

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Making 8

Ways of making 10

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Addition Unstructured number lines stage 1 Progress to using a self-drawn number line, placing only the numbers the children need.

The children may add in steps of different sizes depending on the sum and what number facts they notice.

14 + 7 = 21

Unstructured number lines stage 2 (2 digit numbers) Drawing on an empty number line helps children to record the steps they have taken in a calculation. This is much more efficient than counting on in ones.

E.g. My sunflower is 48cm tall. It grows another 36cm. How tall is it now? 48 + 36 = (start on 48, + 30, then + 2 and 4)

Addition with Dienes base ten apparatus Children will be taught to use Dienes base ten equipment to represent tens and ones.

Using Numicon to add tens and ones.

Numicon helps the children see what each digit represents in the 2 digit number, e.g.

24 is not 2 and 4 but 20 and 4. Children begin the strategy of adding by partitioning and then grouping the Numicon into tens and ones, to work out the answer.

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Using a hundred square 2

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21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

E.g. 36 + 23 = 59

61 62 63 64 65 66 67 68 69 70

Move vertically down columns to add 10s.

71 72 73 74 75 76 77 78 79 80

Move horizontally along rows to add 1s.

column

This helps build a solid understanding of the relationships between numbers. Children use a physical number square and negotiate their way around it when adding by moving along or down. Eventually they can do this mentally.

row

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81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Using known number facts When adding 3 numbers together, look at the calculation to see if there are any known number facts which you could add first, for example number bonds for 10 or doubles.

4 + 3 + 6 (6 + 4 makes 10, so 10 + 3 )= 13 12 + 6 + 8 = (12 + 8 makes 20, so 20 + 6)= 26 6 + 4 + 6 = (6 + 4 makes 10, so 10+6=16 or double 6 is 12, so 12 + 4 )= 16 48 + 12 = (8 + 2 = 10, 40 + 10 = 50, so 50+10 )= 60

Partitioning and recombining Partitioning – Splitting a number up into its component values.

123 = 100 + 20 + 3 Recombining – putting a number back together.

100 + 20 + 3 = 123

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Addition Adding by partitioning Add the largest value digit first.

86 Start by adding the tens

+ 57

80 + 50 = 130 6 + 7 = 13

143

127 Start by adding the hundreds

+ 249

100 + 200 = 300 20 + 40 = 60 7 + 9 = 16

376

87 Written methods – expanded method

+

46

E.g. There are 87 boys and 46 girls in or

80 + the football club. How many children are there altogether?

40 +

7 6

Children will be taught written methods for those calculations they cannot do ‘in their 7 + 6 = 13 heads’. Expanded methods build on mental 80 + 40 = 120 methods and make the value of the digits 133 clear to children:

120 + 13 = 133

Compact written method

786

+ 568

When children are confident using the expanded method this can be ‘squashed’

1354 into the traditional compact method.

1 1 1 Children carry ten or hundreds to the column immediately left if needed and add accordingly.

E.g. 786 people visited the museum last month. The numbers increased by 568 this month. How many people altogether visited this year? 786 + 568 = Tens, hundreds, thousands carried over.

The carried number is shown below the line.

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Subtraction Throughout the Foundation Stage and Key Stage One subtraction should be supported by practical models and images. Children begin to record in the context of play or practical activities and problems.

Children are taught to understand subtraction as: ● ‘taking away’ (counting back) ● ‘finding the difference’ (counting up).

Begin to relate subtraction to removing objects Using practical resources to ‘take away’ objects.

Subtraction with pictures and marks on the page Drawing a picture, or using apparatus, helps children to visualise the problem.

E.g. I had 5 balloons. 2 burst. How many did I have left? (take away).

A teddy bear cost €5 and a doll costs €2. How much more does the bear cost? (finding the difference by counting on from the smallest number).

The difference between €5 and €2 is €3.

Subtraction using marks on a page Using dots or crosses is quicker than drawing a detailed picture.

E.g. Mum baked 7 biscuits. I ate 3.

How many were left?

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7 - 3=4

Subtraction Using Numicon Use shapes on top of shapes, subtraction covers or pegs to fill holes.

8-6= 2

Number track Number tracks are used to help the children count back. A counter or similar object is put on the first number and then moved back along the track corresponding with the amount being subtracted.

3–2= 1

Structured number lines Children can use a structured number line to ‘count back’ for subtraction.

E.g. Counting Back 10 - 3 = 7 Children draw the steps under the line when taking away.

Subtraction with Dienes apparatus Children will be taught to use Dienes apparatus to represent Tens and Ones and help with subtractions.

E.g. 48 - 2 = 46

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Unstructured number lines stage 1

12 - 4 = 8

Progress to using a self-drawn number line, placing only the numbers the children need. The children may calculate in steps of different sizes, depending on the sum and what number facts they notice. row

Using a hundred square 1

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Moving horizontally back along rows in 1s.

21 22 23 24 25 26 27 28 29 30

55 – 23 = 32

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

column

Move vertically up columns in 10s.

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Using known number facts Look at the calculation and see if there are any known facts to use, for example number bonds for 10 or halves.

12 – 6 = (half of 12 is 6) 60 - 22 = (60 – 20 is 40, 8 and 2 make 10 so there must be 8 ones left = 38) Unstructured number lines – stage 2 Children should select which strategy to use based on the distance between the amounts in the number sentence. If they are close together they should count back.

If they are far apart they should count on.

‘Counting back’

‘Finding the difference’ and ‘counting on’

61 – 47 = 14

74 – 27 = 47

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Subtraction Subtraction by partitioning (mentally)

45 - 30 = 15

Children partition the number to be subtracted into tens and ones before subtracting first the tens and then the ones digit in their heads.

= 15 - 3 = 12

45 – 33 = 12 Expanded written method

Example: 74 – 27 60

Partitioned numbers are written under one 70 another. Start by subtracting the ones, then

- 20 the tens and finally the hundreds. Children

40 + exchange tens or hundreds from the column to the immediate left if needed and subtract accordingly.

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4 7 7

Compact written method without 58 decomposition - 23 Calculations are written in vertical columns

with no need to exchange.

Compact written method with decomposition

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Example: 748 - 362 6

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7 4 8 When children are ready and confident, - 3 6 2 they learn to use the compact method.

Here the recording is reduced to the minimum.

3 8 6

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Multiplication Multiplication is introduced to children as repeated addition and using visual images or groups of objects in arrays.

Repeated addition using pictures Pictures are key to helping children to understand multiplication.

4 birds have 2 feet each so:

E.g. 2 + 2 + 2 + 2 = 8 Repeated addition using Numicon Numicon provides a visual image of the repeated addition. This leads into the shortening of the number sentence to include the x sign.

Multiplication using marks on a page Dots or crosses are often drawn in groups.

Children will use apparatus such as Multilink to help with these concepts.

E.g. This shows 3 groups of 5.

Doubles of numbers These facts should be learnt alongside the inverse half fact.

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Multiplication 3 x 6 and 6 x 3

Arrays – using Numicon Use Numicon shapes to make inverse arrangements of arrays.

Arrays – using pictures or symbols

4x2=8

Drawing an array (4 groups of 2 or 2 groups of 4) gives children an image of the answer.

It also helps develop the understanding that 4 x 2 is the same as 2 x 4.

2 x 4= 8

Number lines Children use number lines to help them count on in equal steps to calculate answers for multiplication.

Hundred square patterns Finding patterns using different multiples.

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71 72 73 74 75 76 77 78 79 80

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81 82 83 84 85 86 87 88 89 90

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91 92 93 94 95 96 97 98 99 100

Multiples of 2

91 92 93 94 95 96 97 98 99 100

Multiples of 3 Calculation policy | 17

Multiplication square This helps to reinforce that the answer remains the same, no matter which way the multiplication sentence is written (commutative law).

x

E.g. 5 x 6 is the same as 6 x 5

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10 10 20 30 40 50 60 70 80 90 100

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Multiplying using place value When you multiply a number by 10, the digits do not change, but shift to the left.

If you multiply a number by 10, the digits move one place to the left.

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34 34 x 10 34 x 100

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If you multiply a number by 100, the digits move two places to the left.

E.g. 37 x 5 =

35 37 is partitioned into 30 and 7. + 150 x 30 7 Grid method

Numbers are placed in a grid.

5 150 35

185

Multiply each partial product.

Add partial products to find answer to 37 x 5.

Extend to HTO x O and TO x TO (Hundreds, Tens and Ones) Encourage children to estimate first.

E.g. 173 x 3, 173 rounded to nearest 100, so 200 x 3 = 600 E.g. 73 x 35, rounded to nearest tens, so 70 x 30 = 2100

173 x3 = 300 + 210 + 9 = 519 x 100 70 3 3 300 210 9 73 x 35 = 2100 + 90 + 350 + 15 = 2555 x

3

30 2100 90 5

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70 350

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Multiplication Column methods

38

x 7

The next step is to represent the method of recording in a column format, but showing (7 x 8) 56 the working. Children should describe what (7 x 30) 210 they do by referring to the actual values of the digits in the columns. 266

Compact written method

38

Some children may be able to use the

most compact form for TO x O

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Recording is reduced to its lowest form.

E.g. 38 x 7

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x 7

7 x 8 = 56 (carry the 50)

266

7 x 30 = 210 and add the 50 = 260

2 5

Multiplying 2 digit numbers 56

x

When multiplying 2 digit numbers together i.e. TO x TO, children are asked to estimate the answer first. This helps them to get a feel for the size of the numbers involved.

E.g. 56  32

2 2 30 30

x 6 x 50 x 6 x 50

32

12 100 180 1500

56 x 32 is approximately 60 x 30, 1792 so the answer will be around 1800

Long Multiplication

327

x 53

Long multiplication is a method used to solve multiplication problems with large (327 x 3) 9 821 numbers. Children need to (327 be confident x 50) 1 61335 0 with multiplication tables to speed up this 17331 strategy and make it more accurate.

E.g. 327 x 53

1 1

To use this strategy each digit is multiplied by either the tens or the ones number in sequence from ones, to tens, to hundreds etc. Care must be taken to record the answer under the correct column. It may be necessary to carry part of the answer. The carried number is added to the total of the next multiplication in the sequence. When multiplying by the tens digit children put a 0 in the ones column, so that they can then work out single digit multiplication.

Add the two amounts vertically to find the answer.

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Division For children to understand division they need to experience two types of activity: Grouping and sharing. Children should experience the different types of division in a wide range of practical activities within relevant contexts.

Using objects Share objects between different numbers of sets.

Using pictures Equal sharing occurs when a quantity is shared out equally into a given number of portions, and we work out how many there are in each portion.

6 toy cars are shared between 2 children.

How many will they each have?

Answer: They will have 3 cars each.

Grouping occurs when we are asked to find how many groups of the divisor are in the original amount.

There are 6 cars; each child can have 2 cars.

How many children will get 2 cars?

Answer: 3 children

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Division 12 ÷ 4 =

Division using marks on a page Dots or crosses can either be shared out one at a time or split up into groups.

This is then extended into groups including ‘remainders’. It is important to teach the children that these are not always 'left over' but may be shared out as parts of a whole, depending on the context.

Learning Halving Facts These facts should be learnt as the universe facts of doubles.

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Repeated Subtraction Division can be worked out as repeated subtraction.

Number Lines Unstructured number lines can be used to carry out repeated subtraction.

45 ÷ 9 = 5

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Division using Numicon Numicon can be used to clearly illustrate division facts, including when there is a remainder.

20 ÷ 3 = 6r2 20 ÷ 5 = 4 20 ÷ 8 = 2r4 20 ÷ 7 = 2r6

Number lines with remainders Self-drawn number lines can be used to illustrate remainders in a clear and visual way.

E.g. 14 ÷ 4 = 3 remainder 2 Skip counting to the left.

Dividing using place value knowledge When you divide a number becomes smaller.

When you divide a number by 10, 100 or 1000, the digits do not change, but shift to the right.

3400 3400 ÷ 10 3400 ÷ 100

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If you divide a number by 10, the digits move one place to the right.

If you divide a number by 100, the digits move two places to the right.

Division using known facts

E.g. 2763 ÷ 3 =

Children can use their number knowledge to work out division problems mentally.

(27 ÷ 3 = 9 so 2700 ÷ 3 = 900 60 ÷ 3 = 20 3÷3=1) 921

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Division Chunking (or expanded division) This uses the same principle as the number line, but numbers are placed in a column.

Chunking is useful for reminding children of the link between division and repeated subtraction.

95 ÷ 6 = 6 x 10 6x5 Write the division like this: I know that 6 x 10 is 60.

Now subtract 60 from 95. That leaves 35.

I have 35 left. I know that 6 x 5 = 30 Now subtract 30 from 35. That leaves 5.

I add up how many lots of 6 I have subtracted from 95 altogether. (10 + 5 = 15) So the answer is 95 ÷ 6 = 15 r 5

Practise and refine the chunking method.

Initially, children subtract several chunks, but with practice they should look for the biggest multiples of the divisor (9) that they can find to subtract.

Chunking is inefficient if too many subtractions have to be carried out.

Encourage them to reduce the number of steps by finding the largest possible multiples.

97 ÷ 9 = 10 r7

Calculation policy | 23

Compact method

270 ÷ 4 How many 4s go into 2? Answer: 0 (0 recorded above the 2) How many 4s go into 27? Answer: 6 r 3 6 recorded above the 7.

3 carried to the 0.

How many 4s go into 30? Answer: 7 r 2 7 recorded above 0.

We have come to the end

Long division Before a child is ready to learn long division, he/she has to know: 1. Multiplication tables (at least fairly well) 2. Basic division concept, based on multiplication tables (e.g. 28 ÷ 7/ 4 x 7) 3. Basic division with remainders (e.g. 86 ÷ 4 = 21 r 2) Long division is the process of dividing simple or complex numbers by breaking it into simple steps which repeat. The steps are; 1) Divide; 2) Multiply; 3) Subtract; 4) Drop down the next digit.

Using the letters DMSD can help children remember how to use this method.

Single digit example

e.g. 832 ÷ 6 = 8 ÷ 6 = 1 (÷) 1 x 6 = 6 (x) 8 - 6 = 2 (-) Drop 3 down next to 2 23 ÷ 6 = 3 (÷) 3 x 6 = 18 (x) 23 - 18 = 5 (-) Drop 2 down next to 5 52 ÷ 6 = 8 (÷) 8 x 6 = 48 (x) 52 - 48 = 4 (-) The answer is 138 remainder 4.

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Division Double digit example

e.g. 2365 ÷ 15 = 15 can’t go into 2 so start with 23.

23 ÷ 15 = 1 (÷) 1 x 15 = 15 (x) 23 - 15 = 8 (-) Drop 6 down next to 8 86 ÷ 15 = 5 (÷) 5 x 15 = 75 (x) 86 - 75 = 11 (-) Drop 5 down next to 11 115 ÷ 15 = 7 (÷) 7 x 15 = 105 (x) 115 - 105 = 10 (-) The answer is 157 remainder 10.

It is important that the concept of ‘remainder’ is discussed at each stage. There needs to be an understanding that it is part of a whole left over. This then helps in the later stages when it is left as a fraction or decimal.

Calculation policy | 25

Useful websites http://www.bbc.co.uk/schools/ks1bitesize/ numeracy/ Variety of games for KS1 children http://www.bbc.co.uk/schools/ks2bitesize/ maths/ Variety of games for KS2 children http://www.amathsdictionaryforkids.com/ dictionary.html Interactive maths dictionary http://www.oswego.org/ocsd-web/games/ Mathmagician/mathsmulti.html Times tables game www.aplusmath.com Different games and printable flashcards www.nrich.maths.org.uk Games and activity ideas for all ages www.numberlinelane.co.uk Introduction to number lines Fs and KS1 www.brainbashers.com Mind stretching Brain teasers www.funbrain.com Different games www.mathletics.co.uk Personal membership can be taken out, maths questions and rapid recall competition. www.topmarks.co.uk Different games www.ictgames.co.uk Different games http://www.rmeasimaths.com/ To use with school membership year 2–6

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There are many online platforms used across the BSN to support learning, including RMeasimaths, Mathletics and MyMaths; children may have individual logins for these programs in order to aid learning at school and at home.

Please see the Curriculum area of the Gateway to find out the platforms used at your particular campus and how you can find the logins needed.

Resources

Glossary capacity this is the measure of how much a container holds, and can be measured in litres and millilitres. common multiple a multiple that is shared between 2 or more numbers. cubed number the result of using a whole number in a multiplication three times. Example: 3 x 3 = 27, so 27 is a cubed number. denominator the number below the line in a fraction. It tells you how many pieces the object has been divided into. So in ⅜ the denominator is 8. difference the difference between two numbers is what you get if you subtract the smaller number from the larger one.

numerator the number above the line in a fraction. It tells you how many thirds, quarters, fifths, etc you have. The numerator in ⅜ is 3.

Numicon is multi-sensory approach to teaching maths, using Numicon number shapes and focusing on Action, Imagery and Conversation. partitioning splitting a number, often into hundreds, tens, and ones, so 84 can be partitioned into 80 and 4, or into 70 and 14. place value this refers to the fact that digits have different values depending on their place in a number. For example, the 3 in 37 means 30 because it is in the tens column, whereas the 3 in 356 means 3 hundred.

Children also learn that because 4 x 7 = 28, then 4 x 70 = 280, and similar related facts. prime a number which can only by divided by itself and one.

dividend the number that is divided by another, so in 24 ÷ 6, the dividend is 24.

product the answer in a multiplication calculation; the product of 5 and 2 is 10.

divisor the number you divide into another, so in 24 ÷ 6, the divisor is 6.

quotient the answer in a division calculation, as in 24 ÷ 6 = 4, the quotient is 4.

empty number line an empty number line is just a line drawn by the child, without numbers marked on it. The child then write on only the numbers needed to help with the calculation.

square number the product of a number multiplied by itself, e.g. 1, 4, 9, 16.

estimate to have an approximate guess. factor a factor is a number that divides exactly into another, for example, 1, 2, 5 and 10 are all factors of 10.

HTO stands for hundreds, tens and ones. In 279 there are 2 hundreds, 7 tens and 9 ones.

TO stands for tens and ones. In 84, there are 8 tens and 4 ones. units what you are using to measure something, for example centimetres, kilograms, minutes, etc. volume this is a measure of how much of a capacity is filled, usually measured in millilitres or litres.

mass at primary school this is used as an alternative word to weight. The mass of a bag of sugar is 1 kilogram. multiple an operation where a number is added to itself a number of times.

Calculation policy | 27

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