Supporting Your Child in Numeracy

Guide for Parents

Milton of Leys Primary….where the magic of learning comes alive

Helping your child to develop numeracy…..

What YOU do really counts!At Milton of Leys Primary School the Experiences and Outcomes in Mathematics and Numeracy (as outlined in the Scottish Government’s Curriculum for Excellence) are carefully planned for and fully implemented. We firmly believe that the following two documents provide the best Learning and Teaching opportunities for both children and all those involved in their education:

The New Zealand Numeracy Projectwww.nzmaths.co.nz

The Highland Progressions in Numeracy, Time, Money, Measure, and Fractions and Decimals

The above documents aim to improve the quality of maths teaching and raise the level of children’s achievement. They are based on extensive research about how children learn.

Through this approach your child/children will be learning to:

enjoy working with numbers make sense of numbers – how big they are, how they relate to other

numbers, and how they behave solve mathematical problems – whether real life or imaginary calculate in their head wherever possible, instead of using a

calculator or pen and paper show that they understand maths, using equipment, diagrams and

pictures explain and record methods they use to work out problems accept challenges and work at levels that stretch them work with others and by themselves discuss how they tackle mathematical problems – with their peers,

their teacher and YOU!

Some questions you may have……

How important is equipment?

When children meet new mathematical ideas for the first time, it is really important that they explore these ideas using lots of different equipment/materials. This can mean anything from fingers, straws to calculators. Once children understand an idea, they should then try to use it with the equipment screened or hidden and then without the materials completely.

What about times tables?

We think that it is important that children should be able to make sense of addition and multiplication before they try to memorise their tables. But, when they do understand, it is important they do learn these basic facts and can recall them instantly.

What about pencil and paper or calculators?

Children should do most calculations in their heads. They should use pencil and paper or calculators only when the numbers are hard or when they are solving a problem that has several steps.

What about work in their jotters/books?

Children will often use whiteboards to record thinking. They may also record ideas in their group ‘modelling’ book as well as their own maths book. Photographs are also taken showing the children involved in their learning. Children will record their work in a variety of ways, for example using empty number lines, formal algorithms when they are at the right stage for this (also known as chimney sums or column addition) and think boards.

What about the Academy?

To be ready for the Academy, your child/children should be extremely well prepared – they will understand how numbers behave, know their basic facts, be able to do a lot of working without a calculator, and be confident that they will usually be able to ‘work things out’. We also liaise very closely with our maths colleagues in the Academy.

How well is my child doing?

To make progress children need to understand what they are doing and to be able to work with numbers quickly and confidently. Of course, we all learn at different rates. Please do not hesitate to ask your child’s teacher about what they are working on and how they are doing.

You will also want to know how you can help and of course this is the aim of this guide!

Please do spend time reading through it. It is fairly detailed but it does cover most things from Nursery all the way through to P7! If you are not sure of anything, again please do not hesitate to ask your child’s teacher. Also, we would dearly welcome any feedback - what you have found useful, what we have missed out! Comments should be posted on the Maths Blog.

TOP TIP!

IT IS VITAL THAT YOUR CHILD UNDERSTANDS NEW IDEAS THROUGH THE USE OF MATERIALS AND CAREFUL QUESTIONING. ONLY WHEN THEY ARE SECURE IN THEIR OWN KNOWLEDGE CAN THEY THEN MOVE AWAY FROM THE SUPPORT OF OBJECTS.

PLEASE, PLEASE, PLEASE DO NOT SIMPLY TELL YOUR CHILD ANSWERS OR GIVE THEM ‘RULES’. For example, to multiply by ten just add a 0 to the end of a number! NO!!! IF CHILDREN DO NOT

UNDERSTAND THE MATHS INVOLVED AND HAVE SIMPLY MEMORISED ‘TRICKS’ FOR THAT WEEK, IT HAS BEEN SHOWN THAT WHEN THEY ARE ASKED TO WORK OUT MORE ADVANCED PROBLEMS THEY SIMPLY CANNOT DO SO.

Thank you as always for your support!The Staff of Milton of Leys Primary School

Terms often used in the…..Early Level – (Nursery – end of P1)

pre-counting – an understanding of more, less and the same

one to one counting – the strategy of counting each object once and only once by moving each object as you count it is very important

order – irrelevance – when counting the number of objects in a set, the order is not important as long as each object is counted and that the children understand that the last number ‘is the count’

cardinality – the number of items or sets in a group. Children will need to understand that if no more is added or taken away the number will stay the same. Children who do not understand this will start counting from one if the items in a group are shuffled but not added to or subtracted from.

teen numbers – 13, 14, 15, 16, 17, 18, 19, difficult for a lot of children to grasp as the words do not follow the usual pattern with the tens first and then the ones e.g. 13 is ‘thir’ ‘teen’

ones – traditionally the first column on the right has been call the ‘units’ column. Now the children are taught to use the term ‘ones’ instead so that they can talk about ten ones being the same as one unit of ten

subitising – this involves the immediate recognition of the number of objects in a small collection without having to count the objects e.g. the dots on a dice, dots on a tens frame etc. Subitising is an important skill for later numeracy work as it helps build the foundations for part-whole thinking (see definition below).

forwards and backward number sequences – it is really important that the children practise counting backwards just as much as forwards. It is equally important that children practise counting forwards and backwards from different starting points, e.g. 9, 10, 11, 12, 13… 12, 11, 10, 9, 8…. and that they can recall the number immediately before or after another number, e.g. what comes after 6, 7, what comes before 5, 4. This is important to help children to move on to ‘advanced counting’ (see definition below).This is particularly important to keep practising later on. Many children find crossing boundaries such as decades 9/10/11, 29/ 30/31 etc. hundreds 99/100/101, 199/200/201), thousands (999/1000/1001, 1999/2000/2001) etc. difficult.

real-life experiences – problems are always related to real-life experiences

ADDITION addition – needs to move from counting and combining objects to

using abstract methods, e.g. hiding objects behind screens and in boxes, to develop children’s ability to visualise and internalise before introducing written numbers

SUBTRACTION subtraction – this will be done in three different ways:

taking away from a group of objects comparing two groups – finding the difference numerically

between two groups how many more or less are in a group

inverse operation – where possible, addition and subtraction will be taught at the same time to help the children understand this idea. However it is not taught more formally until later.

MULTIPLICATION multiplication - children will begin to use forward and backward

number word sequences using multiples of 2 and 5 e.g. 1, 2,3, 4, 5, 6, 7, 8… and then progress to skip counting – 2, 4, 6, 8When solving multiplication problems at this level they will most likely count in ones, e.g. Two children have three cars each, how many cars have they got altogether? Some children will need to physically touch and manipulate objects as they count in ones. Some children will be able to image (picture the objects in their head) as they count in ones.

DIVISION division – there are two forms:

sharing – when sharing a group of objects fairly, children should understand that their share is the same as everybody else’s

share, i.e. that all fair shares are equal. For example, Jessica has 12 marbles. She shares them equally into 4 bags. How many marbles are in each bag? 12 marbles shared equally into 4 bags gives 3 marbles per bag. Children at this stage will share equally by dealing out items one by one.

grouping- Jessica has 12 marbles. She puts them into bags of 6 marbles. How many bags can she make? (12 is grouped/measured in sixes.) 12 marbles put into bags of 6 marbles per bag gives 2 bags.

children should also have an understanding that within real- life situations, some shares may have some items ‘left over’ or a ‘remainder’ and that they need to think what they are going to do with it

First Level – (P2 – P4)At the beginning of this level, saying one, two or three numbers forwards and backwards is still really important. The range of numbers used is increased, e.g. 27, 28, 29, 30, 31 ………..52, 51, 50, 49, 48…. .Children often use their fingers to keep a track of the numbers. Practising crossing a decade ( e.g. 10, 20, 30 ) is really important as children often find this tricky, e.g. 68, 69, 70, 71……………93, 92, 91, 90, 89, 88…….. It is also important for children just to recall one number after or one number before. Again, crossing certain boundaries is tricky, e.g. before 100 is 99, before 200 is 199, after 799 is 800 etc.

Reversing 2 digit numbers can still be a problem for children, e.g. 16 and 61 sound and look very similar

Children need to understand that the ‘ty’ words means ‘tens’, e.g. sixty means six tens

Fives and Tens frames are used to help children see that 5 and 10 are really useful, helpful numbers especially when it comes to making larger numbers and doubling

Fives Frame

Tens Frame

After children have built up an appreciation that there are 5 in a row and 10 altogether they can then just get a ‘quick flash’ of the tens frame and subitise the number. For example, flash When they can say 9 just by recognising it and no longer need to count in their mind, this is called SUBITISING. Activities with fives frames can be extended to asking additional questions, e.g. How many dots? How many gaps? How many on the top row? How many on the bottom row? How many altogether? This supports children to learn some of their early basic facts.

Other materials such as a Rekenrek, bead strings, dot cards and counters are used in the classroom to help children with their

understanding.

Tidy numbers – these are numbers which end with a zero, e.g. 10, 50, 100. Some people also call them friendly numbers.

Compatible numbers – these are numbers which when added together give a tidy number e.g. 41 + 59 = 100. Tidy numbers can also be compatible, e.g. 20 + 20 = 40

Commutative – 2 + 3 is the same as 3 + 2. Also, starting with the larger number when joining two amounts as this a more efficient use of time. Again, children need to come to this realisation themselves through lots of practice, experience and careful questioning. They should not be simply ‘told’.

Doubling and halving – it is important that the children know their doubles and the corresponding halves to 20. This helps children to partition and use larger numbers/calculations

Part, Part-Whole strategies – once children have shown that they can solve simple addition and subtraction problems by counting on or counting back, they then partition (split) and then recombine numbers to make to ten to help addition and subtraction problems e.g. 9 + 6 = 9 + (1 + 5) = ( 9+ 1) + 5 + = 15. Part, Part-Whole strategies involves the children seeing numbers as being made up of two or more parts

Imaging – when children are confident using a wide range of equipment and materials, these are then screened to encourage the children to build images of the materials in their minds. Imaging materials acts as a bridge between using materials and being able to answer questions using numbers only. The teaching model below is referred to and embedded in all learning with even children in P7 being introduced to new concepts through the use of materials.

Number stories and sentences – children are encouraged to create their own number stories related to their own lives and experiences. This helps to make things real and meaningful.

Equal sign – this means ‘is the same as‘. Both sides balance. At first children understand the equals sign to mean “find the answer”. For example, 2 apples plus 3 apples equals how many apples (2 + 3 = 5).When children’s thinking develops, a broader definition of “equals” is needed. For example, to work out 28 + 6 using a tidy number strategy, children need to understand that 28 + 6 = 28 + (2 + 4) = (28 + 2) + 4 = 30 + 4 = 34. Here, “equals” means “is the same as”. An important development of this more general understanding is when Academy school pupils realise that, to find the solution of algebraic equations, they need to understand that the equals sign also means “balance”. So, in 3x + 11 = 11x – 5, pupils see = as meaning “is the same as”, not “get the answer”.

Think board – in class children are asked to show a number story with objects on a think board. Children can also write the problem on the board as well as showing it as a sum. For example, there were eight cats in one house and six cats in another house. How many are there altogether.

The four parts of the think board might be representing the number sentence (e.g. 8 + 6 = 14) as follows:

- A word problem- Show how you worked it out and which strategy was used.- Stating which knowledge was required for the strategy used.- Showing how this problem could be represented using materials.

PLACE VALUE Zero is used as a place holder. It shows that there is none of a

particular quantity and that it holds the other digits in a number in place. For example, 62 (sixty two) may be written incorrectly as 602 or 104 (one hundred and four) as 14

Place value is a really important concept at this stage and children often use straws/lolly sticks to make bundles of 10 and ones. There are two central ideas to place value: the place holder, zero, and the concept that if, as a result of addition or multiplication, the numeral in any place exceeds 9, then 10 of these units must be traded for one unit that is worth 10 times as much. Conversely, for subtraction or division, if a unit needs to be broken down, it must be traded for 10 units worth 10 times less.The idea that once we have 10 of something we call this group one of something else is not at all straightforward for young children. However, understanding that ten “ones” are equivalent to one “ten”, for example, is really important. Initially, children need to crack the language and symbolic code for naming and reading the number names from one to nine. Saying “ten, eleven, twelve” and writing “10”, “11”, and “12” may seem no different than counting from one to nine aloud, or writing the words and symbols for these

numbers, but the difficulty of doing this should not be underestimated. The main idea of place value can be summed up by saying that numbers greater than 9, whether spoken or written, have different representations. For example, 67 can mean 67 single objects, or 6 tens and 7 ones.

Partitioning – breaking numbers up (see two examples below of different ways to partition)

Splitting and partitioning 2 and 3 digit numbers into standard form – e.g. 369 = 300 + 60 + 9

Splitting 2 and 3 digit numbers into non-standard form – Non-standard form can produce an extensive combination of numbers, e.g. 237 has 23 tens and 7 ones or 237 ones; 237 could also be seen as 22 tens and 17 ones. Understanding non-standard form relies heavily on good place value understanding and is crucial later on for understanding formal written algorithms like column addition/subtraction (chimney sums).

ADDITION AND SUBTRACTIONBelow are a series of strategies for addition and subtraction that might be used at this stage. There are some examples of how this might be represented in written recording and in some cases, examples of how this might be represented on materials. There would be other ways to represent the same concepts using different materials.At this stage, calculations often involve either two single digit numbers, e.g. 7+8, or a two-digit number and a one-digit number, e.g. 28+7. This is a general guide but not true for all strategies.

Compensating from a known fact, e.g. using doubles knowledge to work out near doubles, e.g. 7 + 8: 7 and 7 is 14 so 7 and 8 is 15.

Using a standard place value partitioning strategy e.g. 43 + 35 is (40 + 30) + (3 + 5) = 70 + 8 = 78

Rounding and compensating. One number is rounded up or down to make it easier to add or subtract. This needs to be compensated for at the end by ‘undoing’ what you did at the beginning. This concept can be particularly difficult for children to grasp… ‘I can’t remember if I need to add a bit on now or subtract a bit’ is a common statement from children when they get to the final part of the calculation. This is why, modelling with materials first is so important. E.g. 24 – 9 = (24 - 10) + 1 = 15

Bridging/jumping through a tens number this involves partitioning one of the numbers and jumping up or back through the next/previous decade.E.g. 38 + 7 = (38 + 2) + 5 = 45

+1

1514 24

-10

+5

4038 45

+2

E.g. 56-8 = (56-6)-2 = 48

MULTIPLICATION AND DIVISION Counting rhythmically – helps children identify number patterns

e.g. 1, 2, 3, 4, 5, 6, 7, 8, 9. This helps them to use skip counting e.g. 3, 6, 9, 12

Skip Counting – At first level children will initially learn to skip count in 2s, 5s and 10s to 100 and later skip counting in 3s.

Times Tables – Later on at this level (after children are confident at skip counting and after they have UNDERSTOOD what multiplication is) children will learn their 2, 5 and 10 times tables and know the matching division facts.

Arrays – these are used in the classroom and help children to understand the concept of multiplication. They also help children to move from repeated addition to other multiplication strategies.

Using skip counting to solve multiplication or division problems – at this level, children will initially solve multiplication problems by skip counting, e.g. 5 children have 2 sweets each. How many sweets did they eat altogether? So, 5 x 2 (where the multiplication sign means groups of or lots of, ie. 5 groups of/lots of

5048 56

-6-2

2) is solved as 2, 4, 6, 8, 10. (Children might track the count on their fingers, raising one finger each time one set of 2 is counted.)

Using repeated addition to solve multiplication or division problems – after skip counting children will see multiplication as repeated addition e.g. 5 x 3 is seen as 5 lots of 3 which is 3 + 3 + 3 + 3 + 3They will solve division problems in a similar way e.g. How many bags will I need if 15 sweets are put into bags of 5 sweets? 5 + 5 = 10 10 + 5 = 15 so it’s 3 bags.

Using known facts to solve unknown facts:

Extending knowledge of doubles to seeing that this is the same as the two times table, e.g. double 7 is 14 as the same is 2 x 7 = 14.

Using knowledge of 10 x table and understanding of doubling and halving to solve the 5 x table. In the example below, 4 x 10 is the same as 8 x 5

Second Level – (P5 – P7) Forwards and Backwards Number Word Sequences are still

really important at this level but the number range is extended to the millions and also includes decimals and fractions. The same principles apply as at Early and First Level.

Cyclical pattern – this is used to help children read very large whole numbers

4,027,346,427

Relative magnitude of a number – to find the quantity that a digit represents, the value of the digit is multiplied by the value of its place. For example, in the number 3264, the 3 represents 3 x 1000, 2 represents 200 because it is 2 x 100, the 6 represents 6 x 10 and the 4 represents 4 x 1. Children need to know that, for example 5730 is ten times as much as 537

Decimal system – the values of the number increases in powers of ten from left to right

Problems set out in horizontal form – this encourages children to give a more flexible response. Often textbook questions are set out vertically and this sadly encourages children to follow one set procedure rather than thinking intuitively.

Estimation – it is really important that children estimate answers before attempting to solve a calculation. They should then use their estimate to assess if their final answer was reasonable.

Inverse relationship between addition and subtraction – children are encouraged to choose the most efficient strategy between counting on or counting back. Initially they need to re-interpret, for example, 47 – 26 as, ‘what do you have to add to 26 to get to 47’ and so count by tens and ones. As the numbers increase, children may use other, more efficient strategies.

Prime number – a number which can only be divided by one and itself, i.e. has two factors. One is not a prime number as it has only one factor – itself.

Integers – there are a set of whole numbers called integers e.g. 0, 1, 2, 3….. and also -1, -2, -3 ……. The numbers e.g. 2.6 and 8 and a half are not integers.

Choosing Wisely – this is a key element later on in second level and means that the children have a wide range of strategies that they are confident in using and they are now beginning to think about which strategy would be the most efficient one to use for a particular set of numbers. Once children are able to do this, they then move onto using formal algorithms such as column addition (chimney sums) to solve problems. Again, these form part of the choosing wisely selection as they are used selectively when the

numbers become too complex to calculate mentally and this would be the most efficient strategy to use.

ADDITION AND SUBTRACTIONBelow are a series of strategies for addition and subtraction that might be used at this stage. There are some examples of how this might be represented in written recording and in some cases, examples of how this might be represented on materials. There would be other ways to represent the same concepts using different materials.Strategies from First Level are still used but may be extended by increasing the range of numbers that are being used. See First Level for examples.

Rounding and Compensating For example, 28 + 37. Round 28 up 2 to make 30. Round 37 up 3 to make 40: 30 + 40 = 70: Take off what I’ve rounded up: 70 – 5 = 65

Or solve 28 + 37 by just rounding up one of the numbers e.g. round 28 up to 30 (so the problem becomes 30 + 37 and then compensate by subtracting the 2 you added at the end so 30 + 37 – 2 = 65

Early on, pupils might add the 37 by adding 10 at a time…

However, later we would expect them to apply their basic facts knowledge to be able to add the 37 in one jump rather than needing to go up in tens.

4030 60

+10 +10 +10 +7

50 67-2

65

6530 67

+37-2

Here’s an example for rounding and compensating for subtraction:63 – 29 = ? becomes 63 – 30 + 1 = ?

* For rounding and compensating, the part children often get stuck with is whether to add a bit more or take some away at the end… again, this is why it is so important to model the strategy with materials to allow children to UNDERSTAND the strategy before progressing to imaging (screening the materials) and then just the problem by itself usually with more complex numbers (number properties).

Transformation strategy ( or ‘Same Difference’ strategy for subtraction) – when dealing with numbers that look tricky, they can be changed by addition or subtraction to make them more manageable:

Equal Adjustments: Add or subtract the same amount to both sides for subtractionE.g. 4.8 – 2.76 = ? By adding 0.24 to both sides, the calculation becomes easier… 5.04 – 3 = 2.04Similarly, for a different calculation such as 487 – 309 = ? 9 could be taken away from both sides so the calculation becomes 478 – 300 = 178* As with all new strategies, it is important that children experience this first through materials so they UNDERSTAND why adding or subtracting the same amount to each side will still give the correct answer even though the numbers have both changed. If children LEARN THIS AS A RULE without UNDERSTANDING, they may incorrectly apply it to addition and not know why it works for one but not the other.Strategies at this level become more reliant on quick recall of a

WIDE RANGE OF BASIC FACTS which is why they are so crucial to practise.

Add to one side and take exactly the same amount off the other side for additionFor the rounding and compensation problem above, this could be done using this strategy too e.g. 28 + 37 by giving two from the 37 to the 28 therefore changing the calculation to 30 + 35 = 65

Reversibility StrategyE.g. 53 – 26 = ? as 26 + ? = 53…

…so 26 + (4 + 20 + 3) = 53 so 53 – 26 = 27.

Semi – formal strategies for addition and subtraction – these are well-organised, standardised written strategies that use place value partitioning. This is an important stepping stone in order to help children understand why numbers are carried/borrowed in column addition/subtraction.

Formal algorithms for addition and subtraction. These will be introduced once the children have a clear understanding of place value, have a wide range of mental strategies and can choose wisely, i.e. choose the most efficient strategy based on the numbers rather than simply using a formal written sum as the ‘default’ strategy. It is an extension of the semi-formal written method above but is the next step to supporting children to understand why numbers are carried/borrowed.

Written recording – calculations can be recorded in a range of ways, e.g. empty number lines (as above), semi-formal recordings and formal algorithms (examples above). Written recording such as empty number lines can be used to record thinking when mental strategies are not yet secure and need to be written down. Written recording such as formal algorithms can also be used when the numbers get too large/difficult to calculate mentally.

MULTIPLICATION AND DIVISION

Doubling and Halving to solve multiplication problems E.g. 3 x 8 = 24, so 6 x 8 = 24 + 24 = 48 (doubling)

E.g. 4 x 16 as 8 x 8 = 64 (doubling and halving)

E.g. 72 ÷ 4 as 72 ÷ 2 = 36, 36 ÷ 2 = 18 (dividing by 4 is the same as dividing by 2 twice… halving and halving)

Compensation, e.g. 5 x 3 = 15, so 6 x 3 = 18 (3 more; compensation using addition)

10 x 3 = 30, so 9 x 3 = 27 (3 less; compensation using subtraction)

Place Value Partitioning, e.g. 13 x 3 = 39

Reversibility and Place Value Partitioning e.g. 72 ÷ 4 as 10 x 4 = 40, 72 – 40 = 32, 8 x 4 = 32, 10 + 8 = 18 so 18 x 4 = 72 so 72 ÷ 4 = 18

32 72

-40 (10 x 4)-32 (8 x 4)

0

Semi – formal strategies for multiplication

Grid method – this method of recording multiplication is used for a Place Value Partitioning Strategy. Children may initially solve it using squared paper so they can UNDERSTAND how the method works but over time, this becomes compacted to what is called the Grid Method of Multiplication.

E.g. 3 x 14

E.g. 4 x 127

Semi – formal strategies for divisionChunkingE.g. 96 ÷ 6 = 16

E.g. 400 ÷ 17 = 23 r9

Formal strategies for multiplication and divisionThese will be introduced once the children have a clear understanding of place value, have a wide range of mental

GRID METHOD

strategies and can choose wisely, i.e. choose the most efficient strategy based on the numbers rather than simply using a formal written sum as the ‘default’ strategy. It is an extension of the place value partitioning strategy for multiplication above but is the next step to supporting children to understand why numbers are carried and what you do with these.E.g. 68 x 5 = ?

E.g. 92 ÷ 4 = ?

can be recorded as (partitioning strategy) then

moving onto . Again, this allows children to understand why certain numbers are carried and what happens to them.

Basic FactsThere are certain number facts that children need to remember as they meet new ideas in mathematics. Children need to first UNDERSTAND the facts and may initially arrive at an answer by using a strategy. With time and lots of practice, these facts need to become KNOWLEDGE and be INSTANTLY RECALLED.

This involves knowing about the relationships between numbers, e.g. knowing that 7 is made up of 5 and 2, or 6 and 1 or 4 and 3

Known facts can be used to find others, for example using doubling; 2 x 3 = 6 so 4 x 3 = 12

Children are often challenged by: Understanding basic facts learned by rote Understanding that a fact such as 5 x 8 has the same answer as 8 x

5 Not being put off memorising because they think there are too

many facts to learn Accepting that they still need to instantly recall multiplication

tables even though they can work them out by using a few known facts, for example knowing 8 x 5 = 40 or using 8 x 5 is (5 x 5 ) + (3 x 5 ), which is 25 + 15.

Ways to develop understanding:

Rhythm counting (in time 1,2,3,4,5,…), stress counting ( 1,2,3,4,5, 6..), double counting ( 3 x 5 is the same as 5, 10, 15 and knowing that 5 is one group of 5, 10 is 2 groups of 5 and 15 is 3 groups of 5)

Counting in 2s – people, eyes, ears, feet, shoes, etc!

Counting in 5s and 10s – relate this to fingers and toes As the children become more confident, make connections

between counting and 5s and 10s 2s and 4s and 8s; then 3s, 6s, and 9s

Progression of Basic Facts

Children will: Recognise patterns to 5, e.g. dice patterns, five frame patterns, etc. Recognise patterns to 10, e.g. dot patterns, tens frame patterns,

etc. Recall addition facts to 5, e.g. 1 + 4 = 5 Recall subtraction facts to 5, e.g. 4 – 1 + = 3 Revisit addition and subtraction facts to 5 Recall doubles to 10, e.g. 2 + 2 = 4, Recall halves of numbers to 10, e.g. half of 8 is 4 Revisit doubles and halves to and from 10 Recall ‘five and’ facts, e.g. 5 + 4 = 9 Recall addition facts to 10, e.g. 6+ 4 = 10 Recall addition facts within 10, e.g. 4 + 3 = 7 Recall subtraction for ‘five and’ facts, e.g. 8 - 5 = 3 or 8 – 3 = 5 Recall subtraction facts to 10, e.g. 10 – 6 = 4 Recall subtraction facts within 10, e.g. 7 - 3 = 4 Recall doubles to 20, e.g. 7 +7 = 14 Recall halves of numbers up to 20, e.g. half of 18 is 9 Recall ‘ten and ‘ facts and the corresponding subtraction, e.g 10 +

5 = 15, 15 - 10 = 5 Recall multiples of 10 which add to 100 e.g. 30 + 70 = 100 Recall 2 times table and the related division facts Recall 10 times table and the related division facts Recall 5 times table and the related division facts Recall ‘5 and’ facts within 14, e.g. 5 + 7 = 12 Recall addition facts to 20, e.g. 14 + 6 = 20 Recall subtraction facts from 20, e.g. 20 – 7 = 13 Recall addition facts within 20, e.g. 8 + 9 = 17 Recall subtraction facts within 20, e.g. 17 – 8 = 9 Recall multiples of 100 that add to 1000 Recall 3 times table and the related division facts Recall 4 times table and the related division facts Recall 6 times table and the related division facts Recall 7 times table and the related division facts Recall 8 times table and the related division facts Recall 9 times table and the related division facts Recall multiplication facts with 10s, 100s and 1000s Convert fractions to decimals to percentages Divisibility rules for 2,3,5,9 and 10 Square numbers to 100 and their corresponding roots

Children will be working through the above at their own pace and will carry out a ‘quiz’ once a week to check progress. This will involve the children completing their ‘quiz sheet’ in no more than a minute and getting at least 18 out of 20. By doing this, the children are showing that these facts have become knowledge. Children love to keep a track of their own progress by completing related bar graphs which can be found at the back of their maths jotters.

Examples of basic facts ‘quiz’ sheets can be found on the school maths Blog.

Ideas to Support your Child at HomeMany of these activities require no resources and are very easy to practise. Children who do small bits of regular practice are showing the most improvement. Reinforcement of these concepts can be done in a spare five minutes whenever you get the chance.

Thank you so much for your continued support.

Early Level – (Nursery – end of P1)

Children at this age learn through play so make sure the activities are fun, we want children to understand that maths and numbers can be fun and not something they don’t like. Many of these ideas you will no doubt already be doing but hopefully there will be a few new ideas for you to try out!

Forward Number Word Sequences

Children should be encouraged to say forward number sequences (e.g. 1, 2, 3, 4, 5) as much as possible so they become confident with these. Numbers from 1to10, then numbers up to 20, then numbers beyond 20. Don’t always start at 1 when you are saying the numbers, try starting at different numbers.

Backward Number Word Sequences

Children should also be encouraged to say backwards number sequences (e.g. 5, 4, 3, 2, 1). Numbers from 5 to 1, then 10 to1. This is much more difficult than forwards counting and will take a lot of practice. Counting forwards up stairs then backwards when you go down is a good idea.

Number Songs

There are lots of songs which involve numbers suitable for Nursery age children. Many of these can be found on Youtube along with little videos which are fun to watch.E.g. ‘5 little ducks’, ‘1 little finger, tap, tap, tap’, ‘10 in the bed’. Children could try to hold up the correct number of fingers or set out figures to add on/take away along with the song lyrics.

Books

There are some lovely books available which involve counting and recognising numerals. Even when books aren’t specifically designed to teach numeracy, they can still be used to reinforce simple number concepts.

E.g. When reading the Gruffalo to your child you could ask, ‘How many different animals did the mouse meet?’

More or Less?An essential skill for children to develop is the understanding of working out ‘more’ or ‘less’ without

Recognising Numerals

counting.

E.g. ‘Do you think that I have more peas on my plate than you or less? Why do you think that?’

Counting ObjectsChildren should have opportunities to count real objects regularly, pointing to each object when counting to develop their ability to count accurately.

E.g. ‘How many teddiesare on your bed? Howmany cushions are onthe sofa?’

Numbers in the Environment

There are numbers all around us and children should be encouraged to look for these. Maybe pick a ‘Number of the Day’ when you are out shopping and see how many of themyour child can find.These could be spotted onnumber plates, road signs,clocks, door numbers, pricelabels etc.

Writing Numerals

Children begin to be able to write numerals by copying or overwriting. (Overwriting is when your child is just copying over a numeral which is already there.) Writing numerals can be done in a number of ways. People always think that paper and pencil is the only way to practise writing numerals but be creative and use other things which are available to you.

E.g. fingers in the sand, chalk boards,paint brushes with water on the gardenpath (in nice weather!), painting on stones, etc.

It is important that children form their numerals correctly right from the start so here is a quick guide to how these should be written.

0 1 2 3 4 5 6 7 8 9

Counting OnChildren should have opportunities to explore simple addition with objects that they can see. E.g. ‘You have 3 teddies on the rug, how many will you have if I put this one on?’

This leads on to more abstract concepts where they can’t see the objects e.g. the same example as above could be done but this time the teddies are in a bag so are unseen.

Practical SubtractionChildren should have opportunities to explore simple subtraction with everyday objects that they can see. E.g. ‘How many chips do you have on your plate? Now you’ve eaten three how many do you have now?’

As with addition, this then leads on to items that they can’t see. E.g. ‘I had four grapes in my tub but I’ve eaten two, how many must I have left?’

Recognising dice patterns

Playing games with a dice is an excellent way to develop your child’s numeracy skills. Your child will begin by counting the number of dots but will then begin to recognise the dot patterns without having to count the individual dots.

This is a really usefulskill to acquire and

Sharing

Through play, children should be encouraged to ‘share’ items fairly. E.g. ‘You have four teddies there, can you share them so that we both get the same amount? How many do we get each?’

Even at this early stage, children should be aware that sometimes items can’t be shared fairly. E.g.

will help them withtheir understandingof number.

‘There are seven toy figures, can you share them equally between the three teddies? How many do the teddies get each and how many are left over?’

Websites and Apps

As you will all know, technology is a great motivator for children! There are numerous websites and apps available with really good activities for young children to develop their numeracy. A couple of good ones are:

‘Learning4kids.net’ and ‘uk.ixl.com’.

Pinterest.com has a lot of super practical numeracy ideas.

There are lots of apps available, many of them free so try them out!

Meal Time Maths

Use meal times as a learning experience by talking about items of food.E.g. ‘You can take two pieces of bread today’ or, ‘You had four fish fingers and you’ve eaten one, how many are left now?’

Recognising Patterns

Children should be encouraged to look for patterns and numbers in everyday situations. E.g. when putting on socks they could notice that socks come in pairs or twos. Gloves always have five fingers; there are seven days in a week.

Some ideas for children working at the First Level

(P1 –P4 but mostly children in P1/P2). Simply increase/decrease the range of numbers according to your child’s needs. Reciting Number Sequences – no resources needed

Children need to continue to practise their short forward and backward number sequences up to for example, 45. Some are still unsure of 29, 30 and 39, 40 going forwards and backwards. If you feel your child is confident with these numbers and ready to move on, then increase the numbers a little bit at a time up to 100 and later onto 1000. Remember, don’t always ask them to start at 1 and make the sequences short. E.g. start at 28 and count to 33. Reciting the ‘tens’ numbers in order ‘on the decade’ 10, 20, 30, 40 etc. forwards and backwards is also a great idea to help them to see how the numbers increase/decrease. After children are familiar with reciting them on the decade they could practise counting forwards and backwards in tens off the decade e.g. 46, 56, 66 etc.

Number Words Before and After – no resources needed

Give your child three numbers in a sequence (within the same number range as above) and ask them to tell you what comes next, i.e. 26, 27, 28, _. Do the same for numbers before, i.e. 36, 35, 34, _. If your child can do this confidently, just give them the two numbers before, then finally just one number before and ask them, “What comes after__?” or “What comes before__?” Children are often good at doing this when it is a number like 16 but find it more difficult when the number is crossing a tens number. E.g. ‘What comes after 29?’ or ‘What comes before 40?’

Place Value – you will need some items which can be put into bundles and tied with an elastic band e.g. pencils, lolly sticks, cotton buds (TOP TIP - a simple way to get enough to practise larger numbers is to buy a box of plastic straws and cut them in half).

Ask your child to collect the items into bundles of ten and then put an elastic band around them, leaving some not bundled which can be used as ‘ones’. These bundles can then be used in a number of ways.

a) Set them out a bundle at a time and ask your child to count forwards and backwards in tens. If your child can do this easily, put the bundles into a bag or under a screen so they are unseen. Try adding two bundles instead of one and see if your child can jump up or down two bundles at a time.

b) ‘Show me__’, ask your child to show you a number. E.g. for ‘Show me 34’, your child would set out 3 bundles of tens and four ones. Or you can make a number using the tens and ones and ask them to tell you the number you have made. Your child can also practise writing the number s/he has made.

Addition – you will need a tub/box with a lid and some small items, e.g. buttons, pieces of pasta, paper clips, etc.

Here children need to move on from the figurative counting stage where they need to count from one (often using their fingers) to being able to ‘count on’ from a number. To help the children to develop this strategy, a simple activity can be done.

a) Ask your child to place a number of items in the box and put the lid on, then place some more items outside the box. Ask your child to work out how many altogether. You are looking for them to say the number in the box and then count on. E.g. 5 in the box and 3 outside the box they should say ‘5 - 6, 7, 8’, NOT 1, 2, 3, 4, 5 – 6, 7, 8. If they are tempted to go back to 1, encourage them to point to the box and say the number and then point to the items outside the box as they count on. (Resist the urge just to tell your child to start counting at the bigger number or counting

on, they need to figure this out for themselves.) Start with small numbers then once your child becomes confident with these, try increasing the numbers gradually. (Keep the number outside the box to 4 or less at this stage.) If you choose the same number in the box and outside the box we would expect your child not to use the ‘counting on’ method but just to know it.

b) Once your child can do this confidently, increase the difficulty of the numbers and try covering up the items which are outside the box and see if they can work out the totals without seeing the items. (You can increase the number outside the box up to 6 if they are confident with ‘counting on’ up to 4.)

c) Once the above activity has been mastered, you can move on to the stage where your child doesn’t have any items, just ask them to imagine them. So 7 add on 4 would be 7…8, 9, 10, 11 not 1, 2, 3, 4, 5, 6, 7… 8, 9, 10, 11.

Addition using the bundles and ones

Only do this activity when children are fully confident with the above activities.

For all of these activities start with the bundles and ones being seen, then once your child develops their confidence, start screening (hiding) them. Always let your child check their answers by looking at the resources afterwards when screening.

a) Use the bundles and ones to practise adding and subtracting. ‘I have 24, if I add another 2 ones, how many will I have now?’ or ‘I have 52, if I take out a bundle of ten, how many will I have left?’ Only add and subtract ones or tens at this stage, not both together.

b) Only move on to this activity when confident with activity above . As activity a, but now try adding and subtracting tens and ones e.g. ‘I have 36, if I add one bundle of 10 and 3 ones how many will I have now?’ Begin without crossing over any tens, e.g. set out 67 and take away a ten and 3 ones.

c) Only move on to this activity when confident with activity above . Now try crossing over the tens. E.g. 58 add on a ten and 6 ones or 41 take away 1 ten and 5 ones. These are harder, particularly the subtraction examples, and your child will need to ‘unbundle’ a ten to take some out.

Addition using playing cards – two suits given –

Playing cards are another great simple resource to use for practising number facts.

a) Practising pairs (take out face cards) – set all cards face down and play a game of ‘pairs’. Your child must work out the totals if they want to keep the pair though!

b) Addition within twelve (only use ace to 6 cards for this first activity) - pick two playing cards and add the totals. Children should now be able to work out addition facts within ten without using their fingers. The children will have been practising imaging dice dot patterns to help them instead of using fingers. E.g. for 3 and 5 they should picture 3 dots and 5 dots in their heads rather than putting up 3 fingers and 5 fingers. We are aiming for these facts to be automatic and ‘known’.

c ) Only move on to this activity when fully confident with activity above. Addition crossing the 10 (only use 5 to 10 cards) – as activity above but this time the numbers will be crossing above 10. Here, children are at the stage where they need to begin to realise that a simple ‘counting on’ strategy is NOT the most efficient way to work out a problem. (E.g. for 8 + 5 to think 8 - 9, 10, 11, 12, 13.) There are two different strategies which should be encouraged here.

* If the two numbers are doubles or close to doubles, then this knowledge should be used e.g. 7 + 8 could be thought of as 7 + 7 and 1 more or 8 + 8 minus 1.

* The second strategy is a bit harder and involves partitioning (breaking up) one number to ‘aim for 10’ then use their 10+ knowledge to help them. E.g. 8 + 5 could be thought of as 8 + 2 to make 10 and then 10 + 3 to make 13. (The 5 was split into 2 and 3)

Dominoes – real dominoes (or the cut out cards which can be found on the school maths Blog)

a) Look at the number of dots on the left side of the domino and then cover it. Then encourage your child to ‘count on’ the number on the right side to find the total.

b) ‘Flash’ the domino for a second and ask your child to tell you what they saw. Ask them to work out the total number of dots without starting at 1, but by using the ‘counting on’ method.

c) Use the dominoes to work out more difficult number problems by covering the dots on one side and telling your child the total number of dots on the domino. E.g. for a domino with four dots on both sides, tell your child that the total is 8 and show them a 4 on one side. Then ask ‘How many dots must be on the other side?’

Subtraction – counters (coins, stickers, tiddlywinks, buttons, etc.) and a screen (piece of paper, a magazine, an upside-down ice-cream tub, etc.)

There is a progression for developing their knowledge and this should be worked through in the following order - only move on when your child is confident at the previous activity. a) Set out a number of objects and let your child see them, then cover them up with the screen. Remove some of the objects and put them to the side of the screen and see if your child can work out how many are left under the screen. Encourage your child to point to the screen and say the starting number and then point to the items which were removed while counting backwards. E.g. 7-2 would be 7 – 6, 5. So there must be 5 left under the screen. b) Once your child can do this confidently, just tell them how many you have removed but hide them don’t show them. E.g. ‘How many are left under the screen if I have taken 2 out?’ See if your child can count back 2 without pointing to the removed items this time.c) The next step is to tell your child how many you have removed and they have to work this out. E.g. there were 8 paper clips under the screen, I’ve taken some out and now there are 6, how many did I take out? This is a much harder concept and may take a lot of practice to master. d) Lastly, don’t tell your child how many are under the screen to start with and see if they can work it out. E.g. I’ve taken 3 out and there are still 5 left, how many were there to begin with? Again, a much harder concept and one which may take a number of sessions to master.

With all these activities, it is important to let your child check the number of items once they have answered to see if he/she is correct.

Thank you to Carol Begge at Hillhead Primary School

Second Level – (P5 – P7)Many of the activities described above can be adapted to suit Second Level. Descriptions of a range of strategies for addition and subtraction and multiplication and division can be found above in the definition of terms. These explanations can be used to support your child with any homework they may have.

The most valuable experiences children can get would be to apply the strategies they have been taught in school to real- life contexts, e.g.:

- calculating a bill when in a restaurant- working out savings when a sale is on, e.g. what is the new

reduction/what was the original price?- in the supermarket compare similar products with different

quantities/offers… which bag of oranges is actually the best value?

The games and activities below also include suggestions for Second Level.

Playing lots of games – all ages!

Playing games provides really good opportunities for children to develop their understanding. The following list consists of games and activities which can be used at home. A description of each game and how to play it is on the New Zealand Maths website at:

http://www.nzmaths.co.nz/home-school-partnership-numeracy-activities

Additional games can be found in the ‘families’ section on the nzmaths website

Games to develop counting, place value, addition and subtraction

Rachel’s millions Grab Bag On and Back Doubles and Halves Froggo Car Plate Numbers Dice Number Track Card Number Track Make 10 Circus Clock Maths Gold Mine Monster I–scream Spider and Fly Dough Numbers

Bean on the Track Towers to 10 Rocket to 7 Difference Between Dice Add Up Action Cards Your Choice Salute Memory Horizontal Rocket Cover Up Kiwi Pile Up with 10 Frames What’s Missing? Bubble Jigsaws Bingo Teens and Tys Cover Up Cars I like Maths Doubling Using Finger Patterns

Games to develop multiplication and division

Multiplication Bubble Puzzles Start Unknown Kiwi Multiplication Motocross Multiplication Rocket Multiplication Four in a Row Multiplication Multiplication Madness Loopy Tennis Ball Multiplication

Additional suggestions for activities can be found on the following website: http://www.nzmaths.co.nz/maths-kete . Again, there are a range of activities for ALL levels.

Packs of cards are also great resources!

Please do look at the school’s maths blog for lots of ideas!

http://molmaths.wordpress.com

Other Websites which are useful are:

http://www.interactive-resources.co.uk

When using the Interactive Resources site, the pupil log-in is molpupil and the pupil password is school

http://www.maths-games.org/

http://nrich.maths.org/frontpage

www.woodlands-junior.kent.sch.uk/maths

www.bbc.co.uk/schools/website/4-11/sit/numeracy.shtml

www.topmarks.co.uk

www.EducationCity.com

http://www.sumdog.com