Download pdf - Lancashire Primary Mathematics Newsletter - … Lancashire Primary Mathematics Newsletter Summer Term 2011 The Lancashire Primary Mathematics Team Welcome back to another very busy

Lancashire Primary Mathematics Newsletter

SummerTerm 2011

The Lancashire Primary Mathematics Team

Welcome back to another very busy summer term. Let's hope we've not had the best of the year's weather over

the Easter break and there is some still left for sports days and school trips.

This term's theme is based on Counting and Place Value. These two areas of the mathematics curriculum

are essential building blocks for success, and recent research has suggested that children's lack of understanding

of our number system and reliance on naive counting strategies can severely hinder children's progress.

Our newsletter aims to support teachers and schools in these areas by:

Exploring children's development of counting;• Emphasising the links between counting and place value and other areas of the • mathematics curriculum;Highlighting progression and age related expectations in counting and place • value;Suggesting essential resources, and how to use them, to support children's • understanding of place value and development of counting strategies;Underlining the value and importance of existing resource materials including • Wave 3.

As well as the themed articles and items, there are also useful updates, more of which can be found on our website at www.lancsngfl.ac.uk/curriculum/math.

We value your feedback and any comments regarding the newsletter or website can be made using the links on the website or by emailing [email protected].

QUALITY AND CONTINUOUS IMPROVEMENT SERVICE

The Lancashire Mathematics TeamTeam Leader / Alison HartleySenior Adviser

Primary Mathematics Lynsey Edwards (Senior Consultant), Sue Bailey,Consultants Sue Farrar, Emma Radcliffe, Andrew Taylor, Peter Toogood

Team Contact Details Phone: 01257 516102 Fax: 01257 516103 E-Mail: [email protected] Write to: LPDS Centre, Southport Road Chorley, PR7 1NG Website: www.lancsngfl.ac.uk/curriculum/math

ContentsAPP - Evaluating the impact 3

Improving teaching and learning in mathematics 4

Courses and consultancy 6

Closure of the National Strategies and QCDA websites 7

Mathematics from stories 8

The Purpose of Counting 10

The Development of Counting 12

Number rhymes and songs 1 14

Common counting errors 16

Progression Through Counting – Levels and Year Group Objectives 18

Essential Resources to Support Counting and Place Value 20

Number rhymes and songs 2 22

Place Value – What is it? 24

Progression Through Place Value – Levels and Year Group Objectives 26

Puzzle Page 28

The Lancashire Primary Mathematics TeamThe Lancashire Primary Mathematics Team2

Team Information and Contents

The Lancashire Mathematics TeamThe Lancashire Primary Mathematics Team

Headline

The Lancashire Primary Mathematics Team 3The Lancashire Primary Mathematics Team 3

APP – Evaluating the Impact

Ofsted has recently published a report entitled 'The Impact of the ‘Assessing Pupils’ Progress’ Initiative'.

The research underpinning the report was conducted in 25 primary schools and 14 secondary schools across 11 local authorities and examined the extent to which assessment was used effectively to support learning.

The key findings of the report are:

The introduction of the ‘Assessing pupils’ progress’ initiative had helped to strengthen • assessment practice. However, impact was greatest when it formed part of a strongly led, clear, whole-school vision of teaching, learning and assessment that promoted high expectations and developed consistency.There were improvements in teachers’ subject knowledge, in their understanding of progression • in learning and in the accuracy of their assessment of pupils’ attainment and progress. The extent of the improvement in assessing pupils’ attainment and progress was, however, linked to the quality of other aspects of teaching, particularly in skills such as identifying and explaining objectives, questioning pupils and giving them precise feedback.By using the APP assessment criteria, schools were able to construct a detailed picture of the • strengths and weaknesses in pupils’ learning. Where this information was used well, lessons were better matched to pupils’ needs.Having a common framework provided teachers with a common language to discuss and agree • pupils’ progress. This improved the consistency of assessment practice, increased teachers’ accountability for pupils’ progress and helped to mitigate any loss of momentum in pupils’ learning at transition points.The implementation of assessment techniques based on this initiative had a positive impact • on the curriculum in the majority of the primary schools. In these schools, teachers adapted provision in the light of information obtained through this approach to assessment so that it built on pupils’ prior learning and included a better range of opportunities to develop and assess learning.Teachers’ engagement with the ‘Assessing pupils’ progress’ initiative helped to raise • expectations because they focused on pupils’ next steps in learning as well as their attainment of age-related National Curriculum levels.

The full report and summary documents are available to download from the Ofsted website at www.ofsted.gov.uk/publications/100226.


Improving Teaching and Learning in Mathema

4

Support for Mathematics Development in School

The Lancashire Mathematics Team is dedicated to supporting as many schools as possible

in Lancashire and beyond. No matter what type of school you work in, small or large, rural

or inner-city, outstanding or an Ofsted category, we pride ourselves in providing tailored

support that meets the needs of individual schools and networks of schools.

On the opposite page is a self-assessment audit for the provision of mathematics within your

school. Key areas to consider when auditing mathematics have been identified and some

have been layered so that subject leaders and senior leadership teams can precisely assess

the school's position in these.

Layer 1 is securing the basic foundations within the given theme, with the increasing layers

developing in complexity up to layer 4.

Other areas have not been layered, such as securing subject knowledge, progression and

pedagogy in different areas of the mathematics curriculum.

By using the audit, schools can prioritise areas for

development. The Lancashire Mathematics Team

can support in all layers across all areas, as well

as anything else to further develop provision for

mathematics in schools and across schools. We

are extremely flexible in the support we provide,

which can cater for the range of audiences from

whole schools or networks of schools to individual

teachers.

In the future, there will be a greater range of

courses available which will reflect the content of

the audit. The following page details what courses

and consultancies are available to book now, but

keep checking the Lancashire Mathematics Team

and Learning Excellence websites for updates and

details of course and consultancy arrangements.


atics

5

Layer 1 Layer 2 Layer 3 Layer 4

Planning a unit of work in mathematicsPlanning an effective teaching sequence based on the cycle of assess, teach, practise, apply, review (includes differentiation, pitch and expectation)

Planning for using and applying skills in mathematicsTeaching sequence revisited with focus on application of key skills at age-related level

Planning; Using Process Success Criteria to support understanding in mathematicsTeaching sequence revisited with focus on scaffolding learning

Planning for personalisation including individuals and groups (e.g. SEN, girls, more able children, EAL, GRT, children achieving level 2C at the end of KS1)

Subject knowledge in mathematics: Progression and pedagogyFocus on progression of key knowledge and pedagogical approaches in:- Place value and number sense- counting- mental calculations- written calculations- using and applying mathematics- shape- measures- handling data

Assessment Assessment for learning including:- Objectives and success criteria- An introduction to feedback- Using assessment to inform planning

Assessment- Supporting teacher assessment in MA2, MA3 and MA4- Developing effective questioning- Feedback and next step marking

Assessment- Moderation of mathematics in MA2, MA3 and MA4- Supporting teacher assessment in MA1- Self and peer assessment- Setting effective targets for mathematics

Assessment- Moderation across all attainment targets

Speaking and Listening Strategies to develop speaking and listening skills

Speaking and Listening- Developing children's use of mathematical vocabulary- Talking Maths

Speaking and ListeningUsing Talking Maths as an intervention programme

Speaking and ListeningMetacognitive talk and refining explanations

EAL (English as an Additional Language)Introduction to EAL pedagogy/strategies and how these link to learning in mathematics

EALFocusing on the acquisition of key vocabulary and addressing common difficulties

Girls and MathematicsAn overview of strategies and approaches which engage and motivate girls and build their confidence

Girls and Mathematics- Exploring practical ideas to engage and motivate girls in mathematics- Focus on EY, KS1, KS2, Whole school

Subject Leader’s Role- Introduction to subject leader role- Writing a policy document for mathematics

Subject Leader’s Role- Carry out audit of mathematics across school- Writing an action plan

Subject Leader’s Role- Monitoring and evaluation- Measuring impact

Subject Leader’s RoleDevelop classroom based CPD through Lesson study

Additional Areas of Support

Supporting newly qualified teachers in mathematics

Effective starter sessions in mathematics

Using ICT to enhance the learning and teaching of mathematics

Challenging all children in mathematics

Using practical equipment , models and images to support learning in mathematics

Integrating mathematics across the curriculum

Developing a mathematical learning environment

Supporting teaching assistants

Identifying and implementing intervention approaches

Involving parents in supporting their children's learning in mathematics (may include written calculations)

Mathematics in the foundation stage

Guided group work in mathematics

Closing the attainment and progress gap in mathematics

Transition Securing level 2 at the end of Key Stage 1

Securing progress across key stage 2 for those achieving level 2c at key stage 1

The Lancashire Mathematics Team66 The Lancashire Primary Mathematics Team

Courses and Consultancy

Our team of Mathematics Consultants and Teacher Advisers can support all schools in a variety of ways:Courses:

We continue to provide a wide range of marketed courses. Why not take a look at the Learning Excellence site to see if we are running a course which would benefit the professional development of a member of your staff?

You can access the Learning Excellence site directly (www.learningexcellence.net) or via a link on our own website at www.lancsngfl.ac.uk/curriculum/math/index.php?category_id=18.

We are also able to offer these courses as an INSET day or series of consultancies for your school or local network. Please contact us on 01257 516100 for further details.

Summer Term 2011

Autumn Term 2011

Consultancies:

We are also able to provide consultancies for individual schools or local networks which can be tailor-made to suit your needs or can be based on courses advertised on our site. These can be booked subject to the current rates as advertised on the Learning Excellence website www.learningexcellence.net or by phone on 01257 516100.

Some of the consultancies which have been proving to be popular recently include:

Practical Mathematics• Effective Starters• Mathematics and APP• Using and Applying• Numbers and Patterns• Mental Calculation Strategies•

We are currently planning our Summer Term Mathematics courses, so keep an eye out on the learning excellence website for further courses, and if there is a course that you are particularly looking for then please let us know and we will consider offering this in the near future.

19/10/2011 MAT115d Effective use of the Starter session in Mathematics Lessons

19/10/2011 MAT126c Practical Mathematics

24/11/2011 SEN151a Further Individual Numeracy Support (INS) Training for Teaching Assistants

t

05/05/2011 ABL701g Maths Boxes for Able Pupils

17/05/2011 MAT130a Numbers and Patterns: Laying foundations in mathematics

19/05/2011 MAT127a Progression and Continuity: Knowing and Using Number facts and Calculating

14/06/2011 MAT126b Practical Mathematics

14/06/2011 MAT504a Practical Mathematics

23/06/2011 MAT131a Teaching Mental Strategies

27/06/2011 MAT128a Realising the potential of ICT within Mathematics teaching Key Stage 1

29/06/2011 MAT129a Realising the potential of ICT within Mathematics teaching Key Stage 2

7The Lancashire Primary Mathematics Team

Closure of the National Strategies and QCDA Websites

The National Strategies website will be closing down in June 2011. The contents of the site will be moved to the National Archives where they will still be accessible.

The first stage in the closedown of the site will

be the removal of all ‘interactive elements’, including user log in, by the end of March 2011.

These elements also include groups, discussions and the ability to track e-learning progress.

"It is the Lancashire Mathematics Team's view that teachers continue to use the

framework as it provides effective planning support as well as promoting high

expectations linked to agreed national standards."

QCDA is also closing as part of the Government's education reforms. During March 2011 they

updated their website to reflect their reduced remit until the site closes on 1 October 2011.

All material held on www.qcda.gov.uk, both statutory and non-statutory, has been

transferred to the National Archives web archive.

There is already a link to this archive on the QCDA website.

The Lancashire Mathematics Team88 The Lancashire Primary Mathematics Team

Mathematics from stories

How Big is a Million? by Anna Milbourne

This is a new picture book to help children

understand the concept of big numbers. Pipkin the

smallest penguin is always asking questions, but

what he wants to know most of all is how big a

million is? So he sets off to find out.

A special fold-out poster at the end of the book shows Pipkin looking at the

sky, which is printed with exactly one million stars. It is beautifully illustrated

by Serena Riglietti.

We All Went on Safari: A Counting Journey

through Tanzania by Laurie Krebs

Join Arusha, Mosi and Tumpe as they set out on a

counting journey through the Tanzanian plains.

Along the way, they spy all sorts of animals -

elephants, lions and monkeys - while learning to

count from one to ten in both English and Swahili.

One is a snail. Ten is a Crab by April Pulley Sayre

and Jeff Sayre

If one is a snail, and two is a person... we must be

counting by feet! Children will love this hilariously

illustrated introduction to simple counting and

9The Lancashire Primary Mathematics Team

multiplication with big feet and small - on people and spiders; dogs and insects;

snails and crabs - from one to one hundred

Fruits by Valerie Bloom

How much fruit do you think one small girl can manage to

eat in one day? Count from one to ten and learn the names

of some Caribbean fruits.

Count on Goz by Steve Weatherill

Baby Goz sets out to find his family. Lift the flaps and

count how many other animals he meets! A great first

counting book.

In My Garden by Ward

Schumaker

In this garden the reader learns to count from one

watering can to ten snails; from twenty weepy onions to

fifty cherry pies and even to 233 peas.

Centipede's 100 Shoes by Tony Ross

A counting story involving a centipede with sore feet

trying to give his shoes away to his garden insect

friends.

The Purpose of Counting

The Lancashire Primary Mathematics Team10

Research has shown that young children do not understand the purpose of counting. Many children see counting as a social experience, which is performed for pleasure or to please others. It is rare for young children to explain that counting is ‘to know how many’.

Dr. Penny Munn observed that:

during joint counting activities between very young children and adults the process of saying • words seems important, but the actual aim of finding quantity is often not emphasisedthe strength of children’s own natural concentration on the physical aspects of counting • activities, touching and handling, often obscures the intended mental function of finding quantitychildren are dependent on adults to provide for them, they have no urgent real reason to check • and tally, so counting is usually a gamecounting words often occur as parts of games that are not to do with quantity, e.g. One, two, • three – go!

Excerpt taken from 'Counting – a deceptively simple skill' – Les Staves (NCETM)

The relevance of counting skills across the maths curriculum

We often ask children to count aloud at the beginning of lessons, but do children see the relevance of this in other areas of learning. If the children do not make the links themselves, then we have to make those links for them.

Multiplication

Counting on in equal groups

Shape

Counting sides and angles

Measures

Reading scalesCounting squares

for area

Handling Data

Reading the y axis that may be in different steps;

Tallying (counting in 5s)

Division

Counting back in equal groups

Addition

Counting up from one number a given amount (the other number) to find the total.

Subtraction

Counting on to find the difference and

counting back to take away.

Counting

Starter counting activity

Framework objective Possible strategy involving counting

Count forwards and backwards in 10s starting from any number

Calculating

Year 2 – add or subtract mentally a one-digit number or a multiple of 10 to or from any two-digit number...

Consider 47 + 30One method of solving this would be to count on 30 from 47 in three jumps of 10, which would be modelled on a number line like this:

Identify missing numbers within a counting sequence

Measuring

Year 3 – read to the nearest division and half-division, scales that are numbered or partially numbered...

How much sugar hasbeen added to the flour?

Use a counting stick to recognise the steps of 100 and then work out intermediate steps of 50 before finding the difference between 450g and 600g.

Count in 2s forwards and backwards from any given number

Handling data

Year 2 – represent data as block graphs or pictograms to show results

If each represents 2 people, how many people are represented by each column, and how many children are represented in total?

Create and continue the sequence of triangular numbers

Using and applying

Year 6 – recognise and interpret sequences, patterns and relationships involving numbers...

Describe in words how the sequenceis changing. Tabulate the sequence in order to support the identification of a rule for the nth term.

Term Triangular number 1 1 2 3 3 6 4 10 n n² + n 2

The Lancashire Primary Mathematics Team 11

The table below demonstrates how counting can be used in different contexts across the mathematics curriculum. Whilst counting can be a relatively quick element of the starter session, children need to see how it can be applied.

The Development of Counting


Counting is an essential skill which

underpins many areas of later

mathematical knowledge and

understanding. It is, however, a

complex area which comprises

a number of different

principles.

These universally acknowledged five principles of

counting were identified by Rochel Gelman and C R Gallistel in their 1978 book 'The Child's

Understanding of Number'. Whilst the names of these principles are not important, it is important

that children experience all these elements in order to fully develop their knowledge and

understanding of counting.

How to count principles

The one-one principle

The understanding that when counting, each object

counted has to have a distinct word, or number name,

assigned to it. A child who gives each item a different

number name, irrespective of whether these names

are in the correct order understands this principle.

However, a child who repeats number names, for example counting 2, 3, 4, 4, does not.

The stable-order principle

To count effectively, the list of number names must always

be in the same order and follow the conventional list of 1, 2,

3, 4... Children who use the same order of counting all the

time, irrespective of whether it matches the convention, are

following this principle.

kill which

ater

and

ever, a

prises


The cardinal principle

The cardinal principle refers to the fact that, when

counting a group of items, the last number counted

is the total number for the set. Children who do not

understand the cardinal principle will often have to

recount the items when asked how many there are.

What to count principles

The abstraction principle

Children should understand that the one to one, stable order and cardinal principles can be

applied to any group of entities irrespective of size, appearance or similarity and whether these

can be seen or touched.

The order-irrelevance principle

Children should know that, when counting, as

long as each item is counted only once, how the

items are counted is irrelevant and that even if

these items are rearranged, the total will remain

unchanged.

You may find the following resources helpful:

The Child's Understanding of Number – Rochel Gelman and CR Gallistel

Understanding Mathematics for Young Children: A Guide for Foundation Stage and Lower

Primary Teachers – Anne Cockburn and Derek Haylock

Teaching and Learning Early Number – Ian Thompson

Counting – A Deceptively Simple Skill – Les Staves (https://www.ncetm.org.uk/resources/17690)

If children have an issue with counting it

may be that only one of these principles is a

barrier. Further investigation will enable the

specific barrier to be identified. If this is done

at an early stage it will prove less of a problem

to future mathematical development.


Number rhymes and songs 1

Sing a song of pocket money sung to sing a song

of sixpence (can be differentiated with amounts)

Sing a song of £5

A pocket full of money

Standing in the newsagent

My brain is feeling funny

23p a comic

That's what I'll have to pay

So how much change will I have left

To spend another day?

Monkeys On the Bed

(Action poem)

Five little monkeys jumping on the bed

One fell off and bumped his head

Mummy called the doctor and the doctor said,

"No more monkeys jumping on the bed!"

Four little monkeys...

Three little monkeys...

Two little monkeys...

One little monkey...


Here is a Beehive

(A fingerplay)

Here is the beehive, where are the bees?

(Clench fist)

Hidden away were nobody sees

Watch and you will see them come out of their hives,

(Bring out fingers quickly one by one)

One, two, three, four, five,

Buzz, buzz, buzz.

Counting Apples

(A fingerplay)

Five red apples

Hanging on a tree (five fingers held up)

The juiciest apples you ever did see!

The wind came past

And gave an angry frown (shake head and look angry)

And one little apple came tumbling down.

Four red apples, etc.

y)

Common Counting Errors


'Supporting children with gaps in their mathematical understanding'

This resource, better known as 'Wave 3 Mathematics', has been available since 2005 and contains a number of practical teaching sessions focused on helping children overcome common difficulties in number and calculations. The resource is organised into two sections, Addition/Subtraction and Multiplication/Division, for the Year groups Reception, Year 2, Year 4 and Year 6. These year groups have been chosen as representative milestones in a child's development, but the materials are designed to be used to support children in all year groups who demonstrate difficulties catered for in the pack.

An example of a Reception teaching session is given below and supports children who have some of the following difficulties:

Can only begin counting at one; inaccurately counts objects when rearranged and has no consistent recognition of small numbers of objects. They also lack a systematic approach to counting.

Teaching activity

We are going to look at our concept map today to remind us what you have learned so far about counting, then we are going to do some work with these hoops, balls and bricks.

Can you remember from the last session what happened when we moved things from a short • line to a long line? (Help the child to talk about the number of things staying the same even when they were in a longer line.)Build two towers (with different-sized bricks), both with the same number of bricks. •

Hoops, balls and bricks

ResourcesSmall and large bricks• Number cards (Resource sheets 1 and 2)•

Key vocabularyhow many? count on, count back, same, different, larger, smaller, taller, shorter, tally.

Time 10 - 15 minutes


Which tower is taller?• How many bricks in the short tower? How many in • the taller tower?So are there more bricks in the taller tower? •

If the child is unsure about this, you might find number cards helpful – both towers need a 4 card.

Emphasise that there are the same number of bricks, but some of them are larger so those make a taller tower.

There are several important aspects related to counting and measuring that the child will need to understand, for example, taking long paces. Count how many of your paces from one side of the room to the other. Then ask the child to take ordinary sized steps across the room.

Why do you think it was only six of my paces but ten of yours?• (You need to get to the idea that the smaller the pace, the more you need to measure the same distance.)

Lay out some hoops and small and large balls like this:

What do you notice about the number of balls in each hoop?

Repeat with other items if needed, for example 1p and 2p coins in purses, bulbs in flower pots and so on, until the child is clear that the number can be the same even when it might look as if there is more of something.

If the child needs more support you might find that making a tally for each object can focus the child onto the number and away from the visual impression of size.

What did you learn new today?• Who has got the smallest hands? How many • little hand spans across the table? How many of my big hand spans across the table? What is happening?If we covered the carpet with lots of these small • rectangles of paper, would we need more of them or fewer of them than if we covered the carpet with these large pieces of paper?

Further activities from the pack, centred on number and calculations, can be found on the Lancashire Mathematics Team Website (intervention section) or on the Lancashire Planning Support CD.

Progression Through Counting – Levels and Yea


The following table illustrates the progression through children's understanding of counting from the Early Learning Goals to Level 5 and also through the year groups to Year 6/7.

The examples on the opposite page are taken from the Securing Level suite of materials, Pitch and Expectations and 1999 Framework – Supplement of Examples

Level features Objectives

EYFSP NLC 2Counts reliably up to 3 everyday objects.EYFSP NLC 3Counts reliably up to 6 everyday objects.EYFSP NLC 4Says number names in order.EYFSP NLC 5Recognises numerals 1 – 9.EYFSP NLC 6Counts reliably up to 10 everyday objects.

EYFS 40-60+ MonthsCount up to three or four objects by saying one number name for each item.• Count out up to six objects from a larger group.• Count actions or objects that cannot be moved.• Begin to count beyond 10.• Count an irregular arrangement of up to ten objects.• Estimate how many objects they can see and check by counting them.• Count aloud in ones, twos, fives or tens.• Know that numbers identify how many objects are in a set.•

Level 1Count up to 10 objects.

Year 1Count reliably at least 20 objects, recognising that when rearranged the number of objects • stays the same.Estimate a number of objects that can be checked by counting.• Say the number that is 1 more or less than any given number, and 10 more or less for • multiples of 10.Count on or back in ones, twos, fives and tens.•

Level 2Count sets of objects reliably.Recognise sequences of numbers, includ-ing odd and even numbers.

Year 2Describe and extend number sequences and recognise odd and even numbers.• Count up to 100 objects by grouping them and counting in tens, fives or twos.• Describe and extend number sequences.•

Level 3Recognise negative numbers in contexts such as temperature.Recognise a wider range of sequences.

Year 3Count on from and back to zero in single-digit steps or multiples of 10.•

Year 4Recognise and continue number sequences formed by counting on or back in steps of • constant size.Use positive and negative numbers in context.•

Level 4Recognise and describe number patterns. Year 5

Explore patterns, properties and relationships.• Count from any given number in whole-number and decimal steps, extending beyond zero • when counting backwards.Use sequences to scale numbers up or down.•

Year 6Represent and interpret sequences, patterns and relationships involving numbers.•

Level 5Recognise and use number patterns and relationships.

Year 6/7Generate sequences and describe the general term.•

ar Group Objectives


Count a collection of up to ten objects in more difficult formations, using a strategy for keeping track of where the count begins. For example:

Count objects that are out of reach: for example, panes in windows, pictures on the wall, • lights hanging from the ceiling…Count objects in a ring, such as different coloured beads on a necklace or a group of • children in a circle, marking the starting point in some way.Count some mixed objects that vary markedly in size.• Count some moving objects: for example, children playing, floating objects, fish in a fish • tank, hatched chicks, the bubbles that I blow…Begin a count starting with a named object: for example, count the animals starting with • the horse.

Count up from one as far as you can, saying each number clearly. Continue this sequence - count until you get to zero: 17, 16, 15...

Put 5 bricks in a line, 5 cubes in a cup, 5 animals on top of a box, 5 beads in a bowl... Is there the same number of each?

Here are some numbers in a sequence: ..., 7, 9, 11, 13... Will the following numbers be in the sequence: 3, 16, 21, 58? Explain how you know.

Write the missing numbers in this sequence. 53, 48, 43, 38, �, �, 23, 18, Explain how you identified them.

Count in equal steps including counting in decimal numbers and measures, for example: 25cm, 50cm, 75cm, 1m, 1m 25cm...

Find the missing numbers: �, 738, �, 718, 708, �

Find the missing number on this number line.

A sequence starts at 500 and 80 is subtracted each time. 500, 420, 340, ... The sequence continues in the same way. Write the first two numbers in the sequence which are less than zero.

The rule for a sequence of numbers is ‘add 3 each time’. 1, 4, 7, 10, 13, 16 … The sequence continues in the same way. Mary says, ‘No matter how far you go there will never be a multiple of 3 in the sequence’ . Is she correct? Explain how you know.

Essential Resources to Support Counting and Pl


Base 10 equipment/ bundles of straws

Exemplifies the relationship between hundreds, tens and units.Can be used to demonstrate what happens with calculations and to model the 'difference in value' between one number and another.

Arrow Cards

Use arrow cards to make numbers, e.g. 27, 247, 702, 74, 740 What numbers would these arrow cards represent? 40 + 3 500 + 30 + 1 600 + 5 Show me a number that doesn’t contain any units/tens/hundredsMake a three digit number with the digits all the sameMake a number between . . . 70 and 80 320 and 330

Counting stick

Counting in stepsCount along in multiples of numbers; 4, 8, 12 etc.Label a place with a key number e.g. 24 and ask pupils to work out the value of other markings.Ensure that zero is not always at the end of the counting stick to enable children to work with negative numbers.Use the counting stick vertically to model a scale or the y axis on a graph.

Place Value Dice

Use the dice to generate numbers. Good for reinforcement of partitioning and recombining numbers.

Numicon

This resource can help to reinforce the concept of grouping in tens and the symbolic system for recording numbers where the place of the digit signifies its value.

lace Value


Number tracks

In a number track, each number occupies a cell and identifies or labels that cell. The numbers should start at 1 (not at 0) and each number may have an illustration matching the amount. Number tracks can be used to support the reading of numerals and locating numbers by using their order.

Number lines

In a number line, the divisions rather than the spaces are numbered. This means they can begin at any number, they can show any number sequence and ultimately they can be expanded ‘backwards’ into negative numbers or enlarged to show decimal numbers and fractions. They allow the continuous nature of number to be represented and encourage children to count in steps.

Hundred Grid

When children are starting to use a hundred grid, show them that it is a number track that has been cut up and reorganised into rows of tens, as this will support their understanding.

Thing on a String

The thing on a string helps to regulate the speed of the count and prevent children from racing ahead of others in the group. The string can be lengthened or shortened to speed up or slow down the count.

Money

Use to support counting in1s, 2s, 5s, 10s, etc. Ask children to close their eyes and count when they hear the coins drop into the tin. Tell the children that there is 7p already in the tin and you are going to add some 5p coins. Record the count as 7p, 12p, 17p, 22p... What do the children notice and why?

Using 1p, 10p and £1 coins supports children's understanding of place value and our base 10 number system, by exchanging, for example, ten 1p coins for one 10p coin.

1 2 3 4 5 6 7 8 9 10


Number rhymes and songs 2

One little elephant

(Counting up)

One little elephant went out one day

Upon a spiders web to play;

He found it such tremendous fun,

He sent for another elephant to come.

(2,3,4,5….)

One, two, three, four, five

(Counting up)

One, two, three, four, five

Once I caught a fish alive

Six, seven, eight, nine, ten

Then I let it go again

Why did you let it go?

Because it bit my finger so

Which finger did it bite?

This little finger on my right.


Five little seashells(Subtracting Numbers)

Five little seashells

(Hold out five fingers.)

Lying on the shore.

Swish went the waves

(Open your other hand and pass it over the five

fingers and make a light fist with the first hand.

Pass the open hand back over the first,)

And then there were four.

(... and hold out four fingers.)

Continue these motions for the following verses:

Four little seashells, pretty as can be.

Swish went the waves. Then there were three.

Three little seashells, all pearly new.

Swish went the waves. Then there were two.

Two little seashells, lying in the sun.

Swish went the waves. Then there was one.

One little seashell, lying all alone.

I picked it up.

I took it home. (...and put it in your pocket.)

Counting by...

Hey kids, it’s time to count today. Let’s count by 1’s.

You know the way: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.


You know the way: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.


You know the way: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.


You know the way: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

Place Value – What is it?


So when we consider the two numbers 36 and 68 we can recognise that the 6 in each number is representing a different amount (6 units or ones in 36 and 6 tens or 60 in 68).

The elements of place value children need to understand include:

Therefore, the definition could be expanded to include:

Recognising the value of a number in relation to other numbers in our number system.

This understanding can be shown when children are asked to order numbers on a partially labelled number line, particularly when the number line does not start at 0 and end at multiples of 10 or 100.

Position these numbers on this number line:

Base 10

One of the key resources to develop children's understanding of place value is Base 10 equipment, but do children understand why it is called this and the importance of the number 10 in our number system?

Our number system is based on the number 10. Every possible number can be represented by a combination of the ten digits 0 – 9 and when considering the positions within a number as you move from right to left the digits increase in powers of 10 i.e. there are 10 units in every 1 ten, there are 10 tens in every 1 hundred and so on.

This principle of 'ten of those are the same as one of those' is crucial to children's confidence in dealing with numbers.

45 31 60

24 72

Write numbers

Read numbers

Round numbers

Position numbers Partition numbers

Compare numbers

Order numbers

Place Value

A very simple definition might be:

"The value of a digit within a number is determined by its position or place."


Use base 10 equipment, bundles of straws and 1p, 10p and £1 coins to allow children to experience exchanging between units/ones, tens and hundreds and vice versa, as this will support their understanding of calculations involving 'carrying', decomposition and multiplying and dividing by 10 or 100.

One way of modelling 17 x 10 could be to take each element of the number, 1 ten and 7 units, and increase them 10x:

This allows children to see why moving the digits one place to the left 'work' for multiplying by 10. This way of modelling could be extended to multiplying by 100 and dividing by 10 and 100.

The Lancashire Mathematics Team website contains a variety of resources linked to base 10 materials including:

A Powerpoint demonstration of how to model decomposition • using base 10 equipment and arrow cards;

A selection of number lines scaled • so that base 10 equipment can be used with them.

Progression Through Place Value – Levels and


The following table illustrates the progression through children's understanding of place value from the Early Learning Goals to Level 5 and also through the year groups to Year 6/7.

The examples on the opposite page are taken from the Securing Level suite of materials, from Level 1 to Level 5 and from Pitch and Expectations.

Level features Renewed Framework Objectives

EYFSP NLC 4 Says number names in order.EYFSP NLC 5Recognises numerals 1 – 9.EYFSP NLC 7 Orders numbers up to 10.EYFSP C 2Recognises differences in quantity when comparing sets of objects.EYFSP C 7Finds 1 more or 1 less than a number from 1 – 10.

40-60+ months- Begin to represent numbers using fingers, marks on paper or pictures.- Select the correct numeral to represent 1 to 5, then 1 to 9 objects.- Know that numbers identify how many objects are in a set.- Match then compare the number of objects in two sets.- Use language such as 'more' or 'less' to compare two numbers.- Find one more or one less than a number from one to ten.

Level 1 Order numbers to 10.

Year 1 - Compare and order numbers, using the related vocabulary; use the equals (=) sign.- Read and write numerals from 0 to 20, then beyond.- Use knowledge of place value to position numbers on a number track and number line.- Say the number that is 1 more or less than any given number, and 10 more or less for multiples of 10.

Level 2 Begin to understand the place value of each digit; use this to order numbers up to 100.

Year 2 - Read and write two-digit and three-digit numbers in figures and words.- Explain what each digit in a two-digit number represents, including numbers where 0 is a place holder.- Partition two-digit numbers in different ways, including into multiples of 10 and 1.- Order two-digit numbers and position them on a number line.- Use the greater than (>), less than (<) signs.

Level 3 Understand place value in numbers to 1000.Use place value to make approximations.Order decimals with one decimal place, or two decimal places in context of money.

Year 3 - Read, write and order whole numbers to at least 1000 and position them on a number line.- Partition three-digit numbers into multiples of 100, 10 and 1 in different ways.- Multiply one-digit and two-digit numbers by 10 or 100, and describe the effect.

Year 4 - Partition, round and order four-digit whole numbers.- Use positive and negative numbers in context and position them on a number line.- State inequalities using the symbols < and >.- Use decimal notation for tenths and hundredths and partition decimals.- Position one-place and two-place decimals on a number line.- Multiply and divide numbers to 1000 by 10 and 100 (whole number answers), understanding the effect.

Level 4 Order decimals to three decimal places.Use place value to multiply and divide whole numbers by 10 or 100.

Year 5 - Relate whole and decimal numbers to their position on a number line.- Explain what each digit represents in whole numbers and decimals with up to two places, and partition and order these numbers.- Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000.

Year 6 - Use decimal notation for tenths, hundredths and thousandths, partition and order decimals with up to three places, and position them on the number line.

Level 5 Order fractions and decimals.Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 and 1000 and explain the effect.Order negative numbers in context.

Year 6/7 - Compare and order integers and decimals in different contexts.- Order a set of fractions by converting them to decimals.

Year Group Objectives


Max puts these numbers in order, from smallest to largest. What would be the third number? 835, 535, 538, 388, 508

The temperature at noon on Monday is –2°C and on Tuesday is –6°C. Which day was warmer at noon? Explain how you know.

Which is larger, 1/3 or 2/5 ? Explain how you know.Write these fractions in order of size.

Put these birthday cards in order, starting with the smallest value.

2 8 74 5

Numbers in this count are mixed up. Can you put them in order?18, 16, 17, 15, 13, 14, 12, 10, 11Look at these number cards.Which card shows the smallest number?Put the numbers in order, from smallest to largest. 15 7 5 12

If you write these numbers in order, smallest first, which number comes third?37, 13, 73, 33, 3

Write the same digit in each box to make the number sentence true: � 1 > 6 �Now do the same for this number sentence: � 1 < 6 �

Put the correct symbol, < or >, in each box. 3.03 � 3.3, 0.37 � 0.327Order these numbers: 0.27 0.207 0.027 2.07 2.7

3 3 9 17

4 5 10 20

Puzzle Page


Answer to last term's puzzle

Imagine you have 27 balls and a balance but no weights.

All the balls look the same but one weighs more than the others.

How can you find the heavier ball by using the balance only three times?

By using the rules given for each colour shirt, and knowledge of inverse operations, the following

answers should be found (numbers already given are in red):

5 9 10 19

4 8 8 16

3 7 6 13

2 6 4 10

1 5 2 7