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These templates are all set to print as one per page. To reduce the size select 'multiple' in the print options and ensure 'landscape' is selected.

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These templates are all set to print as one per page. To reduce the size select 'multiple' in the print options and ensure 'landscape' is selected.

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Sing along and learn all about numbers with the Numberblocks!

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Counting Series - Session 2 - Subitising

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The Count On Races game, played by an adult and a child, helps children learn to count on mentally. A coin or a dice with 1 or 2 on each face is used. Children say the next number when counting on. For example, when starting from 7, for a jump of 2 we say '8,9'.

The Cube Model (4-6) and Cube Model Advanced (4-6) tasks, children recreate the models. This task develops visual-spatial skills and helps children to recognise two parts within the whole.

The Reasoning in Addition Puzzles get children thinking deeply about the value of different shapes. This Mathsbot link allows you to generate new reasoning in addition puzzles.

Visual Representations

This article explains the importance of children's finger discrimination skills and this article gives different ways in which fingers can be used. Here are some Finger Discrimination tasks by Youcubed.

These Base-5 and Base-10 Number Tracks are coloured to help children to see quantities within a number track.

This Online Base-5 Abacus by Math Rack represents quantities 10-100 using a base-5 colouring.

The Coloured 100-Squares help to identify patterns in the 100-square and can support children as they count in 2s and 5s.

The Teens & Tens Cards help children to discern between teen and tens numbers. The Place Value Sorting Task show different representations of teen numbers and challenge children to spot misconceptions.

Progression in Pattern

The Progression in Pattern guidance shows how children's understanding of repeating patterns can be built. The Grids for Repeating Patterns can be used as children look to create circular patterns with a fixed number of spaces.
Number Foundations Assessment Fluency in Calculation Within 20 Spatial Reasoning in Early Childhood, Early Childhood Maths Group
Deconstructing Word Questions KS1 Tasks and Build-Up Presentation

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A range of resources and games for building children's early number sense with small quantities and developing conceptual understanding.

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Realising the Ambition: Being Me builds upon the original principles and philosophy of Pre-Birth to 3 and Building the Ambition. The new guidance retains the relevant content from the previous guidance which it replaces, extending and strengthening it in line with current research and evidence about how children develop and learn.

This refreshed early years national practice guidance for Scotland presents key information about the characteristics of child development based on research and evidence.

In essence, 'Realising the Ambition: Being Me' increases expectations of high quality but still provides the necessary support for all who work in the early years sector and beyond.

Explore this resource

High quality provision consists of many different interconnected aspects. The imagery of tartan has been used in the guidance to remind us of the uniqueness of our Scottish context - with each section seen as an interconnected thread contributing to the whole piece. Although each section has been developed so it can be used in any order to meet different needs and different contexts, we must always be mindful of this bigger picture.

The terms of 'when I am a baby', 'when I am a toddler' and 'when I am a young child' have been used to illustrate developmental needs over time - but these should not be seen as rigid lines of progression. All babies and young children develop their individual skills, knowledge and attributes at different rates according to who they are. The guidance can be used to support children with more complex needs by taking this into account.

The guidance can be used individually, or in short informal group settings where practitioners have time to come together, or as part of a more substantial CPL programme. We would recommend that at points of transition between ELC and primary school, the guidance can be used by designated staff working together to promote a clear understanding of curriculum progression and continuity in children's learning and development.

Please note that the link to the Leuven scales on page 50 is no longer live. Alternative links are provided in the 'Related links' section below.

Challenge questions

The Challenge Questions PowerPoint contains suggested challenge questions for each section of Realising the ambition: Being me.

Webinars

Our live Realising the Ambition sessions have already been delivered to thousands of early years educators across Scotland. We now have a recorded version available to enable you to share or recap on the themes.

1. Realising the Ambition overview part 1 discusses the guiding principles and the importance of the imagery used in the guidance.

2. Realising the Ambition overview part 2 looks at pedagogy in practice and transitions.

3. Realising the Ambition Overview for Childminders was produced in partnership with the Scottish Childminding Association.

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Education Scotland is a Scottish Government executive agency responsible for supporting quality and improvement in Scottish education.

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Article by Dr Sue Gifford University of Roehampton

Download pdf
Young children have a remarkable skill: they can recognise numbers of things without counting. This is called subitising, and it develops from a very early age. Very young babies can not only tell the difference between one and two but also between large numbers of dots when there are twice as many in one group, as with 16 and 8 (Sarama and Clements, 2009). Young children also have powerful visual memories and some may find it easier to remember images than words: three-year-olds can recognise three things, although they may not say the word. Subitising can help children to build images for numbers, to visualise and to learn number facts. For instance, most four-year-olds readily learn to recognise five dots on a dice, which helps them to understand the cardinal value or 'howmanyness' of five, which they can link to the word and symbol for 5. Structured images like this also help children to begin to see numbers inside numbers, for instance seeing four and one within five.

How do you teach subitising?
Children's ability to subitise can be developed by teaching. Games provide repeated experience of interpreting the dot images, either to decide how many spaces to move, as in our activity Playing Incey Wincey Spider, or how many things to collect, as in our activity Dice, where the dotty number determines how many animals to put in your pen. (To find both of these activities, scroll down the collection of number based EYFS tasks.) For children who are unfamiliar with dot images, dice can be adapted to just show numbers up to three. Large dotty dice are good for outdoor games, like jumping along the track. Spinners with dots on provide an alternative, as with the child in the picture, who has his own spinner on a lanyard: he spins it and then makes that many jumps around the circuit track, then does the same again and again and again..! Having your own dice or spinner is a good option for younger children and avoids waiting for turns.

Large floor dominoes invite children to match number patterns, indoors or out.

Fingers also provide subitisable images for numbers, with the added advantage that they are embodied in muscle memory. Showing all-at-once finger numbers is the key skill here: Marton & Neuman (1990) found that older children with maths difficulties tended to count fingers one at a time, rather than using all-at-once 'finger numbers'. You can ask young children to first 'grow', then 'show' and finally to 'throw' finger numbers.

Using a range of objects and apparatus in different arrangements helps to make children familiar with different images for numbers, while also emphasising different number properties. For instance, Numicon presents numbers as even or odd, whereas linked cubes show numbers as lengths: connecting all these images helps children build a rich network of understanding to link to number words and symbols.

Subitising games can involve less common arrangements of numbers of objects. Games which involve revealing hidden objects will prompt young children to say how many they see (see the NRICH activity Hidden Jewels). One game involves upturned dishes hiding three, four and five objects, rapidly swopping them around and challenging children to keep track of the dish with four. When you stop and briefly lift the dish, children intuitively subitise the number revealed. This activity is taken from Clements and Sarama's very useful website, which presents a learning trajectory for subitising, supported by videos of activities for each stage.(If you have not already done so, you will need to create an account before accessing the free resources.)

https://www.learningtrajectories.org/math-activities/fantastic-five-tricky-two

Activities include auditory subitising, or recognising numbers of sounds, such as claps or drum beats, linking with movement and music.

Conceptual subitising
Subitising can also help children learn addition and subtraction facts. In some of the images below the total number of five is recognised by adding subgroups, like three and two, or four and one (Back, 2014 - see the NRICH article Early Number Sense). This involves part-whole awareness, which enables children to simultaneously see the whole number and numbers which make it up. The ability to think about numbers as compositions of other numbers was described by Resnick (1983) as 'probably the major conceptual achievement of the early school years'.

Recognising how many there are by combining numbers of smaller subgroups is called conceptual subitising: this is more advanced than perceptual subitising, which involves instant recognition (Clements, 1999). Seeing numbers as combinations of other numbers helps children to develop part-whole awareness and build familiarity with number combinations. It is also much more effective than giving children number sentences to complete by counting cubes and hoping they will remember the numbers involved!

Number talks
Showing children 'quick images' and asking them how many they see is one way of developing subitising. An alternative way of developing conceptual subitising is to show children a number of dots and ask them to say how they see the number (see the NRICH activity Number Talks). Teacher Janine Davenall engages young children by showing an image and asking, 'What numbers can you see hidden inside this number?'

They may reply, 'I see three and four', or 'six and one' or 'two and two and two and one'. This is an inclusive activity with many 'right' answers and the opportunity to discover that others see the same thing differently. Children also learn about all the different combinations which can make the same number. An alternative is to use giant magnetic buttons on a tray, which you turn over to secretly rearrange and show different combinations of the same number.

( www.teachingchannel.org/videos/visualizing-number-combinations)

Not only do younger children respond more to real objects than to images on a screen, but they can also see that the number of buttons stays the same despite being rearranged.

More complex images can present greater challenges for some children. Mulligan and Mitchelmore (2009) showed young children a 6 dot triangle and asked to draw it from memory: they found their responses varied significantly, with some just drawing a lot of dots.

Even when asked to copy the image, many five-year-olds produce dotty triangles like the one on the right, apparently finding it hard to focus on the number and the arrangement of the dots (Gifford & Thouless, 2018). This implies that some children will need a lot more practice in looking and talking about number patterns, in order to see how they are organised. Daily 'number talks' can help children to analyse and visualise number images, building an understanding of cardinal values, like the 'sixness' of six.

Reception children enjoy creating their own arrangements for numbers like seven and nine, and seeing which their friends recognise most easily. Older children with mathematics difficulties found the 'lollipop seven' image most memorable, at the same time learning a key number fact, that four and three make seven (Emerson & Babtie, 2010).

In Hungary, children are taught to recognise such numbers as 'five and a bit', using the dice image for 5 and linking with finger numbers (see the NRICH article From Objects and Images to Mathematical Ideas).

In the Netherlands, researchers developed bead-strings and rekenreks (counting frames) using groups of five, as they found these helped children to 'see' numbers more quickly (Gravemeijer, 1991). Being able to subitise groups supports children's understanding of larger numbers and later multiplicative thinking: for instance, recognising larger numbers by counting groups of two, three or five.

(The above images are taken from the Number Talk Images website.)

Subitising with everyday objects is more challenging than with simpler shapes, like dots. However, it can be more engaging for children to discuss images which are of particular interest and relevance to them, or even to create their own images for number talks.

Acknowledgments:

Janine Davenall
Buckinghamshire, Berkshire & Oxfordshire Mathematical Pedagogy Work Group

References:

Back, J. (2014) Early Number Sense
Clements, D.H. (1999) Subitising: What is it? Why teach it? Teaching Children Mathematics 5(7) 400-405
Emerson, J. & Babtie, P. (2010) The dyscalculia assessment: Emerson House Mathematics London: Continuum.
Thouless, H. & Gifford, S. (2018) 'Dotty triangles: two different approaches to analysing young children's responses to a pattern replication activity' in Golding, J., Bretscher, N., Crisan, C., Geraniou, E., Hodgen J. and C. Morgan (Eds). (2018) Research Proceedings
of the 9th British Congress on Mathematics Education (3-6 April 2018, University of Warwick, UK) 175-182 Online at www.bsrlm.org.uk/bcme-9/
Gravemeijer, K.P.E. (1991) An instruction-theoretical reflection on the use of manipulatives in Streefland, L. Realistic mathematics education in primary school. Utrecht: Freudenthal Institute 57- 76
Marton, F. & Neuman, D. (1990) 'Constructivism, phenomenology and the origin of arithmetic skills' in Steffe, L.P. & Wood, T. (1990) Transforming children's mathematics education: international perspectives NJ: Lawrence Earlbaum Associates 62- 75
Resnick, L.B. (1983) 'A developmental theory of number understanding' in Ginsburg, H. (ed) The development of mathematical thinking. London Academic Press 109 - 181.
Sarama, J. S., & Clements, D. H. (2009). Early childhood mathematics education research. London: Routledge.

here.

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In this article for EY practitioners, Dr Sue Gifford outlines what we mean by subitising and how we can teach it.

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Scottish Book Trust: Books that Support Numeracy

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Scottish Book Trust: Books that Support Numeracy

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Looking for more in Book Lists?

There are so many ways to bring numbers to life for little ones. Sharing stories, songs and rhymes that feature counting or other mathematical concepts can help to lay the foundations of numeracy - and it's never too early to start! Here is a selection of new and classic stories that explore numbers in very different ways.

Pick up these books through our bookshop.org affiliation! As well as supporting independent bookshops, a small portion of the profits helps our programmes to change more lives through reading and writing.

Buy and support

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Bring numbers to life for little ones by sharing stories, songs and rhymes that feature counting or other mathematical concepts

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Erikson Institute Early Math Collaborative

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Series: Book Ideas

This series of book ideas encourage using stories to infuse the early years with mathematical learning. From the infant years until they are putting together more advanced numeracy concepts in elementary school, books can be a gateway for early math discussions.

Below find all the resources we have placed in our series titled BOOK IDEAS.

September 28, 2022

Counting books that offer children opportunities to participate bring play into math learning. These books engage children physically, cognitively, and emotionally-making them favorites that children will ask to read again and again.

Free videos.

Free newsletter packed with ideas.

Free professional learning modules.

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Book Ideas | Early Math Collaborative at Erikson Institute

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Book ideas for using stories to infuse the early years with mathematical learning and exploring. From birth to age eight.

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Math Games | Educational Games for Kids | Toy Theater

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Fun & Free online math games for kids K-5, featuring addition, multiplication, subtraction, line plots, pictographs, virtual manipulatives, and more.

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You can find songs and rhymes to suit different moods or times of day. Try a range of songs and rhymes and discover your child’s favourites!

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Bookbug Session Plans: Maths Week Scotland

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We are a national charity bringing the benefits of reading and writing to everyone in Scotland.

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These lower primary tasks are all based around the idea of counting and ordering numbers.

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The Count On Races game, played by an adult and a child, helps children learn to count on mentally. A coin or a dice with 1 or 2 on each face is used. Children say the next number when counting on. For example, when starting from 7, for a jump of 2 we say '8,9'.

The Cube Model (4-6) and Cube Model Advanced (4-6) tasks, children recreate the models. This task develops visual-spatial skills and helps children to recognise two parts within the whole.

The Reasoning in Addition Puzzles get children thinking deeply about the value of different shapes. This Mathsbot link allows you to generate new reasoning in addition puzzles.

Visual Representations

This article explains the importance of children's finger discrimination skills and this article gives different ways in which fingers can be used. Here are some Finger Discrimination tasks by Youcubed.

These Base-5 and Base-10 Number Tracks are coloured to help children to see quantities within a number track.

This Online Base-5 Abacus by Math Rack represents quantities 10-100 using a base-5 colouring.

The Coloured 100-Squares help to identify patterns in the 100-square and can support children as they count in 2s and 5s.

The Teens & Tens Cards help children to discern between teen and tens numbers. The Place Value Sorting Task show different representations of teen numbers and challenge children to spot misconceptions.

Progression in Pattern

The Progression in Pattern guidance shows how children's understanding of repeating patterns can be built. The Grids for Repeating Patterns can be used as children look to create circular patterns with a fixed number of spaces.
Number Foundations Assessment Fluency in Calculation Within 20 Spatial Reasoning in Early Childhood, Early Childhood Maths Group
Deconstructing Word Questions KS1 Tasks and Build-Up Presentation

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A range of resources and games for building children's early number sense with small quantities and developing conceptual understanding.

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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100 Subitizing Slides & 10 Challenge Patterns - Steve Wyborney’s Blog: I’m on a Learning Mission.

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I have a new resource for you. 100 Subitizing Slides & 10 Challenge Patterns.

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Explore this resource

This package of professional learning resources aims to enhance knowledge and understanding of effective learning and teaching progression, whilst impacting positively on numeracy attainment. It includes the following resources:

Guidance document

Number and Number Processes

Fractions, Decimal Fractions and Percentages

Time

Data and Analysis

Ideas of Chance and Uncertainty

Money (New 2022)

Glossary

These resources, produced as part of the National Improvement Framework, aim to support schools and establishments to identify opportunities for targeted learning and enhance the effective teaching of numeracy concepts and associated skills. They also aim to help practitioners to:

identify methods for enhancing learners' progression and skills in numeracy and support application;

plan how to develop their own practice to ensure the progression of skills when teaching numeracy.

Within each document there is progressive guidance for each level from early through to fourth. Each level includes the following:

Effective learning and teaching approaches;

Things to consider;

Links to other curricular areas;

Reflective questions.

In addition to supporting practitioners to review and reflect on the current progress of their learners, this resource also supports practitioners to identify development themes required for the reinforcement of learning. Furthermore, this resource can support practitioners to review and reflect strengths and improvement areas within their own professional learning.

School leaders can use this resource to support curriculum development and improvement. Local authority leaders can use this resource to support consideration and enhancement of centrally provided professional learning offers to practitioners.

Downloads

Guidance documents
PDF file: Guidance document (510 KB)PDF file: Guidance document (Gaelic version)(480 KB)
Professional Learning resource documents
PDF file: Number and Number Processes (2.7 MB)PDF file: Number and Number Processes (Gaelic version) (3.2 MB)PDF file: Fractions, Decimal Fractions and Percentages (1.9 MB)PDF file: Fractions, Decimal Fractions and Percentages (Gaelic version) (2.2 MB)PDF file: Time (2.1 MB)PDF file: Time (Gaelic version)(2.2 MB)PDF file: Data and Analysis (1.8 MB)PDF file: Data and Analysis (Gaelic version)(2 MB)PDF file: Ideas of Chance and Uncertainty (652 KB)PDF file: Ideas of Chance and Uncertainty (Gaelic version) (900 KB)PDF file: Money (2.6 MB)
Money - Gaelic Version coming soon.

Sketchnotes
PDF file: Early Level Sketchnote - Number and Number Processes (267 KB)
Glossaries
PDF file: Glossary (436 KB)PDF file: Glossary (Gaelic version) (480 KB)PDF file: Numeracy Glossary (Gaelic version - alphabetical) (479 KB)

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This package of professional learning resources aims to enhance knowledge and understanding of effective learning and teaching progression, whilst impacting positively on numeracy attainment.

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Numeracy and Mathematics : Thematic Report

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Numeracy and Mathematics : Thematic Report

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Counting Series - Session 1 - An Overview of Counting