Mathematics in Early Years

Natalie Alty & Claire Green

What is early mathematics? What are the key priorities for our children in Early Years? Discuss with your colleagues.

What is early mathematics?

‘The world is a mathematical place. For young children who are naturally curious there are shapes, numbers, moving objects and patterns to behold, things to count and investigations to be undertaken. It is a creative, challenging and wonderous way of looking at life and exploring the world. Maths is an inherent part of being human. Framing the world through maths helps us make sense of what is happening and how it affects us’. J Robertson 2017

Problem – solving

Making connections

Real world scripts

Language and reasoning

Pictures and symbols

Expectations for number by the end of the EYFS.

Number ELG Children count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing. What have been the difficulties or problems with this Early Learning Goal? Discuss with your colleagues.

Challenges include:

- Numbers are learnt by rote and pupils can purely put them in order to identify one more or one less

- Little understanding of how these numbers are made and the number facts within them

- Little time can be given to teaching concepts in depth because there is so much knowledge to teach

- Can be challenging for SEN pupils to reach this goal but can be successful in understanding numbers to 10, however this isn’t recognised in data collection.

- Not enough time to model how concepts can be applied across different areas of the curriculum so that pupils can make real life connections in their learning.

Mathematics Educational Programme Developing a strong grounding in number is essential for providing children with the platform to excel mathematically. Children should develop a deep conceptual understanding of the numbers to 10, the relationships between them and the patterns therein. By providing frequent and varied opportunities to build and apply this understanding, children will develop a secure base of knowledge from which mathematical mastery is built. ELG Number: Children at the expected level of development will:

- Have an understanding of number to 10, linking names of numbers, numerals, their value, and their position in the counting order; - Subitise (recognise quantities without counting) up to 5; - Automatically recall number bonds for numbers 0-5 and for 10, including corresponding

partitioning facts. ELG Numerical Patterns: Children at the expected level of development will: - Automatically recall double facts up to 5+5; - Compare sets of objects up to 10 in different contexts, considering size and difference; - Explore patterns of numbers within numbers up to 10, including evens and odds

This year the DfE is piloting a new Early Years Foundation Stage Profile.

What is maths mastery?

• Depth Mastery

• Manipulatives

• Structured practice (key vocabulary)

• Rich tasks

• Explanation and Reasoning

Connect memory: verbal, visual and spatial

• Conceptual Variation : the variety of ways into a particular concept

• Procedural Variation: what the children should be able to do in relation to a particular concept

Number Sense

A sense of the size of a number

Rounding

Estimating

Use an empty number line to assess understanding of a range of numbers

Number sense Estimation

How many in the jar?

The basis of mathematics is… Pattern

• Children need to be able to see patterns, predict and generalise

• This includes growing patterns, making comparisons, logic, reasoning and working systematically

• Understanding how they work in a non-numerical sense is an essential first step in developing comprehension of pattern. Therefore must be linked to daily routines, songs, stories, movement.

Numicon 2014

Pupils need to have a good understanding of pattern. To be mathematical it must have some element of repetition or symmetry.

Growing Patterns

Important skill to have acquired is seeing the odd one out and being able to explain what is same or difference between objects? This also supports the development of reasoning skills.

Counting

- 1:1 correspondence - Stable order e.g 1,2,3,4,5,6…. - Abstraction: many items or objects can be counted • Order irrelevance • Cardinality - last number said is the number of the group Gelman & Gallistel 1978 Pupils need everyday opportunities to hear and use the language of number.

Use pictures and storybooks to discuss positional number, addition and subtraction stories as well as same, different and positional language.

Scaffolding the talk

• One less than__ is ___

• I have counted ___ altogether

• __ comes after/before ___

• ___ has more than ___ because___

• __ has the least because___

• __ more than ___ is ___

• I have __ and he has __ so we have ___ altogether

• I had __ and took ___ away so now we have__

Numicon is…

Sensory

Visual

Weighted

Whole class teaching

Numicon – explore

Number blocks - ncetm.org

helps children to develop: • cardinal number values • part whole relationships • number facts

http://pinterest.com/pin/create/bookmarklet/?media=https://playtolearnpreschool.us/wp-content/uploads/2014/12/Picture1-1024x495.png&url=https://playtolearnpreschool.us/subitizing-with-preschoolers/&is_video=false&description=

When learning to subitize children progress from: Linear Circular Scrambled

‘Children need concrete experience of physically manipulating groups of objects into sub-groups and combining small groups to make a larger group. After these essential experiences more static materials such as 'dot cards' become very useful.’

Let’s play!

How many dots can you see? Play with dot games

Ten Frames Why do we use them? • Builds number sense • Helps children visualise numbers • Help children to be able to deconstruct

numbers and recombine them in a useful way

• Creates a strong understanding of ten which is vital for our number system

If I know 5+5=10…

… What else do I know?

Relationships

True or false

+

8+5 = 13

How does this then support to bridge through 10?

Pupils can then begin to record their understanding.

5 = 2 + 3 5 = 3 + 2 3 + ? = 5 2 + ? = 5 ? + 3 = 5

White Rose Representations

Making Connections

• Half of 8 is equal to 4

• Double 4 is equal to 8

What is the same and what is different? 17 and 71

Mathematics 30-50mths Numbers Beginning to represent numbers using fingers, marks on paper or pictures. Sometimes matches numeral and quantity correctly. 40-60mths Recognises numerals 1 to 10 Counts objects to 10, and beginning to count beyond 10. Selects the correct numeral to represent 1 to 5. Finds the total number of items in two groups by counting all of them. In practical activities and discussion, beginning to use the vocabulary involved in adding.

Find missing numbers – use the part, part, whole method to develop reasoning skills as to how they find the missing number.

Introduce the equal sign, how do you write it, where do you see it and what does it mean? How can they record their own addition number sentences using pictorial representation.

Transfer from pictorial to using numerals with the pictures.

Planning for mathematics.

Plan for differentiation through questioning, resources, depth of mastery dependent on understanding.

We do same day interventions as well as those over time for pupils with specific targets.

Creative What? making wood rubbings/printing poppies with small bottle tops. Why? Children explore variety of different wood/bark and make rubbings. Questioning: what does the wood feel like? Encourage different descriptive words – rough, smooth, bumpy etc. Introduce the word texture.

Malleable/Messy What? Red/Green play dough – making poppies, exploring textures. Why? Sensory play & use to mould into poppy shapes (encourage Tom, Jane and Paul)

Talk Table What? Pictures of poppies, wreaths etc Why? Children to think how they feel when they look at the pictures. (KS to support Jennifer & Alice for language intervention)

Exploration/Investigation – Tuff spot. What? Different red objects to feel. Why? Develop language of how objects feel. Encourage pupils to link their sentences together to extend speaking. Can children imagine what the objects are? Could be made into?

Mark Making What? Design a medal. Why? Using the children’s creative ideas to design a medal. Discuss why people get medals and the pictures that could be drawn on.

Book/Story Telling What? Books about the war / transport used e.g. airplanes / tanks. Why? Encourage pupils to talk about their own understanding of this special event.

Role Play – to be changed Thursday What? PSED & CLL – working together to listen to each other’s ideas and take responsibility for the area in which they are playing. Why? Currently a castle, vote as a class and change to what the children would like it to be.

Mathematics: What? Balance scales, numicon, equals signs, boards, pegs. Why? Develop & reinforce pupils understanding of = through continuous provision. (Extend EXC pupils to use = on both sides – Dan, Jake, Charlotte, Sam)

ICT: What? Draw and colour a poppy picture Why? Drawing and painting skills. https://www.purplemash.com/#app/pap/nature/poppy - purple mash – draw a poppy

Music What? Drums, beaters, rhythm cards. Why? Develop co-ordination between beats and physical movement (JM for physical development group with Aron, Charlie & Tilly)

Physical (fine/gross) What? Paper patterns Why? Use scissors for fine motor skills (CG to work with Billy, James, Ravi)

How do you plan for mathematics in your setting, are there any difficulties or challenges with this?

https://www.purplemash.com/#app/pap/nature/poppy

Mathematics in our learning environment.

Make number stories with puppets.

Organise the numbers in order but different presentations.

Use the children as counters. Take pictures of pupils in different organisations of the same number and then sort the pictures to match the same number.

Use different types of objects to sort and find many ways of making the same number.

Working walls in EYFS

Mathematics outdoors

- Positive role model as a mathematician - Use the language of mathematics in everyday

conversation with their children - Parent workshops to explain how you teach maths - Parents understand the expectations for their

children in mathematics - Parents to watch maths lessons - Maths challenges & wow stars, displayed in the

classroom

Story books for mathematics

https://www.mathlearningcenter.org/web-apps/number-frames/ Use to model how to make each number.

Online resources and games

http://illuminations.nctm.org/activity.aspx?id=3565 Use to play each of the games described in the beginning.

http://www.fuelthebrain.com/games/number-flash/ Very good practice for subitizing.

https://www.coolmath4kids.com/manipulatives/ten-frame As above but you can change the counters to different pictures.

https://www-k6.thinkcentral.com/content/hsp/math/hspmath/na/common/itools_int_9780547584997_/main.html Lots of different counters to organise for subitizing and tens frames to explore.

http://www.glencoe.com/sites/common_assets/mathematics/ebook_assets/vmf/VMF-Interface.html A huge range of manipulatives and storyboards

https://www.bbc.co.uk/cbeebies/curations/numberblocks-songs A song to introduce each number.

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