The first few years of a child’s life are especially important for mathematics development. In EYFS, we aim to provide children with firm foundations in a way that is stimulating, engaging and appropriate for their age.
There are six key areas of early mathematics learning, which provide a platform for everything children will encounter as they progress through their maths learning at primary school, and beyond.
"I like learning about Numberblocks."
Cardinality and Comparison Composition
See below for more information about these areas.
We begin this program in Reception and continue it throughout KS1. Mastering Number aims to secure firm foundations in the development of good number sense for all children from Reception through to Year 1 and Year 2. Over time, children will leave KS1 with fluency in calculation and a confidence and flexibility with number. Key knowledge and understanding acquired in our Reception classes and through KS1 will support future success!
"I like counting new Numberblocks."
At the end of a Mastering number session, children reinforce newly learnt mathematical concepts by following the adventures of the Numberling characters in Numberland! Initially, children are introduced to single digit characters (one, two and three etc), this then progresses to characters that recombined to make 'new numbers'. For example. five is made of two and three! These short clips embed the precise mathematical language modelled by class teachers during the Mastering number sessions, as well as providing children time for practice of key stem sentences/generalisations learnt in sessions.
" I love learning about adding the Numberblocks."
Ideas for developing these areas at home:
Cardinality and Counting
The cardinal value of a number refers to the quantity of things it represents, e.g., the numerosity, or ‘threeness’ of three. Counting is one way of establishing how many things are in a group, because the last number you say tells you how many there are. Children enjoy learning the sequence of counting numbers long before they understand the cardinal values of the numbers.
These activities will help your child develop Cardinality and Counting:
- counting rhymes and songs, including counting backwards
- counting actions during play, steps, jumps, counting along a track game
- counting objects of different sizes
- counting things that cannot be seen, such as sounds, actions, words
- counting things that cannot be moved, such as pictures on a screen, candles on a cake, birds at the bird table, faces on a shape
- playing dice games to collect a number of items or to move along a track
- playing ‘hidden objects games’ where objects are revealed for a few seconds than moved – How many?
- reading number books
- matching numerals with varied group of things
- arranging a group of objects in different ways to realise the quantity remains the same
- finding the same amount of different items
Comparing numbers involves knowing which numbers are worth more or less than each other. This understanding underpins the mental number line which children will develop later and that represents the relative value of numbers, i.e., how much bigger or smaller numbers are than each other.
These activities will help your child to develop Comparative Skills:
- comparing collections and beginning to talk about which group has more/less things
- matching counters, coins or seeds to a collection of objects
- asking children to convert two unequal groups into two that have the same number, e.g. ‘There are 6 toys in one bag and 2 in another bag; can we make the bags equal for the two children?’
- comparing numbers and reasoning, for example, numbers that are far apart, near to and next to each other, ‘8 is a lot bigger than 2 but 3 is only a little bit bigger than 2’
- explaining unfair sharing, 'This one has more because it has 5 and that one only has 3'
- ‘labelling groups with the correct numeral. Do children spot the error if a group is mislabelled? For example, 'The label on the pot says 4 and we have 5 – what do we need to do?’
Knowing numbers are made up of two or more other smaller numbers involves ‘part–whole’ understanding. Learning to ‘see’ a whole number and its parts at the same time is a key development in children’s number understanding. Partitioning numbers into other numbers and putting them back together again underpins understanding of addition and subtraction as inverse operations.
These activities will help your child develop understanding of Composition:
- ‘Number Talks’ to discuss what the children see, e.g. ‘There are 5 spots altogether. I can see 4 and 1, I can see 3 and 2, or, I can see 1 and 1 and 1 and 1 and 1.’
- encourage exploration of all the ways that ‘five’ can look. for example, playing with 5 cars, “2 on the rug and 3 on the floor”, or “2 on the rug, 2 on the floor and 1 on the sofa.”
- putting things into two containers in different ways
- role play, e.g., in a toy shop, ten toys need arranging onto the three shelves. How will you organise them?
- playing hiding games with a number of objects in a box, under a cloth, in a tent, in a cave, etc.
- using a pot with some items and a number label. Play hiding games – how many are missing?
Seeking and exploring patterns is at the heart of mathematics (Schoenfeld, 1992). Developing an awareness of pattern helps young children to notice and understand mathematical relationships as they provide the opportunity for young children to observe and verbalise generalisations.
These activities will help your child develop understanding the Pattern:
- exploring patterns in stories, songs and rhymes
- extending patterns using a wide range of identical objects in different colours, e.g., small toys such as bears, dinosaurs, vehicles
- accessing a range of patterns to copy. For example, using cutlery: big, small, big, small, big… Or, spoon, fork, knife, spoon, fork, knife…
- play actions and sounds: jump, twirl, jump, twirl, jump… or clap, stamp, clap, stamp…
- ensuring that there are numerous opportunities to create patterns – e.g. in the outdoors, using natural materials such as sticks, leaves, stones, pine cones; in craft activities, using stamping, sticking, printing; with musical instruments, using sounds such as drums, shakers, triangles, etc.
- challenging your child to change one element of the pattern they have created, e.g. 'Can you change the red Lego to a blue Lego? What is the pattern now?'
- presenting patterns with deliberate errors, including extra, missing and swapped items, e.g. red cube, blue cube, red cube, blue cube, red cube, red cube, blue cube – identifying there is an extra item and fixing it by removing the extra red cube, putting in an extra blue cube, or swapping the final cubes.
Shape and Space
Mathematically, the areas of shape and space are about developing visualising skills and understanding relationships, such as the effects of movement and combining shapes together, rather than just knowing vocabulary. Spatial skills are important for understanding other areas of maths and children need structured experiences to ensure they develop these.
These activities will help your child develop understanding the Shape and Space:
- construction activities
- printing and making pictures and patterns with shapes
- making a complete circuit with a train track
- Using Tangrams or 2D shapes: 'Can you make a person with the shapes?'
- with toys in a line: 'Can you say what the teddy on the other side is seeing?'
- hunting for hidden objects, with some prompts, e.g., 'Look behind the shed, or take three steps from the front of the cupboard…'
- developing and talking about small-world scenarios, e.g., doll's house, miniature village, play park
- directing each other as robots
- follow a simple map of an excursion
Mathematically, measuring is based on the idea of using numbers of units in order to compare attributes, such as length or capacity. Children need to realise which attribute is being measured, e.g. weight as opposed to size. Additionally, children need to understand how equal size units are used repeatedly to express an amount as a number.
These activities will help your child develop understanding of Measure:
- ensuring adults model language which highlights the specific attribute that is the focus of attention
- water and sand-play, which can provide lots of opportunities to highlight capacity.
- encouraging children to compare different attributes in everyday situations: ‘I wonder who has the longest snake?’ ‘I wonder whose pot will hold the most water?’ ‘I wonder which ball is the heaviest?’
- cutting a piece of ribbon as long as a child’s arm and encouraging them to find things in the environment that are longer, shorter or the same length
- using a simple spring balance to compare the weight of cargo for a toy boat
- comparing different parcels, ensuring some of the smaller parcels are heavy, and some of the larger parcels are light