Let’s visit Numberland
Initial thoughts
Before we dive into the Numberland elements and what number sense is in detail, please allow me a quick reminder:
Despite the polarising image of maths, all children start with a natural love for it! They want to learn this language we developed to describe our world and which we use all the time. Unfortunately, these great conditions are often crippled by too formal tuition too early in too big steps or incomplete. We avoid this! With easy going and little means but maximum outcome and joy.
Neither do we start from scratch, nor does number sense just develop by itself.
We all have a natural understanding of quantities! We can see up to 3 items at a glance, without counting in ones. This is called perceptual subitising. We also “see” which group is one more/one less. Beyond three, i.e. quantities with four or more items, are just “many”.
Actually, our (still) prehistoric brain is quite happy with this “one, two, three, many”. Yet ambitious as we are, we moved on and developed this formal language of maths which is so polarising for many… Fortunately, children WANT to learn this language, it is part of their development. They gradually build their bridge into this full understanding of numbers. How solid and thorough their bridge will be, how positive and motivating, depends on how we support our children on their journey.
More than ever do you need means that integrate and engage all children, especially those from diverse backgrounds. The key is an environment of play in which the good things happen. Because all children are natural learners and come with the same chances. Forcing something on them they are not ready for just does not work.
Do you agree? Then come along with me and let’s enter Numberland… But before let’s acknowledge the complexity of number sense and the usual steps in which children usually grow into their number sense.
What is number sense?
Number sense means to fully understand what numbers are and being able to use this for describing our world, with operations being a huge part of it. Developing this number sense is a process that takes time and many tangible experiences for children through play with all their senses. Formal academic drill is toxic here!
— Step One: We build on our natural subitising power
- Each group of the items I grasp at a glance have their own name: number one, two, three
- Two is always two! Two flowers, two small pebbles, two big tables. They can even be close to each other or further apart, even on top of each other.
- I can show these quantities with my fingers.
- These names are written with special symbols: 1,2,3.
- The numbers have an order, following the pattern of one more/ one less.
— Step Two : The pattern continues beyond three
- The pattern of one more/one less continues with more quantities and names: four, five, six and symbols 4,5,6…
- There is also a name and symbol for nothing, one less than one: zero, 0.
- Numbers have a fixed order: 0,1,2,3,4 …
- I can split quantities/ numbers into other quantities/ numbers. I can also make numbers out of other numbers.
- Subitising: I do not have to count in ones but use my natural (perceptual) subitising power. In 5, I can see 3 and 2 or 2 and 2 and 1 (conceptual subitising).
— The Next Milestone
- I can even see 5 items at a glance if they are organised: like on dice, or in a five frame/ten frame.
- It is helpful to know which numbers make up 10 and have an internal picture of this. These number bonds help me later.
- The pattern goes on beyond ten.
- I need only 10 symbols to make up any number in the world, no matter how big: 0,1,2,3,4,5,6,7,8,9. Much less letters than the alphabet 😉
- Numbers even relate to shapes!
This is quite complex and children need time to grow into this – through play, tangible experiences, exploration, with all their senses; through informal play, not formal training.
They also need to organise and structure all these experiences they make daily.
This is where Let’s visit Numberland comes in! It translates all these number aspects into the world of children and helps them organise their findings. We connect to the world around us, and can even use Numberland as a starting point for any other activities.
-> More details and the entire mathematical background in the Masterclass.
What is Let’s visit Numberland?
Let’s visit Numberland is a research-based holistic and field proven concept which translates numbers into the emotional world of 3 to 6 yo children. Numberland is beloved around the globe and in any setting, because children are the same everywhere and maths knows no language barrier! Therefore Numberland is also highly integrative.
Let’s visit Numberland is the irresistible translation of crucial basic mathematical knowledge into the emotional world of 3 to 6 year old children.
We develop the story that numbers are alive and have a home – just like us!
We build and explore this home, which happens to be packed with maths, connecting to whatever we find interesting or useful…
We bring in anything children like: stories, playing, crafting, exploring, songs, active games, …
That way, Numberland helps to build a bridge from the imaginative and emotional world of 3 to 5 year olds over to the formal, abstract language of maths. Supporting a thorough understanding of essential basic maths plus confidence and motivation. Engaging, opening and preparing for any further maths to come.
More than that, Numberland sparks communication, reasoning, helping each other and can be used to deliberately address an abundant choice of content. It is a starting point for cross curricular activities and support the transition to further, more abstract maths learning.
You can use it as a group activity or as individual work (or both), for your continuous provision, in a bilingualism context, for SEN, inclusion, therapy.
For maximum flexibility, you can choose among large and small, coloured and b/w resources.
Let’s visit Numberland elements
We weave all these keywords into Let’s visit Numberland:
Quantity, order, Perceptual/Conceptual Subitising, Un-/Organised Groups, Shapes, Five/Ten frames, Place holder, Partitioning.
Happy neighbours with gardens full of maths!
The numbers Zero to Ten live here as happy neighbours and their homes display essential number sense knowledge in an organised and structured way.
You can use each of the following elements according to your individual needs.
Usually, children travel to Numberland by visiting one number after the other. Finally, they will have built an entire Numberland to play with in their continuous provision.
The basic idea is that we turn abstract symbols into living individuals. Because for young children, everything is alive.
Each number is unique and has individual, but not too loud features: Four has 4 braids, Five 5 buttons, Ten has a backpack with 10 pockets … Of course, Number Zero is part of the team.
The numbers zero to ten live along Number Street as happy neighbours. Each number has
- a house with a house number and windows
a flowerbed / garden frame - a geometrically shaped garden
Number Line Street
… stands for the Number Line and shows the order of the numbers with the pattern of always one more.
When we decorate Number Street, we relate to how numbers represent a quantity. We also see the pattern of always one more/one less.
Tip: A large Number Street on the floor enables children to experience numbers with their entire body! We can play lots of active game with and on Number Street! It can also be our way into and out of Numberland.
Always include zero from the start! Later, we extend Number Street up to twenty.
Gardens full of maths
Number Six has a chat with his neighbour: Look, Five, what the children found for my home! Everything matches six:
6 pebbles, 6 stars, six buttons, a tower with 3 red and 3 yellow blocks. Also 6 trees, of which 4 are conifers. -> 6 is always six, no matter what it consists of or how we arrange it!
My house has the house number and two floors with 5 + 1 windows: like the hands of children.
Very advanced: Yes, the cow is also allowed to graze in my hexagon garden! As it would in Number One’s, Number Four’s, even Number Seven’s garden. Why?! Let’s think about it and reason! 🙂
Five frames and ten frames
… display number representations as organised quantities (like the windows on the houses). They help children grow towards more abstract internal pictures of numbers, also knowledge about number bonds, plus place holder value and beyond ten.
In Numberland, we call them garden beds or flower beds! Gardening requires rules, so instead of just planting as we wish, we need to follow rules…
We play gardening – starting very simple and then more elaborate, to ensure children have a smooth ride on their (long) way from their concrete to the abstract understanding. For us, the counters start with being flowers or vegetables that we plant, water, prune, buy and sell with care. This is also a chance to speak about colours.
While we garden with our number friends, we move towards organising our internal pictures of number representation, quantities, partitioning – also subitising and number bonds.
Number Bonds
Number Four contemplates: Who could be my gardening buddy?
Children explore who could garden together to fill the entire garden bed!
Thus, we create emotional internal pictures! Moving on to more abstract ways of number representation becomes much easier.
What will happen, when Number Four and Number Seven decide to garden together?? Let’s find out!
Oh no, Trickster was here!
To become confident learners, children need to know that making mistakes is absolutely no problem.
Our mischievous Trickster ever and again messes up Numberland, and children love to spot his tricks and correct them. Trickster serves the Good-versus-Bad thinking of children.
If the children want support to fix the mistakes, they can call Numberilly for help …
Shapes
The gardens introduce shapes and make them meaningful to children. And it is great to explore how they relate to the specific number.
Why does Number One have a circular garden? Why would Number Two live either in a semicircle or in an ellipse?!
Let’s make a circle with our full bodies!
However, what other shape could Number One or Number Two have as a garden? Whatever we reason and can agree upon is fine in this context!
Finally: A full Numbertown
In one spot, children can see and grasp all relevant aspects of numbers. Numbertown helps them structure and organise their findings. We create memories and a foundation to build on.
This picture will soon be updated
(different number representation in the five/ten frames)
A complete Number Town will look something like in the picture. Complexity varies according to age group and possible cognitive load.
Each time, relevant knowledge is organised and displayed in a way that helps children to develop correct and positive inner pictures. Children can then build on this structure and any further maths can properly connect.
You can use each of the Numberland elements according to your individual needs. Let’s visit Numberland is not a strict programme you had to follow, though there are suggestions on how to go about it.
Usually, children travel to Numberland by visiting one number after the other so that Number Town will gradually grow from one number to the next, allowing time to explore and address whatever and as much as needed.
Start the journey with a story
Children love stories and books – so we created My Garden is a Square.
It is your conversation starter and eye opener, and available in 8 languages.
The children learn about the home of their number friends and are invited to detect details and relate to the real world.
The book invites the children to craft their own Numberland or Numbertown and thus turn abstract numbers into tangible, happy role play…
This is all optional!
… and the complexity/ cognitive load will depend on the age of your children, where they stand and what they need.
Of course, you can use any book or story and, of course, you can craft your own resources the way you/your children prefer. We only ask you to follow the thought through design principles! More about the book and resources
As I said: A neighbourhood full of maths! And tons of opportunity for active games, general knowledge, creativity, cross-curricular activities.
And voilà: The bridge from the emotional world of young children over to the abstract language of maths is becoming joyful and solid! Because we put things into a context!
Would you like to get started with Numberland? Learn more?
➜ Download your free trial pack with a Number One cutout, wall poster, numeral writing practice + colour sheet.
➜ Read about the underlying research project
➜ Or just email me at barbara@numberland.net
Follow this link to read about Numberland in various languages …
kindly translated by Numberland enthusiasts around the world.