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How our Early Years pupils learn maths Ⅰ

22 Mar 2022

Jingwen Chen

Assistant Head of Early Years


Maths is everywhere. Going to the supermarket, baking pastries, walking up and down the stairs, riding an elevator, helping set the dinner table — all of these everyday activities present opportunities to teach maths. 


Pupils can also learn basic mathematical principles from everyday items such as licence plates, traffic signs, houses numbers, building structures, songs and stories. Maths is not just about counting and computing. It is also about shapes, patterns, order, size, weight, estimation and problem-solving skills.



Let us take a look at how the Learning and Development Guide for Children 3 to 6 Years Old describes mathematical learning targets for young children in different ages.

Target 1: mathematical cognition

3-4 years old
  • Knowledge of and interest in different kinds of shapes

  • Recognising that numbers are used regularly in daily life

4-5 years old
  • With guidance, able to recognise that shapes can be used to describe   certain objects

  • With guidance, able to recognise that certain objects can be described   with numbers and have an interest in exploring the meaning of numbers


5-6 years old
  • Able to understand the rules of simple arrays and can attempt to create   new pattern rules

  • Able to understand that many problems can be solved using numbers and enjoy solving problems


Target 2: understanding the relationship between number and quantities

3-4 years old
  • Able to identify and describe size, quantity and length

  • Able to compare the amount of two group of things by counting

  • Able to count up to five with fingers and correctly quantify objects

  • Able to describe objects and actions with numbers, e.g. I have four books

4-5 years old
  • Able to identify and describe the thickness and weight of objects

  • Able to compare the amount of two groups of objects by counting.

  • Able to understand relationship between numbers, e.g. 5 is 1 more than 4;   2 and 3 make 5

  • Able to describe the order of objects using numbers


5-6 years old
  • Able to understand the relativity of the quantities

  • Able to understand the concepts of addition and subtraction in practical   situations

  • Using objects, able to add and subtract quantities less than 10

  • Able to express simple numerical relationships using simple charts


Target 3: understanding shape and space

3-4 years old
  • Able to identify and describe shapes of objects

  • Able to identify the position of objects and understand the concept of up   and down, front and back, in and out

4-5 years old
  • Able to identify the shape and structure of objects and draw or make it

  • Able to describe the properties of common shapes and classify them into groups

  • Able to describe position and movement direction of objects, such as up and down, front and back, in and out, between and beside


5-6 years old
  • Able to creatively draw and make shapes using other common shapes

  • Able to take and put away objects according to oral and simple picture   instructions

  • Able to distinguish left from right





Elaine found a watering can on the balcony. She tried spraying only to discover that it was empty. "There is no water in the watering can," she told her teacher. 

The teacher asked: "Where can we find water?" Elaine looked around and found a faucet in the water play area. She filled the watering can and watered the grass in our outdoor play area.


This instance demonstrates Elaine's capacity for observation. She is able to recognise patterns, discover the changes around her and build connections between them. She is also willing to try new things and solve problems under a teachers’ guidance.




During circle time, a teacher and pupils played a game of numbers called 'silent counting'.

After snack time, a pupil named Andana asked some of her classmates if they would like to play the 'silent counting' game again. They agreed, and she began to mimic her teacher, saying, "Please close your eyes. Peeking is not allowed." 

She then took toy bears and dropped them one by one in a metal box, which made a clear sound. Her peers then had to count on their fingers how many bears she dropped in the box.


After dropping the sixth toy, Andana said, "Please open your eyes and tell me how many bears are in the box." Some of the children said "six" and some said "five". She said, "Let's count together to get the correct answer." 

The children who counted six bears were right. They had the chance to be the 'little teacher' in the next round.

Andana's story illustrates that our EY2 not only acquire the ability to count, but also have confidence to express themselves. In such a positive and supportive environment, they also feel comfortable and secure enough to forge friendships with their peers.  



Activities for our EY3 pupils often involve scenarios and rules. Recently, the pupils were assigned the task of investigating the teachers' and classmates' favourite pets. They were asked to complete a survey and instructed on how to record what they heard.

A pupil named Chloe filled her survey form out according to the example provided, but she chose to record her figures in her own way. She tallied the numbers up directly behind each pet icon. Although she had not attended school for several days, Chloe was not shy when she interviewed others.


While she interviewed Jennifer, her fellow pupil, Chloe even wrote the English initials of different pets next to each icon with some help from a teacher. This helped her distinguish those pets in the future.

By developing their capacity for communication and expression, our pupils learn maths in situation-based activities and express themselves more confidently as they interact with their peers.




EY4 pupil Quentin found a large set of hole-board toys on the balcony, and, along with some friends, he lined them up on the floor.

Shortly thereafter, he ran to the teacher and told her that there were 29 holes in the floor. The teacher asked him how he arrived at this number and firmly believed that he had calculated it correctly.


Moments later, the teacher observed him stepping into one hole at a time and counting the number of holes. Finally, he confirmed that the total number of 29 was correct. Here, Quentin exhibited quantitative abilities as well as self-evaluation.

From observation and research to repeated verification, EY4 children achieve complete research loop. This level of growth and discovery never ceases to amaze us.

Play is the most basic activity for a young child's holistic development. It allows for unmediated experiences in which they form connections with the outside world.


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We often observe children playing their favourite games and activities over and over again. This helps them to think and adapt relevant learning experiences. It is why learning through play is such a powerful learning tool.

In the next article, we will talk about more activities that support children's maths learning in a real-life context. Stay tuned.