NURSERY 1 (born in 2017)

Young children generally learn the first 10 number words by rote memorisation and are therefore neither familiar with number symbols nor understand the relation between number and quantity, at this stage of development.
 
Hence, this lesson will focus on these interlinked components of number skills, including: 1) number symbol recognition and 2) number-to-quantity association.
 
Especially since many number symbols closely resemble one another (i.e 2 vs 5 & 6 vs 9), children will need to learn how they can be visually discriminated (specifically, left-right orientation).
 
Children will then familiarise themselves with number word-symbol pairs and the association between number and quantity, through rational counting. This process involves a one-to-one correspondence procedure of assigning one number at a time, in sequential order, to each object or image being counted.
 
Subsequently, to demonstrate an understanding of number-quantity association, your child will be tasked to add/remove objects to obtain the desired quantity.

• For instance, if there are six counters inside the bowl labelled “5”, your child will need to remove one counter from the bowl.

 
Building an understanding of one-to-one correspondence will therefore be critical for your child’s mathematical skill development, as he/she is introduced to concepts of increasing complexity moving forward (i.e. addition and subtraction).

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NURSERY 2 (born in 2016)

In Singapore, children are first introduced to multiplication/division in Primary 1 and 2, where they are taught to recite the multiplication table for efficient computation.

However, true math fluency involves a conceptual understanding of multiplication/division, built upon the idea of one-to-many correspondence – whereby quantity and unit are linked through a specific ratio.

Using real-life scenarios, arithmetic division will be introduced to your child as a sharing operator that seeks to achieve a fair outcome. Children will be tasked to distribute objects fairly/evenly across a fixed number of parties.

Here, he/she will discover that fair/even distribution is only achievable for certain quantity-unit combinations. In other instances where fair/even distribution is not achievable, your child will then be guided to figure out the leftover quantity (remainder) as well as the additional amount required to make it work.

Conversely, as a precursor to arithmetic multiplication, children will also be engaged to tabulate the total quantity of objects present, given a specified number of parties with each party having the same number of objects.

Building the concept of division/multiplication around the idea of “sharing” improves relatability and gives us the opportunity to go through with your child the moral principles of equality and fairness.
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KINDERGARTEN 1 (born in 2015)

Subtraction is not an entirely different concept from addition; they are inversely linked based on the combination and separation of numbers.
 
This lesson seeks to reinforce the part-whole relationship of arithmetic addition and subtraction, through number bonds.
A number bond is a visual representation of this relationship – showing the link between one larger number and its constituents (smaller numbers).
 
Through number bonds, children will familiarize themselves with the idea of breaking down or forming a larger number, in different combinations.  With this understanding, we will then familiarize your child with the “counting on” strategy; and be better equipped to tackle mathematical questions involving the combination of smaller parts to find a whole (a ± b=?) or solving for one of the parts that make a whole (a ± ? = c).
 
This idea of “breaking down” a larger number into smaller parts is also an applicable technique for understanding, calculating and simplifying large/complex numbers.

• Example : 432 → 400(hundreds) + 30(tens) + 2(ones)

Children are thus trained to place more reliance on relational understanding rather than rote memorization - to navigate through increasingly difficult mathematical problems and concepts. This process also develops your child’s mental computational competence.

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KINDERGARTEN 2 (born in 2014)

 “2 + 8” and “1 + 3 + 6” are some examples of complements of 10.

Number complements, particularly complements of 10, are important building blocks for
(A) understanding the part-whole relationship of numbers (a+b+c=10; a+?=10), which is a precursor for mastering addition and subtraction;
(B) performing mental sums; and
(C) establishing a unit, which helps build a strong foundation for computing 2-digit numbers.

This lesson, your child will practice with a combination of two (i.e. 2+8=10) or three (i.e. 2+3+5 = 10) numbers, presented in a linear, Sudoku or story problem format.

Through this process, your child can gain a better understanding of arithmetic addition’s commutative property, i.e. 8 + 2 is the same as 2 + 8. Moreover, he/she will be better equipped to tackle addition/subtraction problems beyond the “a + b = ?” format, to solve for an unknown change (i.e. a + ? = c) or unknown start (? + b = c).

Here, children will also learn how values and/or operators can be assigned to abstract symbols, as a precursor to algebraic substitution.

While navigating mathematical story problems, the CPA (concrete, pictorial, abstract) three-step developmental strategy will be applied. It involves the gradual transition away from concrete-physical aids, to visual aids, before removing all forms of aid. This seeks to train your child to focus, listen and solve problems mentally, thus strengthening mental visualisation and computational capabilities.

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Next LESSON'S focus:
THINKING WITH WORDS