The document discusses Singapore's math curriculum and its success on TIMSS tests. It summarizes that Singapore uses a spiral curriculum where concepts are revisited each year with increasing difficulty. It emphasizes concrete, pictorial, and abstract representations of concepts. Number bonds are introduced in grade 1 to help students understand the relationship between numbers and their parts for addition and subtraction. Grade 1 covers addition and subtraction within 100 using various methods including regrouping. Mental math strategies are also practiced in grade 2.

1. SINGAPORE MATH CURRICULUM
GRADE 1 ADDITION & SUBTRACTION
WITHIN 100
26 JANUARY 2015

3. TIMSS RESULTS
Country Ave Score
Singapore 590
Japan 567
Hong Kong 557
Netherlands 549
Hungary 521
United States 518
Latvia-LSS 499
Australia 495
Scotland 493
England 484
Country Ave Score
Singapore 594
Hong Kong 575
Japan 565
Netherlands 540
Latvia-LSS 533
England 531
Hungary 529
United
States
518
Cyprus 510
Australia 499
1995 Results
International Average = 529
2003 Results
International Average = 495
Country Ave Score
Hong Kong 607
Singapore 599
Chinese
Taipei
576
Japan 568
Kazakhstan 549
Russian
Federation
544
England 541
Latvia-LSS 537
Netherlands 535
Lithuania 530
2007 Results
International Average = 500

4. Country Ave Score
Singapore 606
Korea 605
Hong Kong 602
Chinese
Taipei
591
Japan 585
Northern
Ireland
562
Belgium 549
Finland 545
Russian
Federation
542
England 542
2011 Results
International Average = 500

5. WHAT IS THE SECRET RECIPE IN
SINGAPORE MATHEMATICS?
Spiral
structure
Concrete
Pictorial
Abstract
Algebraic
thinking

6. SPIRAL
 Adopts a spiral structure in the development
of concepts, skills & processes.

7. EXAMPLE: WHOLE NUMBERS
 Grade 1- Numbers within 100
 Grade 2- Numbers within 1 000
 Grade 3- Numbers within 10 000
 Grade 4- Numbers within 100 000
 Grade 5- Numbers within 1 000 000
 Grade 6- Algebra
SPIRAL CURRICULUM
 The spiral opens up to revisit a concept taught in an earlier
year and to introduce related but more difficult concept.

8. SPIRAL CURRICULUM FROM GRADE 1 TO 2
Number Bonds
• prepare the children to learn their addition facts
• help in mental computations
Numbers to 100
• Interpret numbers within 100 in terms of tens
and ones
Addition and
Subtraction Within
1000 with renaming
• Prior knowledge
• Rote learning V.S conceptualised understanding

9.  Activities and curriculum enable children to progress
from concrete and pictorial levels to abstract
representation.
 Adopting Jerome Bruner: Enactive Iconic Symbolic
learning.
CONCRETE PICTORIAL ABSTRACT

11. WHY NUMBER
BONDS?

12. THE IMPORTANCE OF NUMBER BONDS
 An important foundation for understanding how numbers
work. A whole thing is made up of parts. If you know the parts,
you can put them together (add) to find the whole. If you know the
whole and one of the parts, you take away the part you know
(subtract) to find the other part.
 Number bonds let children see the inverse relationship
between addition and subtraction. Subtraction is not a totally
different thing from addition; they are mirror images. To subtract
means to figure out how much more you would have to add to get
the whole thing.
WHAT IS A NUMBER BOND?
A number bond is a mental picture of the relationship between a number
and the parts that combine to make it.

13. A) 1310 – 480 = ?
Compute the following subtraction equations.
B) 1000 – 480 = ?
Which equation is easier to compute? A or B? Why?
It is easier to take the place value of 10, 100 or 1000 to add or subtract.
By using 10, 100 or 1000 as a mean to add or subtract, it serves as a
effective tool of mental calculation.
A) 1310 – 480 = ?
1000 310
Working:
1) 1000 – 480 = 520
2) 520 + 310 = 830

14. 16 – 7 = ?
‘Count Back’
method
‘Subtraction with
renaming’ method
• Takes a longer time.
•Higher chance to make careless
mistakes.
• Fast
•Accurate
•Effective
•Prepares them for formal
addition & subtraction
involving larger numbers
162
- 37
9 10 11 12 13 14 15 16
10 6
Working:
1) 10 – 7 = 3
2) 3 + 6 = 9

15. GRADE 1- ADDITION & SUBTRACTION WITHIN 100
 add ones and tens
 subtract ones and tens
+
23 + 3 = ?
20 3 3

16. ADDITION & SUBTRACTION WITHIN 100
 add two 2 digit numbers
Eg. 33 + 12 =

17. ADDITION & SUBTRACTION WITHIN 100
 subtract a 2 digit number from another 2 digit number

18. ADDITION & SUBTRACTION WITHIN 100
 addition with renaming

19. ADDITION & SUBTRACTION WITHIN 100
 subtraction with renaming

20. 13 – 8 = ____
Working:
10 – 8 = 2
2 + 3 = 5

21. 13 – 8 = 5
10 3
Working:
10 – 8 = 2
2 + 3 = 5

23. MENTAL ADDITION
61 is 6 tens and 1 one.
1 one + 8 ones = 9 ones
What number is 8 more than 61?
Tens Ones
6 1
8 ones
60
1
60
9
Add 8 ones
61 + 8 = 69
Grade 2

24. MENTAL
ADDITION
Grade 2

25. MENTAL ADDITION
WITHOUT REGROUPING
Mental Addition
with regrouping
Grade 2

26. MENTAL SUBTRACTION
WITHOUT REGROUPING
Mental Subtraction
with regrouping
Grade 2