Singapore Math Strategies You Can Count On!
NCTM Annual Meeting in Philadelphia
April 26, 2012
Char Forsten, Presenter
www.sde.com
Booth # 1012
A Quick Overview of Singapore’s Primary Mathematics Curriculum

The term “Singapore Math” refers to the mathematics curriculum in the
country of Singapore, developed by the Curriculum Planning &
Development Institute of Singapore and approved by Singapore’s Ministry
of Education. (Primary Mathematics includes grades 1 – 6)

Strengths:
o Has a proven track record
o Is taught in English
o Builds understanding through part-whole thinking
o Emphasizes “why” before “how”
o Bases instruction on student background knowledge
o Is coherent and teaches for mastery
o Develops strong written computation, mental math, & problem
solving skills

Research Base:
o “Concrete-pictorial-abstract” & “Teaching for mastery” (Jerome
Bruner
o Relational understanding (Richard Skemp)
o Multiple models and varied practice and experiences (Zoltan
Dienes)
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Singapore Math Strategies You Can Count On in Grades 3 – 5!
1. Using number bonds to show part/whole thinking
. “Making Tens” – A pathway to developing mental math skills –
Concrete:
Pictorial
8+5
38 + 7
292 + 119
14 oz. + 7 oz.
45 min. + 35 min.
2,389 + 35
2 + 2
3
3
Abstract
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2. Place value is not a chapter in a book! Teaching computation methods
through an understanding of place value and “visual” language.
3 x 14
2 31
3. Adding and subtracting unlike fractions:
Concrete: Use pattern blocks
Pictorial:
Abstract:
4. Multiplying a fraction by a fraction
Concrete: Paper folding
Pictorial: Draw a model
Abstract: Solve
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5. Model Drawing (Bar modeling)
1) Cal scored 6 more points than Max in last night’s basketball game.
Together, they scored a total of 38 points. How many points did Max
score?
2) Justin Case had $10. Frank N. Stein had 3 times as much money as
Justin. How much more money did Frank have than Justin?
3) The ratio of blue marbles to red marbles in a bag is 2:3. If there are 25
marbles altogether, how many red marbles are there?
4) If 2/3 of a number is 6, what is the number?
5) One number is 2/5 of another number. If the difference between the 2
numbers is 15, what are the two numbers?
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6) Kate spent 3/5 of her money on a pedicure and 2/3 of the remaining
money on a manicure. She had $10 left. How much money did Kate have
at first?
7) Harold ran 2.3 miles each day during the month of April. How many total
miles did Harold run in April?
8) Anthony played in 3 basketball games during vacation week. He scored
24 points the first game, 18 points the second game, and 27 points the
third game. What was his average score for the 3 games?
9) Twenty percent of the 5th graders from Antrim Middle School went on a
field trip. If 120 students went on the field trip, how many total students
were in the 5th grade at Antrim Middle School?
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Steps for Model Drawing - Possible Scoring
Reads the entire problem. (1)
Rewrites the question in sentence form, leaving a space for the answer. (1)
Determines who and/or what is involved in the problem. (1)
Draws the unit bar(s). (1)
Chunks the problem and adjusts the unit bars to match the information in
the problem. Fills in the question mark. (3)
Correctly computes and solves the problem. (2)
Writes the answer in the sentence. (1)
REFERENCES & RECOMMENDED RESOURCES
1. Forsten, Char. (2005) Math Strategies You Can Count On! Peterborough, NH:
Crystal Springs Books.
2. Forsten, Char. (2010) Step-by-Step Model Drawing. Peterborough, NH: Crystal
Springs Books.
3. Lee, Peng Yee (Edited by) (2007) Teaching Primary School Mathematics.
Singapore: McGrawHill.
4. Parker, Thomas and Scott Baldridge. (2003) Elementary Mathematics for Teachers.
Michigan State University.
5. Polya, George. (1945) How to Solve It. Princeton University Press.
6. Ministry of Education, Singapore. (2009) The Singapore Model Method for Learning
Mathematics. Singapore: EPB Pan Pacific.
7. Walker, Lorraine. (2010) Model Drawing for Challenging Word Problems – Grades 69) Peterborough, NH: Crystal Springs Books
8. Word Problems for Model Drawing Practice:- available through Crystal Springs Books
9. Yeap, Banhar, Ph.D.(2010) Bar Modeling – A Problem Solving Tool. Singapore:
Marshall Cavendish.
WEBSITES
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Crystal Springs Books - www.crystalsprings.com
Staff Development For Educators
www.sde.com
Singapore Math - www.singaporemath.com
National Council of Teachers of Mathematics - www.nctm.org
Thinking Blocks – www.thinkingblocks.com
Great Source (Math in Focus): www.mathinfocus.com
Conceptua Math www.conceptuamath.com
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