September 8th, 2010
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Mathematics is an “excellent vehicle
to develop and improve a person’s
intellectual competence”
Singapore Ministry of Education,
2006
The math curriculum in Singapore
has been recognized worldwide
for its excellence in producing
students highly skilled in
mathematics.
Educators in the United States took
notice when students in Singapore
ranked top in the world in mathematics
on the Trends in International
Mathematics and Science Study (TIMSS) in
1993, 1995, 2003, and 2007. (Study done in
Massachusetts)
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Bruner – CPA Approach
 What students say about...
◦ Concrete
“I like to learn with something I can touch, not just watching
my teacher touch it. My teacher lets me touch and move lots
of different things, too.”
◦ Pictorial
“…pictures in my math and reading books, magazines,
pictures I can color, and pictures I can draw…”
◦ Abstract
“Numbers that my teacher writes, that I write, tally marks
that I draw, number bond cards and numbers in books…”
Singapore Math curriculum…
◦ Helps students develop the necessary
math concepts and process skills for
everyday life and
◦ provides
formulate,
students with the ability
apply,
problems.
and
to
solve
 Fewer
topics are covered in
greater depth enabling students
sufficient time to gain mastery.
 We
can use this to our advantage
during this time of transition…
Curriculum Sequence (Sample)
Level 3A
Level 4A
Level 5A
Numbers to
10,000
Numbers to
1,000,000
Numbers to
1,000,000,000
Addition and
Subtraction
Mental Math
Addition and
Subtraction
Mental Math
Addition and
Subtraction
Mental Math
Two-Step Word
Problems
Multi-step Word Multi-step Word
Problems
Problems
Learning the
Division
Algorithm
concretely with
place value
charts and disks
Re-teach
division
Algorithm
concretely with
place value
charts and disks
Re-teach
division
Algorithm
concretely with
place value
charts and disks
Fractions
Fractions
Fractions
Kindergarten
Earlybird A, Earlybird B
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First Grade
Second Grade
Third Grade
1A and 1B
1B and 2A, extension to 2B
2B and 3A, extension to 3B
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Fourth Grade
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Fifth Grade
3A (with extension to 4A)
3B (with extension to 4B)
4A (with extension to 5A)
4B (with extension to 5B)
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Program Architecture
◦ The Core Curriculum for each semester comprises
one Textbook and one Workbook.
◦ Teacher Resources support the teacher to carry out
effective lessons.
◦ Supporting Materials complement the Core
Curriculum and provide opportunities for extra
practice, review, assessment, and enrichment
Student Textbook (T.B.)
Math Journal
Non-consumable – students
do not write in this book.
(textbook
exercises,
Word problems,
and misc.)
Student Workbook (W.B.)
Consumable – students must
write in this book .
Extra Practice**
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**may be used for test preparation
Teacher Guide (T.G.)
Model
drawing
guide
with
solutions
Extra
Practice **
**may be used for test preparation
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Increased Teacher Collaboration
◦ On-Campus Instructors
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Monthly planning meetings to discuss:
pacing,
pedagogical content
Lesson modeling
Coaching
Creating grade specific www.spiritmath.com webpages
Send a Teacher to Math Camp!
Home-Teacher
On-going Training
conducted by Laurie Ruwe and Carol Lowry
(Monthly, Thursday afternoons, 2-3 p.m. in fellowship hall)
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Mental Math
Teacher Directed Lesson
Activity
Problem Solving (Models)
Independent Practice
5-10 min.
20 min.
15 min.
15 min.
15 min.
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Simply put…it’s
calculating in your
head. It’s “playing
with” or manipulating
numbers in your head
in order to solve a
problem. Sounds
simple, right?
What is Mental Math?
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Using your head to calculate is practical
Solidifies understanding of place value
Can make written computation easier
Teaches manipulation of numbers and creative
thinking skills
Can lead to improved estimation skills
Demonstrates how answers can be achieved in
different ways
Develops understanding of mathematical
operations
Helps students move from arithmetic to algebra
Develops mathematical thinkers
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Use as a daily warm up
Include mental math in problem solving
*Mental math should only include concepts
that have already been mastered
 All
of the Mental Math Strategies
for Addition and Subtraction and
learned by the end of 2B.
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Students in 3rd – 5th grade will
learn these strategies and will also
learn strategies for Multiplication
and Division.
Compensation – make a hundred
456 – 98
becomes 458 – 100 = 358
(Uncle / Nephew)
I can add the same number to the minuend
and the subtrahend and the difference stays
the same.
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400-198
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726-397
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1001-475
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236-98
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187-99
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Concrete
◦ Story, manipulatives, discovery!

Pictorial
◦ Students show understanding by relating by
constructing a picture or diagram
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Abstract
◦ Students find meaning to their pictures and
conceptualize or visualize the math behind the
concrete and pictorial
Place Value Teacher
Directed Lesson
With Char Forsten
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Ones
Tens (red)
Hundreds (orange)
Thousands (yellow)
Ten Thousands (green)
Hundred Thousands (blue)
Millions (purple)
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Ones (red)
Tens (blue)
Hundreds (green)
Thousands (yellow)
Each Teacher Guide Lists Suggested Materials
for your level.
Many of these materials can also be accessed
electronically.

Virtual manipulatives
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More
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Handmade manipulative instructions
Overview for each unit lists the suggested materials for each lesson.
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Making Math Manipulatives on a budget
How to use electronic “Manipulatives” or
virtual manipulatives
Good websites for “hands on” practice
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Support Classroom Activities by preparing an
activity (rules, materials, teacher aid during
activity if necessary)
Using the internet to find math content
appropriate activities
Extra-Curricular Activities - Math Olympiad,
Math clubs, Field trips...
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Foundations for Model Drawing in K-2nd
grade

Formally introduced in 3rd grade
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Singapore Maths Teacher
(really helpful website for model drawing help and practice!)
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Model Drawing is one of the most powerful
tools of Singapore Math.
Expect several opportunities to learn more at
workshops and through personal discovery!
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Singapore Math Success!
Mental Math site
Branching Tutorial PDF
Char Forsten Place Value Lesson
Virtual manipulatives
More manipulative
Handmade manipulative instructions
Place Value Charts (Printable)
Hundreds Chart (Printable)
Singapore Maths (Model Drawing)