August 24, 2010
Today’s Training
 Opening Prayer
 Singapore Math Background
 Become acquainted with the Key Pillars of Singapore Math through…
-
Grade 1 Lesson Demo (Lisa Jacobson)
-
Grades K-2 Math Strategies ( Laurie Ruwe)
-
Grades 4 – 5 Lesson Demo (Carol Lowry)
-
Singapore Model Drawing Demonstration (Laurie Ruwe and Carol
Lowry)
 Closing Comments
Singapore Math Success!
What is Singapore Math?
 Background
 Singapore Math refers to the mathematics curriculum in the
country of Singapore
 Its greatest natural resource, according to the Ministry of
Education, is its people
 Singapore Math description
Why Singapore Math at Spirit?
Why are Singapore Math strategies being used by so
many American teachers and schools?
Singapore is an international leader in math.
What is the TIMSS Report?
-Trends in International Mathematics and Science Study
Singapore's 4th & 8th grade students have scored first
for Mathematics in 1995, 1999, and 2003.
The latest TIMSS report (2007) shows Singapore in second place, topped by Hong
Kong. (American students fall in the middle, out of 46 countries.)
Why Singapore Math at Spirit?
 Typical math instruction is heavily weighted
by procedures (algorithms) – we teach
HOW to solve particular problems but fail
to address the foundational knowledge
that makes solving those problems
meaningful, relevant, and reasonable.
Why Singapore Math at Spirit?
 The goal of Singapore Math is conceptualization and
mastery for all learners.
Key Pillars of Singapore Math
 Mental Math of mastered concepts
 Introduction of Concepts through Concrete, Pictorial,
Abstract (CPA) Approach
 Problem Solving with Model Drawing
 Meaningful activities
 Independent Practice until mastery
CPA Demonstration
(Concrete/Pictorial/Abstract)
3=2+
YUMMY!
Can you
see it?
Grade 1 Lesson
Number Bonds
Questions?
“Facts on the Brain”
 Groups – Three students
 Materials – Playing or number cards
 Directions: The object of this game is to practice finding sums and missing
addends. One player will be the sum finder, while the other two will be
the addends.
 1. The sum finder gives each addend a pile of cards that are face down.
 2. The sum finder counts aloud, “1..,2…,3!”
 3. On “3”, each addend lifts a card from his or her pile and places it on the
heads.
 4. The sum finder announces the sum of the two numbers.
 5. Knowing the sum, each addend looks at their partner’s number to
determine their missing addend.
 6. The first student to announce the correct missing addend wins that round
and gets both cards.
 7. The student repeats steps 2 through 6 and continue until their card decks are
used.
 8. When finished with the decks, students rotate roles and begin practicing
again.
Break Time!
K-2 Grade Strategies
•Number Bonds
K-2 Strategies (Continued)
•Branching
½ of ¾
¾ of ½
Grade 5
(Level 4A with extension to 5A)
Product of Fractions
 ½ of ¾
 Johnny had 16 cookies. He gave 3/4 of his cookies to his sister, Susie.
She ate 1/2 of her cookies, and saved the rest for her dad. What fraction
of all the cookies did Susie eat? How many cookies did she save for her
dad?
Lesson 4.1a
A Fraction of a
Fraction
(Taken from Primary
Mathematics
Standards Edition
student Textbook 5A)
Teacher Directed
Teacher Directed Instruction
continues from the concrete to
pictorial with students drawing the
models in their math journals or dry
erase boards.
(Students create their own pictures)
Notice that the colored boxes are not
for writing, but discussion
opportunities. (Students should not
write in their textbooks.)
Lesson continues until purple
pencil indicating workbook
exercise to be completed as
independent practice.
Notice the picture to the left.
Students should determine from
the picture what the correct
fraction is. Then, verify their
conclusion by the equation to
the right. Students should be
able to explain what is
happening in the picture.
Perhaps, even tell a story to
match the picture…
Notice the space
allowed on this
practice page.
The expectation is
for the student to
draw a picture,
not just to simply
multiply
numerators and
denominators.
Questions?
Singapore Model Drawing Method
Alice earned money from tips from her waitress job.
She put ¼ of the money in her savings account. She
gave ¾ of the remaining money to the local food bank.
She had $12 left for herself. How much money did
Alice earn in tips?
Let’s Get Started!
 Share how you solve the problem.
 "Get out your work paper." Not your scratch paper.
 Use page protector sheet over text page.
Use dry erase marker.
Step 1: Read the entire problem and underline the question.
Alice earned money from tips from her waitress job.
She put ¼ of the money in her savings account. She
gave ¾ of the remaining money to the local food bank.
She had $12 left for herself. How much money did
Alice earn in tips?
Step 2: Rewrite question as an answer statement.
How much money did Alice earn in tips?
becomes…
Alice earned _________ in tips.
Step 3: Determine who and/or what is involved in the problem.
Alice earned money from tips from her
waitress job. She put ¼ of the money in her
savings account. She gave ¾ of the remaining
money to the local food bank. She had $12 left for
herself. How much money did Alice earn in
tips?

Step 4: Draw a Unit Bar(s)
Alice’s
Tips
Step 5: “Chunk” the Problem
Draw in information that you know
1/4
Alice’s
Tips
savings
Step 5: “Chunking”…
Continue to fill in information that you know…
1/4
Alice’s
Tips
Can you see
what each
fourth is
equal to in
the bottom
bar?
savings
Remainder
Food bank contribution
3/4
$12
Step 6: Perform Calculations
1/4
Alice’s
Tips
savings
Each fourth is
equal to $12,
We use the
calculation
$12 x 4 = $48
So, we know
the remainder
was $48.
Remainder
Food bank contribution
$12
$12
3/4
$12
$12
Step 6: Perform Calculations
1/4
Alice’s
Tips
savings
On the top
bar, the
Remainder is
divided into
thirds.
$48 / 3 = $16
Remainder($48)
$16
$16
Food bank contribution
3/4
$16
$12
Step 7: Conclusion
1/4
Alice’s
Tips
savings
Remainder ($48)
$16
$16
$16
$16
We see that
each fourth on
the top bar is
equal to $16.
So, the total
tips that Alice
earned were
$16 x 4 = $64
Food bank contribution
3/4
$12
Step 7: Conclusion
Alice earned $64 in tips.
1/4
Alice’s
Tips
savings
$16
$16
$16
$16
Food bank contribution
3/4
$12
Singapore Model Drawing
 You Try!
Manipulatives!
 What do I need for my student?
 What will they use in class?
 What should I use at home?
 Parent/student Make and Take.
 Anyone have access to a laminator?
Sept. 8 Singapore Training
 How do I use my curriculum?
 What will my student be learning this year?
 What does a typical week look like?
 What can I do during the day or week if I need help?
 Extra practice or Intensive Practice?
 Future training workshops