1. Dr. Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
SINGAPORE
M AT H
Beyond the Basics
Day One
St Edward’s School
Slides are available at Florida, USA
www.banhar.blogspot.com
Marshall Cavendish Institute
www.facebook.com/MCISingapore www.mcinstitute.com.sg
2. Dr. Yeap Ban Har
CONTACT Marshall Cavendish Institute
INFO yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com Marshall Cavendish Institute
www.mcinstitute.com.sg
www.facebook.com/ MCISingapore
16. Fundamentals of Singapore Math – Review & Extend
Thinking: It’s the Big Idea!
Problem Solving, Visualization, Patterning, and
Number Sense
The Concrete-Pictorial-Abstract Approach
17. Lesson 1
We do a case study on multiplication
facts. We will see the use of an anchor
task to engage students for an
extended period of time.
18.
19.
20.
21.
22. Strategy 1
Get 3 x 4 from 2 x 4
Strategy 2
Doubling
Strategy 3
Get 7 x 4 from 2 x 4 and 5 x 4
Strategy 4
Get 9 x 4 from 10 x 4
24. Strategy 3
Get 9 x 4 from 4 x 4 and 5 x 4
This is essentially the distributive
property. Do we introduce the
phrase at this point? Recall the
discussion on Dienes.
35. … and, later, diagrams. Students also
write multiplication sentences in
conventional symbols.
36. First, equal groups –
three groups of four. Third, four multiplied three
times ….
Second, array –
Three rows of four
37. Textbook Study
Observe how equal group
representation evolves into array and
area models. Also observe how the
multiplication tables of 3 and 6 are
related on the flights of stairs.
52. Students who were already good in the skill of multiplying two-digit number
with a single-digit number were asked to make observations. They were
asked “What do you notice? Are there some digits that cannot be used ta
all?”
53. Multiplication Around Us
Do you see multiplication in these work
of art around the venue of the
conference? Hilton Oak Lawn, IL
54.
55. Lesson 4
We studied the strategies to help
struggling readers as well as those
weak in representing problem
situations.
58. Lesson 5 August 2, 2012
In the end ... At first …
Alice 20
Betty 10
Charmaine
Dolly
59. Lesson 5
Question: How do we help students set up the model?
Students are introduced to the idea of using a
rectangle to represent quantities – known and
unknown. Paper strips are used. Later, only diagrams
are used. Advanced skills like cutting and moving are
learned in Grades 4, 5 and 6. How is the idea of
bar model introduced in Grades K – 3?
Lesson 5 shows a basic bar model solution in Grade
5.
64. 2x + x = 4686
3x = 4686
Students in Grade 7 may use algebra to deal with such situations. Bar model is
actual linear equations in pictorial form.
65. Lesson 6
Let’s look at the emphasis on visualization and
generalization in a task from a different topic –
area of polygons.
66.
67. Differentiated Instruction
Is it true that the area of the quadrilateral is
half of the area of the square that ‘contains’ it?
Why is the third case different from the first
two? What are your ‘conjectures’?
68. It was observed that the area of the polygon is
half of the number of dots on the sides of the
polygon. Thus, the polygon on the left has 22
dots on the sides and an area of 11 square
units. Is this conjecture correct?
69. One of the participants used the
results to find the area of this
trapezoid. The red triangle has 3
dots on the sides (hence, area of
1.5 square units). The brown one
has 6 dots. The purple one has 6
dots, Hence, the area of these two
triangles is 3 square units each.
70. What
• Visualization
• Generalization
• Number Sense
How
• Tell
• Coach
• Model
• Provide
Opportunities
Tampines Primary School, Singapore