oak lawn beyond the basics 01

Dr. Yeap Ban Har Marshall Cavendish Institute

Singapore yeapbanhar@gmail.com

Slides are available at

www.banhar.blogspot.com

www.facebook.com/MCISingapore

Marshall Cavendish Institute www.mcinstitute.com.sg

SINGAPORE

M AT H Beyond the Basics

St Edward’s School

Florida, USA

Day One

Dr. Yeap Ban Har Marshall Cavendish Institute

yeapbanhar@gmail.com Slides are available at

www.banhar.blogspot.com

www.facebook.com/MCISingapore

Marshall Cavendish Institute

www.mcinstitute.com.sg

CONTACT

I N F O

Introduction

We start the day with an overview of

Singapore Math.

Curriculum document is available at http://www.moe.gov.sg/

Singapore Ministry of Education 1997

THINKING SCHOOLS

LEARNING NATION

is singapore what

mathematics

key focus singapore

mathematics of

problem solving

thinking

excellent vehicle

an

for the development & improvement of a person’s intellectual

competencies Ministry of Education Singapore 2006

conceptual understanding

Fundamentals of Singapore Math – Review & Extend Thinking: It’s the Big Idea! Problem Solving, Visualization, Patterning, and

Number Sense The Concrete-Pictorial-Abstract Approach

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.

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

Strategy 1

Get 3 x 4 from 2 x 4

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.

Strategy 2

Doubling

Strategy 4

Get 9 x 4 from 10 x 4

Unusual Response

Get 4 x 8 from 4 x 2. Can it be done? Does the number

of cups change? Does the number of counters per cup

change?

Differentiated Instruction

These are examples of how the lesson can be

differentiated for advanced learners.

Differentiated Instruction

These are examples of how the lesson can be

differentiated for advanced learners.

Exercise

Discuss the four ways to represent 1

group of 4. Which is used first? Why?

Which is used next? Why?

Textbook Study

Observe the various meanings of

multiplication from Grade 1 to Grade

3.

Prior to learning multiplication, students

learn to make equal groups using concrete

materials. Marbles is the suggested

materials.

After that they represent these concrete

situations using, first, drawings ..

Open Lesson in Chile

… and, later, diagrams. Students also

write multiplication sentences in

conventional symbols.

First, equal groups –

three groups of four.

Second, array –

Three rows of four

Third, four multiplied three

times ….

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.

They begin with equal group representation.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

In Primary 2, students learn

multiplication facts of 2, 5, 10 and 3

and 4. In Primary 3, they learn the

multiplication facts of 6, 7, 8 and 9.

Later, the array meaning of

multiplication is introduced.

Square tiles are subsequently used to lead to

the area representation of multiplication.

Lesson 2

Multiplication of multi-digit numbers

taught in a problem-solving approach.

Lesson 2 August 6, 2012

Lesson 2 August 2, 2012

39 x 6

30 9

6

40 x 6 = 240 39 x 6 =

30 9

Method 2 Method 1

Lesson 3

Use digits 1 to 9 to make a correct

multiplication sentence =.

Open Lesson at Broomfield, Colorado

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?”

Multiplication Around Us

Do you see multiplication in these work

of art around the venue of the

conference? Hilton Oak Lawn, IL

Lesson 4

We studied the strategies to help

struggling readers as well as those

weak in representing problem

situations.

Lesson 4 August 6, 2012

Lesson 5

In the end ... At first …

Alice

Betty

Charmaine

Dolly

20

10

August 2, 2012

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.

Lesson 5 August 6, 2012

Carl

Ben

$4686

Differentiated instruction for

students who have difficulty

with standard algorithms. Use

number bonds.

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.

Lesson 6 Let’s look at the emphasis on visualization and

generalization in a task from a different topic –

area of polygons.

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’?

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?

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.

Tampines Primary School, Singapore

What • Visualization

• Generalization

• Number Sense

How • Tell

• Coach

• Model

• Provide

Opportunities