oak lawn beyond the basics 02

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 Two

Yeap Ban Har Marshall Cavendish Institute

yeapbanhar@gmail.com

Open Lesson

Hawaii, USA

Number bonds which is fundamental in number sense

development is emphasized in subsequent levels

even when they are not explicit in the textbooks.

We have seen how number bonds is used in Grade

1 lesson (video). 32 is 10 + 10 + 10 + 2. 32 is also

20 and 12. 32 is also 20 + 10 + 2.

We have also seen how it is used in the development

of number facts.

Lesson 2 August 6, 2012

In Grade 3, we use it doe large number

multiplication when products are found through

partial products.

In the differentiated

approach to doing

long division in the

Grade 5 lesson ,

number bonds

continue to play a

prominent role.

visualization bar model multiplication division fractions conceptual understanding mental computations

Scroll down the page to see Second Grade Mental Math

Lesson 7 Some main reasons why students have difficulties learning fractions.

This lesson focuses on one of them – the naming of fractions.

F R A C T I O N the C P A approach

Lesson 7

10

F R A C T I O N teaching for

meaning

3 fourths 3 4

??

St Edward’s School, Florida

Grade 2

concrete pictorial abstract

St Edward’s School, Florida

It does not show

half. What does it

show then?

It does not show

fourth. What does it

show then?

F R A C T I O N opportunities for

differentiation

My Pals Are Here! Mathematics (Second Edition)

Initial Concrete

Experience

Subsequent Pictorial

Representation My Pals Are Here! Mathematics (Second Edition)

My Pals Are Here! Mathematics (Second Edition)

Eventual Symbolic

Representation

Lesson 8 Another area of difficulty is equivalent fraction.

2 thirds is equal to how many sixths?

2 thirds is cut into 8 equal parts. Are the parts smaller? What is the name of the smaller equal parts?

Lesson 9 Addition and subtraction of fractions – all depends on understanding

what you can add and what you cannot.

Rename as fourths

Make 1 by combining 3 of the fourths with 1 half.

Additional Example Addition and subtraction of fractions – all depends on understanding

what you can add and what you cannot.

Lesson 10 Visualization is the emphasis when students learn, say, multiplications

involving fractions.

24

1

3

2

4

1 thirds

44

1

3

2

4

1 sixth

84

1

3

2

4

1 twelfths

23

2

4

1 twelfths

13

2

4

1 sixth

6

1

3

2

4

1

6

1

3

2

4

1

6

1

3

1

2

1

3

2

4

1

6

1

3

2

4

1

6

1

2

1

3

1

3

2

4

1

Moanalua Middle School, Honolulu

Moanalua Middle School, Honolulu

Lesson 11 How do we help students develop the method to multiply and divide

fraction by a fraction?

Additional Example We studied the strategies to help struggling readers as well as those

weak in representing problem situations.

• Who is in the story? What is it all about?

• Is the sentence easy?

• Read a complex sentence as simple sentences.

• Leave out numbers in reading.

• Which sentence is best to start off with?

• Do as we read.

• Use paper strips.

• How does the model look like? Can you picture it? How should the

bar change?

Let’s look at a word problem involving fractions.

Lesson 12 August 7, 2012

Grade

6 Grade

4 Grade

5

240

Grade

6 Grade

4 Grade

5

240

1 third of all is the same as

one third of the children and

one third of the adults (120)

Lesson 12 August 3, 2012

Grade

6 Grade

4 Grade

5

240

240 + 120

Lesson 12 August 3, 2012

ccaca3

1120

3

1

3

1)(

3

1

4th Graders 5th Graders 6th Graders

c3

1120 240 c

6

1ccc2

1

6

1

3

1

c = 720

Lesson 12 August 3, 2012

Additional Example for Secondary

Lesson Diagrams can be used as a remedial strategy to help students with

solving linear equations in one and two unknowns.

x

x x 1

x x 1

x

x x x x 1

x x x x

x

x x x 2

x x x

x

x x 5

x x

King Solomon Academy, London