Dr. Yeap Ban HarMarshall Cavendish Institute

Singaporeyeapbanhar@gmail.com

Slides are available at

www.banhar.blogspot.com

www.facebook.com/MCISingaporeMarshall Cavendish Institute

www.mcinstitute.com.sg

SINGAPORE

M AT H Beyond the Basics

St Edward’s SchoolFlorida, USA

Day Two

Yeap Ban HarMarshall Cavendish Institute

yeapbanhar@gmail.com

Open LessonHawaii,

USA

visualizationbar modelmultiplicationdivisionfractionsconceptualunderstandingmentalcomputations

Scroll down the page to see Second Grade Mental Math

Lesson 9Visualization 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 twelft

hs2

3

2

4

1 twelft

hs

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 10Some main reasons why students have difficulties learning fractions. This lesson focuses on one of them – the naming of fractions.

F R A CT I O N the C P Aapproach

Lesson 710

F R A CT I O N teaching for

meaning3 fourths 3

4

St Edward’s School, Florida

Grade 2concrete 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 CT I O N opportunities for differentiation

My Pals Are Here! Mathematics (Second Edition)

Initial Concrete

Experience

Subsequent Pictorial

RepresentationMy Pals Are Here! Mathematics (Second Edition)

My Pals Are Here! Mathematics (Second Edition)

Eventual Symbolic

Representation

Lesson 11We 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 11 August 3, 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 11 August 3, 2012

Grade 6

Grade 4

Grade 5

240

240 + 120

Lesson 11 August 3, 2012

Grade 6

Grade 4

Grade 5

240

240 + 120

Lesson 11 August 3, 2012

Grade 6

Grade 4

Grade 5

240

240 + 120

Lesson 11 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 11 August 3, 2012

Types of assessment tasks

Lesson 12Another area of difficulty is equivalent fraction.

How many

twelfths?

What is the name of the

smaller piece

Lesson 13Addition and subtraction of fractions – all depends on understanding what you can add and what you cannot.

Lesson 14Addition and subtraction of fractions – all depends on understanding what you can add and what you cannot.

Lesson 15How do we help students develop the method to divide fraction by a fraction?

Open LessonThis is an Open Lesson on Multiplication of fractions. The lesson began with a review of basic multiplication fact through a simple game (Salute!). This was done in Hawaii – in place of a Lesson Video.

Moanalua Middle School, Honolulu

Students were given a paper strip divided into thirds.

Students were shown one whole which is divided into thirds, sixths, fourths as well as two which were not yet divided into equal parts. They were asked to name the fraction represented by each part if the strip represented 1.

Students were asked the value of one half of 2 thirds – they had difficulty using the diagram although they seemed to know the algorithm.

They had to explain why the value is 1 third and 2 sixthFinal tasks done individually where they had to explain using a diagram the value of this expression.

The main task was 1 fourth x 2 thirds.

The idea of ¼ x 4 sixths

Practice

Without repeating numbers for numerators and denominators make correct multiplication sentences.

Try to keep the numbers small.

x =