Singapore Math Beyond the Basics Day 2

Dr. Yeap Ban HarMarshall Cavendish Institute

Singaporeyeapbanhar@gmail.com

Slides are available at

www.banhar.blogspot.com

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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

Lesson 5We 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 revisit the last problem from yesterday.

Lesson 5 June 18, 2012

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 5 June 18, 2012

Grade 6

Grade 4

Grade 5

240

240 + 120

Lesson 5 June 18, 2012

Grade 6

Grade 4

Grade 5

240

240 + 120

Lesson 5 June 18, 2012

Grade 6

Grade 4

Grade 5

240

240 + 120

Lesson 5 June 18, 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 6Diagrams 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

King Solomon Academy, London

Example of Secondary TextbookThis is how algebra is introduced in a Singapore

secondary textbook.

x x x

x

10

10

76 – 20

3 𝑥+10+𝑥+10=764 𝑥+20=764 𝑥=56𝑥=

564

=14

Lesson 7Four 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 7

Category Criteria

Emerging

Established

Extension

Guided Practice

Independent Practice

Differentiated Instruction

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)

Eventual Symbolic

Representation

My Pals Are Here! Mathematics (Second Edition)

Lesson 8This is an Open Lesson on Multiplication of fractions. The lesson began with a review of basic multiplication fact through a simple game (Salute!).

Moanalua Middle School, Honolulu

Moanalua Middle School, Honolulu

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 =

Equivalent FractionsAnother area of difficulty is equivalent fraction. This was demonstrated during the Open Lesson.

Further ExamplesOther similar examples of drill-and-practice using the fill out the boxes method.

Use the digits 2, 3, 6 and 8 to make the difference as small as possible when a smaller number is subtracted from a larger one.

Another variation is to use any digit without repeating them.

Lessons 9 & 10We studied a lesson on video and round up the institute by looking at a problem on developing the ability to see patterns and also on visualization.

Differentiated instruction and assessment were discussed through the sessions.

HomeworkTry the problems in the course materials.

Singapore Examination & Assessment BoardPrimary School Leaving Examination

1 fourth

4 eighteenths

+ 8 36

9 36

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