Singapore Math Beyond the Basics Day 2
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Dr. Yeap Ban HarMarshall Cavendish Institute
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
Open LessonHawaii,
USA
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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.
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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)
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Lesson 5 June 18, 2012
Grade 6
Grade 4
Grade 5
240
240 + 120
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Lesson 5 June 18, 2012
Grade 6
Grade 4
Grade 5
240
240 + 120
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Lesson 5 June 18, 2012
Grade 6
Grade 4
Grade 5
240
240 + 120
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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
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Lesson 6Diagrams can be used as a remedial strategy to help students with solving linear equations in one and two unknowns.
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x
x x 1
x x 1
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x
x x x x 1
x x x x
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x
x x x 2
x x x
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x
x x 5
x x
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King Solomon Academy, London
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King Solomon Academy, London
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Example of Secondary TextbookThis is how algebra is introduced in a Singapore
secondary textbook.
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x x x
x
10
10
76 – 20
3 𝑥+10+𝑥+10=764 𝑥+20=764 𝑥=56𝑥=
564
=14
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Lesson 7Four main reasons why students have difficulties learning fractions. This lesson focuses on one of them – the naming of fractions.
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F R A CT I O N the C P Aapproach
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Lesson 7
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Category Criteria
Emerging
Established
Extension
Guided Practice
Independent Practice
Differentiated Instruction
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F R A CT I O N teaching for
meaning3 fourths 3
4
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St Edward’s School, Florida
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Grade 2concrete pictorial abstract
St Edward’s School, Florida
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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
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My Pals Are Here! Mathematics (Second Edition)
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Initial Concrete
Experience
Subsequent Pictorial
RepresentationMy Pals Are Here! Mathematics (Second Edition)
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Eventual Symbolic
Representation
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My Pals Are Here! Mathematics (Second Edition)
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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!).
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Moanalua Middle School, Honolulu
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Moanalua Middle School, Honolulu
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Moanalua Middle School, Honolulu
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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.
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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 =
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Equivalent FractionsAnother area of difficulty is equivalent fraction. This was demonstrated during the Open Lesson.
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Further ExamplesOther similar examples of drill-and-practice using the fill out the boxes method.
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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.
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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.
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HomeworkTry the problems in the course materials.
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Singapore Examination & Assessment BoardPrimary School Leaving Examination
1 fourth
4 eighteenths
+ 8 36
9 36
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