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Dr. Yeap Ban Har Marshall Cavendish Institute
Singapore [email protected]
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
[email protected]
Open Lesson
Hawaii, USA
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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.
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We have also seen how it is used in the development
of number facts.
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Lesson 2 August 6, 2012
In Grade 3, we use it doe large number
multiplication when products are found through
partial products.
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In the differentiated
approach to doing
long division in the
Grade 5 lesson ,
number bonds
continue to play a
prominent role.
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visualization bar model multiplication division fractions conceptual understanding mental computations
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Scroll down the page to see Second Grade Mental Math
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Lesson 7 Some 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 C T I O N the C P A approach
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F R A C T I O N teaching for
meaning
3 fourths 3 4
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St Edward’s School, Florida
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Grade 2
concrete 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 C T 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
Representation My Pals Are Here! Mathematics (Second Edition)
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My Pals Are Here! Mathematics (Second Edition)
Eventual Symbolic
Representation
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Lesson 8 Another area of difficulty is equivalent fraction.
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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?
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Lesson 9 Addition and subtraction of fractions – all depends on understanding
what you can add and what you cannot.
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Rename as fourths
Make 1 by combining 3 of the fourths with 1 half.
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Additional Example Addition and subtraction of fractions – all depends on understanding
what you can add and what you cannot.
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Lesson 10 Visualization is the emphasis when students learn, say, multiplications
involving fractions.
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24
1
3
2
4
1 thirds
44
1
3
2
4
1 sixth
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84
1
3
2
4
1 twelfths
23
2
4
1 twelfths
13
2
4
1 sixth
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6
1
3
2
4
1
6
1
3
1
2
1
3
2
4
1
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6
1
3
2
4
1
6
1
2
1
3
1
3
2
4
1
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Moanalua Middle School, Honolulu
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Moanalua Middle School, Honolulu
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Lesson 11 How do we help students develop the method to multiply and divide
fraction by a fraction?
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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.
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Lesson 12 August 7, 2012
Grade
6 Grade
4 Grade
5
240
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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
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Grade
6 Grade
4 Grade
5
240
240 + 120
Lesson 12 August 3, 2012
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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
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Additional Example for Secondary
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Lesson Diagrams 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 x x 1
x x x x
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King Solomon Academy, London