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# Houston Advanced Singapore Math Institute Beyond the Basics 02

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This is the second day of the Advanced Singapore Math Institute, held at Houston, Texas.

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### Houston Advanced Singapore Math Institute Beyond the Basics 02

1. 1. Yeap Ban Har Dr. Yeap Ban Har Marshall Cavendish Institute Marshall Cavendish Institute yeapbanhar@gmail.com Singapore yeapbanhar@gmail.com Day Two SINGAPORE M AT H Beyond the Basics St Edward’s SchoolSlides are available at Florida, USA Openwww.banhar.blogspot.com Lesson Hawaii, US A Marshall Cavendish Institute www.facebook.com/MCISingapore www.mcinstitute.com.sg
2. 2. visualizatiobar modelnmultiplicatiodivisionnfractionsconceptual understandinmentalcomputations
3. 3. Scroll down the page to see Second Grade MentalMath
4. 4. Lesson 9Visualization is the emphasis when studentslearn, say, multiplications involving fractions.
5. 5. 1 2 1 2 thirds4 3 41 2 1 4 sixth4 3 4
6. 6. 1 2 1 8 twelfth4 3 4 s 1 2 2 twelfth 4 3 s 1 2 1 sixth 4 3
7. 7. 1 2 14 3 6
8. 8. 1 2 1 1 2 1 1 14 3 6 4 3 2 3 6
9. 9. 1 2 1 1 2 1 1 14 3 6 4 3 3 2 6
10. 10. Moanalua MiddleSchool, Honolulu
11. 11. Moanalua MiddleSchool, Honolulu
12. 12. Lesson 10Some main reasons why students have difficulties learningfractions. This lesson focuses on one of them – the naming offractions.
13. 13. FRACTIONthe C P Aapproach
14. 14. 10Lesson 7
15. 15. FRACTION 3teaching for 3 fourths 4meaning
16. 16. St Edward’s School, Florida
17. 17. St Edward’s School, FloridaGrade 2concrete pictorial  abstract
18. 18. It does not FRACshow half. What does it show then? TION opportunities for differentiation It does not show fourth. What does it show then?
19. 19. My Pals Are Here! Mathematics (Second Edition)
20. 20. Initial Concrete Experience Subsequent Pictorial RepresentationMy Pals Are Here! Mathematics (Second Edition)
21. 21. My Pals Are Here! Mathematics (Second Edition) Eventual Symbolic Representation
22. 22. Lesson 11We studied the strategies to help struggling readers as well asthose 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.
24. 24. Lesson 11 August 3, 2012 1 third of all is the same as one third of the children and one third of the adults (120) Grade Grade 6 Grade 4 5 240
25. 25. Lesson 11 August 3, 2012 240 + 120 Grade Grade 6 Grade 4 5 240
26. 26. Lesson 11 August 3, 2012 240 + 120 Grade Grade 6 Grade 4 5 240
27. 27. Lesson 11 August 3, 2012 240 + 120 Grade Grade 6 Grade 4 5 240
28. 28. Lesson 11 August 3, 2012 c = 7201 1 1 1 (a c) a c 120 c3 3 3 3 4th Graders 5th Graders 6th Graders 1 1 1 c c c 1 c 120 240 1 c 3 6 2 3 6
29. 29. Types of assessment tasks
30. 30. Lesson 12Another area of difficulty is equivalent fraction.
31. 31. How manytwelfths? What is the name of the smaller piece
32. 32. Lesson 13Addition and subtraction of fractions – all depends onunderstanding what you can add and what you cannot.
33. 33. Lesson 14Addition and subtraction of fractions – all depends onunderstanding what you can add and what you cannot.
34. 34. Lesson 15How do we help students develop the method to divide fractionby a fraction?
35. 35. Open LessonThis is an Open Lesson on Multiplication of fractions. Thelesson began with a review of basic multiplication fact through asimple game (Salute!). This was done in Hawaii – in place of aLesson Video.
36. 36. Moanalua MiddleSchool, Honolulu
37. 37. Students were shown one whole which is divided into thirds, sixths, fourths as wellas two which were not yet divided into equal parts. They were asked to name thefraction represented by each part if the strip represented 1. Students were given a paper strip divided into thirds.Students were asked thevalue of one half of 2 thirds– they had difficulty usingthe diagram although theyseemed to know thealgorithm.They had to explain why thevalue is 1 third and 2 sixthFinal tasks doneindividually where theyhad to explain using adiagram the value of thisexpression.
38. 38. The main task was 1 fourth x 2 thirds. Practice x = Without repeating numbers for numerators and denominators make correct multiplication sentences. Try to keep the numbers small.The idea of ¼ x 4sixths