Professional Development Singapore Mathematics Seoul 9 – 11 July 2012 Dr Yeap Ban Har email@example.com Marshall Cavendish Institute Singapore Presentation slides are available at www.banhar.blogspot.com MAP101 www.mcinstitute.com.sg www.facebook.com/MCISingapore
FUNDAMENTALS of singapore math Mayflower Primary School, SingaporeSlides are available atwww.banhar.blogspot.com
IntroductionThis course is an overview of SingaporeMath. It includes the what and how ofteaching mathematics.
Curriculum document is available at http://www.moe.gov.sg/
THINKING SCHOOLSLEARNING NATION Singapore Ministry of Education 1997
110 g180 g 110 g Bella puts 180 g brown sugar on the dish. 290 g
on an identical dish 110 g 2 units = 180 g 1 unit = 90 g 180 g 110 g 3 units = 270 g Bella puts 270 g brown sugar on the dish. 290 g
Singapore Math is based on the CPA Apporach.Pictorial representations can be more concrete(pictures) or more abstract (diagrams such as barmodel).An alternate way to solve the brown sugarproblem:
Singapore Mathematics focuses on the ability to visualize. For example, bar models are used extensively.Bar models were introduced to overcome thepervasive problems students had with word problems– even the basic ones.
Such word problems are used to helpstudents Deal with information Handle and clarify ambiguity – one dish or two Develop visualization – bar models are used extensively Practice mental strategies – numbers used are not difficult to compute
Procedural & Conceptual UnderstandingSingapore Math places an emphasis onboth. Procedures are explained in aconceptual way. For example, longdivision is seen simply as breakinglarge numbers into smaller ones beforedividing.
Using number bonds to make sense of long divisionDifferentiated Instruction for advanced Over-learners – how does one get the result emphasizing of 51 3 from 60 3. procedural Balancing knowledge procedural knowledge with conceptual understanding
Method 1The positions of 11, 22, 33 are at C, H, E respectively.Positions of multiples of 11 can be located. Method 4 The position for 99 can be found by writing out all the numbers Method 3 but this is not Numbers ending with 9 efficient are at E. So, 99 is at E method. Method 2 too. The positions of numbers ending with 1 and 6 can be located ta either ends. Thus 91 or 96 can be located. Subsequently, 99 can be located.
Method 1The letters under A and I areeven. So 99 cannot be there.Method 2The positions of numbers endingwith 9 form a diagonal pattern.Method 3The numbers under first Dincreases by 8. Thus 17 + 80 = 97is under first D. The position for99 can be worked out.Method 4The positions of multiples of 8 I isdefinitely under A. 8 x 12 = 96 isunder A. The position of 99 canbe worked out.Method 5Numbers under V is 1 less thanmultiples of 4. So, 2011 (1 lessthan 2012) is under V. 99 is lessthan 100.
Method 2The positions of numbers ending with 9form a diagonal pattern.The methods were the ones thatparticipants in Chile came up with.
Another MethodIn a course done in December 2010 with a group ofChilean teachers, there was a method that involvesdivision. For Cheryl, it was 99 10.For David, it was 99 8. Are you able to figure out thatmethod?
Students who were already good in the skill of multiplying two-digit numberwith a single-digit number were asked to make observations. They wereasked “What do you notice? Are there some digits that cannot be used taall?”
Singapore MathDrill-and-Practice Through Problem Solving
FUNDAMENTALS of singapore math The following slides are for additional tasks that are discussed on the second day for Grades 5 – 8 Mayflower Primary School, SingaporeSlides are available atwww.banhar.blogspot.com
Marcus gave ¼ of his coin collection to his sisterand ½ of the remainder to his brother.As a result, Marcus had 18 coins.Find the number of coins in his collection at first. 3 units = 18 8 units = ??? Marcus had 48 coins at first.