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- 1. 1 | P a g e July 2014 Singapore Math Strategies National Conference Staff Development for Educators | Las Vegas yeapbanhar@gmail.com | www.banhar.blogspot.com | Course SE01 | The ABC’s of Singapore Math through Whole Numbers The Singapore approach to teaching and learning mathematics was the result of trying to find a way to help Singapore students who were mostly not performing well prior to 1980’s. The CPA Approach as well as the Spiral Approach are fundamental to teaching mathematics in Singapore schools. The national standards, called syllabus in Singapore, is designed based on Bruner’s idea of spiral curriculum. Textbooks are written based on and teachers are trained to use the CPA Approach, based on Bruner’s ideas of representations. Using the tasks listed here and the observations you share during the session, we learn some fundamentals of good mathematics instruction. These are also elements of Singapore Math. Task 1 | Show 5 beans.
- 2. 2 | P a g e Task 2 | Use 3 tiles to make a shape. Use 4 tiles to make a shape. Use 5 tiles to make a shape. Make different shapes using the same number of tiles. ______________________________________________________________________________ Task 3 | Aaron has 8 cookies. Beth has 6 cookies. How many cookies do they have altogether? ______________________________________________________________________________ Task 4 | 400 – 189
- 3. 3 | P a g e ______________________________________________________________________________ Task 5 | David has 19 more rocks in his collection than Emily. David has 51 rocks in his collection. ______________________________________________________________________________ Task 6 | 3 x 6 4 x 6 8 x 6 9 x 6 9 x 7 ______________________________________________________________________________
- 4. 4 | P a g e Task 7 | ______________________________________________________________________________ Task 8 | ______________________________________________________________________________ Task 9 | Frank has 10 coins more than Gary. Together, they have 34 coins. How many coins does Frank have? ______________________________________________________________________________ Task 10 | At first, Frank had 10 coins more than Gary. Then Gary gave Frank 6 coins. Who had more coins in the end? How many more? ______________________________________________________________________________
- 5. 5 | P a g e Task 11 | Compare these three lessons on division of whole numbers Anchor Task A | Try putting 14 children into 3 equal groups. Anchor Task B | Try putting 41 children into groups of threes. Anchor Task C | Try putting 41 liters of water into 3 containers. Is it possible to make sure each container contains the same amount of water? ______________________________________________________________________________ Task 12 | There are three times as many boys as there are girls in the soccer club. There are 96 children in the soccer club. Is this possible? ______________________________________________________________________________ Task 13 | Use 12 square tiles to make a rectangle or square.
- 6. 6 | P a g e Task 14 | Han arranged 110 squares and circles in a straight line. There are at least3 circles between any 2 squares. What is the largest possible number of squares among the 110 squares and circles? ______________________________________________________________________________ Task 15 | Indra was packing a batch of cookies into some containers she had in her kitchen. She tried to pack 11 cookies into each container but the last one contained only 6 cookies. When she packed 8 sweets into each container, there were 25 sweets left over. How many cookies were there altogether? ______________________________________________________________________________ “A curriculum as it develops should revisit this basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them”. | Bruner 1960 “I was struck by the fact that successful efforts to teach highly structured bodies of knowledge like mathematics, physical sciences, and even the field of history often took the form of metaphoric spiral in which at some simple level a set of ideas or operations were introduced in a rather intuitive way and, once mastered in that spirit, were then revisited and reconstrued in a more formal or operational way, then being connected with other knowledge, the mastery at this stage then being carried one step higher to a new level of formal or operational rigour and to a broader level of abstraction and comprehensiveness. The end stage of this process was eventual mastery of the connexity and structure of a large body of knowledge.” | Bruner 1975 Anchor Task | Bar Model | CPA Approach | Differentiation | Enrichment | Focus | Guided Practice | Homework | Independent Practice | Journal | Kindergarten Math | Learning Theories | Mental Strategies | Number Bonds | Operations | Problem Solving | Questioning | Remediation | Spiral Approach | Three- Part Lesson Format | Visualization | Word Problems | ABC’s of Singapore Math |

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