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2014 WSU Handouts

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  • 1. 1 THE 4th SINGAPORE MATH® INSTITUTE AUGUST 4-6, 2014 Breakout Session: Practice Lessons Using the Problem-Solving Approach Presenter: Yeap Ban Har Singapore’s national mathematics curriculum is a problem-solving one. Lessons to teach new concepts, lessons to consolidate recently learnt concepts, as well as lessons to apply learnt concepts, can all be taught through a problem-solving approach. This session is on doing practice lessons using the problem-solving approach. Task 1 Make a correct division equation. All the five digits are different. Complete instruction. Make a correct division equation such a two-digit number when divided by a 1-digit number gives a two-digit quotient. All the five digits are different. Grade Level What is the skill that students are practicing?
  • 2. 2 Task 2 Start with a certain number of beans / counters / paper clips. Take turns to remove either one or two beans / counters / paper clips. The winner is the player who removes the last beans / counters / paper clips. Is there a way to always win in this game? Grade Level What is the skill that students are practicing?
  • 3. 3 Task 3 Use any five consecutive numbers. Arrange them such that the vertical sum equal the horizontal sum. Grade Level What is the skill that students are practicing?
  • 4. 4 THE 4th SINGAPORE MATH® INSTITUTE AUGUST 4-6, 2014 Breakout Session: Anchor Tasks in Singapore Math Presenter: Yeap Ban Har Singapore textbooks are written with the main learning task being an anchor task. Anchor task is the single tasks used over a prolonged period of instructional time. It embodies the idea of Teach Less, Learn More – a philosophy of the Singapore education system. In Primary Mathematics, anchor tasks are the one that opens the chapter (un- numbered tasks) or the ones which follow a previous day independent Workbook Practice. These tasks are often solved completely for the students. In Math in Focus, anchor tasks are the boxed-up Learn tasks. Typically, a mathematics lesson begin with about 15 minutes or so doing and discussing the anchor task, before moving on to Guided Practice and Independent Practice (if any). Key Questions  What is the research base for Anchor Tasks?  How does a teacher implement Anchor Tasks?  What is the purpose of Anchor Tasks? Task 1 Find the value of 9 x 6.          
  • 5. 5 Board Plan Journal 1 Date Problem 9 x 8 Method 1 Method 2 Method 3           What is the learning outcome for this anchor task? Grade Level
  • 6. 6 Task 2 3 2 2 1  What is the learning outcome for this anchor task? Grade Level Board Plan Journal 2 Date Problem Method 1 Method 2
  • 7. 7 Task 3 Show 4 tiles. Make a shape. Show 5 tiles. Make a shape. Make another one. What is the learning outcome for this anchor task? Grade Level Board Plan Journal Date
  • 8. 8 Board Plan Journal Date Board Plan Journal Date
  • 9. 9 Board Plan Journal Date Board Plan Journal Date
  • 10. 10 THE 4th SINGAPORE MATH® INSTITUTE AUGUST 4-6, 2014 Breakout Session: Challenging Word Problems from Singapore Classrooms Presenter: Yeap Ban Har Singapore schools provide significant opportunities for all students to deal with challenging problems – problems that are more complex than (and sometimes new / novel compared to) textbook problems. This is because the state test includes significant number of such problems. Problem 1 This problem is based on one used by a Primary 3 Lesson Study done by a Professional Learning Team in Kong Hwa School, Singapore. Mr Lee had 3 durians more than Mr Kim. Mr Kim then gave Mr Lee 2 durians. Who had more durians in the end? How many more? Primary 3 ________________________________________________________________
  • 11. 11 Problem 2 This problem is based on one given on a state test for Primary 6 students in a recent examination. This particular problem is new to the group of Singapore students who took that test. Han arranged 110 squares and circles in a straight line. There are at least 3 circles between any 2 squares. What is the largest possible number of squares among the 110 squares and circles? Primary 5 – 6 Based on Primary 3 Content ________________________________________________________________
  • 12. 12 Problem 3 This problem is from Catholic High School (Primary). It was given to its Primary 6 students during a Preliminary Examination in preparing them for the national Primary School Leaving Examination, PSLE. A total of 325 boys and girls attended a performance in the school hall. 5 4 of the boys and 4 3 of the girls left the hall after the performance ended. There were 29 more boys than girls who remained in the hall. How many girls attended the performace? Primary 5 – 6 Based on Primary 4 Content ________________________________________________________________
  • 13. 13 Problem 4 This problem is based on one given on a state test for Primary 6 students in a recent examination. This particular problem is new to the group of Singapore students who took that test. 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 cookies into each container, there were 25 cookies left over. How many cookies were there altogether? Primary 5 – 6 Based on Primary 4 Content ________________________________________________________________
  • 14. 14 THE 4th SINGAPORE MATH® INSTITUTE AUGUST 4-6, 2014 Breakout Session: Teaching Geometry in Grades 4 – 6 Presenter: Yeap Ban Har Students in Grade 4 are expected to be on van Hiele Level 2 of Geometric Thought. Task 1  Cut out a triangle.  Investigate the three (interior) angles of the triangle.
  • 15. 15 Task 2 Find the sum of the angles in each polygon.
  • 16. 16 Task 2 Find the sum of the angles in each polygon. Number of sides Method 1 Method 2 What if … ?
  • 17. 17 Task 3 Is it possible to calculate the sum of the angles at the corners of the star?
  • 18. 18
  • 19. 19  Please cut these out.