Singapore Math Strategies You Can Count On! NCTM Annual Meeting in Philadelphia April 26, 2012 Char Forsten, Presenter www.sde.com Booth # 1012 A Quick Overview of Singapore’s Primary Mathematics Curriculum The term “Singapore Math” refers to the mathematics curriculum in the country of Singapore, developed by the Curriculum Planning & Development Institute of Singapore and approved by Singapore’s Ministry of Education. (Primary Mathematics includes grades 1 – 6) Strengths: o Has a proven track record o Is taught in English o Builds understanding through part-whole thinking o Emphasizes “why” before “how” o Bases instruction on student background knowledge o Is coherent and teaches for mastery o Develops strong written computation, mental math, & problem solving skills Research Base: o “Concrete-pictorial-abstract” & “Teaching for mastery” (Jerome Bruner o Relational understanding (Richard Skemp) o Multiple models and varied practice and experiences (Zoltan Dienes) 1 Singapore Math Strategies You Can Count On in Grades 3 – 5! 1. Using number bonds to show part/whole thinking . “Making Tens” – A pathway to developing mental math skills – Concrete: Pictorial 8+5 38 + 7 292 + 119 14 oz. + 7 oz. 45 min. + 35 min. 2,389 + 35 2 + 2 3 3 Abstract 2 2. Place value is not a chapter in a book! Teaching computation methods through an understanding of place value and “visual” language. 3 x 14 2 31 3. Adding and subtracting unlike fractions: Concrete: Use pattern blocks Pictorial: Abstract: 4. Multiplying a fraction by a fraction Concrete: Paper folding Pictorial: Draw a model Abstract: Solve 3 5. Model Drawing (Bar modeling) 1) Cal scored 6 more points than Max in last night’s basketball game. Together, they scored a total of 38 points. How many points did Max score? 2) Justin Case had $10. Frank N. Stein had 3 times as much money as Justin. How much more money did Frank have than Justin? 3) The ratio of blue marbles to red marbles in a bag is 2:3. If there are 25 marbles altogether, how many red marbles are there? 4) If 2/3 of a number is 6, what is the number? 5) One number is 2/5 of another number. If the difference between the 2 numbers is 15, what are the two numbers? 4 6) Kate spent 3/5 of her money on a pedicure and 2/3 of the remaining money on a manicure. She had $10 left. How much money did Kate have at first? 7) Harold ran 2.3 miles each day during the month of April. How many total miles did Harold run in April? 8) Anthony played in 3 basketball games during vacation week. He scored 24 points the first game, 18 points the second game, and 27 points the third game. What was his average score for the 3 games? 9) Twenty percent of the 5th graders from Antrim Middle School went on a field trip. If 120 students went on the field trip, how many total students were in the 5th grade at Antrim Middle School? 5 Steps for Model Drawing - Possible Scoring Reads the entire problem. (1) Rewrites the question in sentence form, leaving a space for the answer. (1) Determines who and/or what is involved in the problem. (1) Draws the unit bar(s). (1) Chunks the problem and adjusts the unit bars to match the information in the problem. Fills in the question mark. (3) Correctly computes and solves the problem. (2) Writes the answer in the sentence. (1) REFERENCES & RECOMMENDED RESOURCES 1. Forsten, Char. (2005) Math Strategies You Can Count On! Peterborough, NH: Crystal Springs Books. 2. Forsten, Char. (2010) Step-by-Step Model Drawing. Peterborough, NH: Crystal Springs Books. 3. Lee, Peng Yee (Edited by) (2007) Teaching Primary School Mathematics. Singapore: McGrawHill. 4. Parker, Thomas and Scott Baldridge. (2003) Elementary Mathematics for Teachers. Michigan State University. 5. Polya, George. (1945) How to Solve It. Princeton University Press. 6. Ministry of Education, Singapore. (2009) The Singapore Model Method for Learning Mathematics. Singapore: EPB Pan Pacific. 7. Walker, Lorraine. (2010) Model Drawing for Challenging Word Problems – Grades 69) Peterborough, NH: Crystal Springs Books 8. Word Problems for Model Drawing Practice:- available through Crystal Springs Books 9. Yeap, Banhar, Ph.D.(2010) Bar Modeling – A Problem Solving Tool. Singapore: Marshall Cavendish. WEBSITES 1. 2. 3. 4. 5. 6. 7. Crystal Springs Books - www.crystalsprings.com Staff Development For Educators www.sde.com Singapore Math - www.singaporemath.com National Council of Teachers of Mathematics - www.nctm.org Thinking Blocks – www.thinkingblocks.com Great Source (Math in Focus): www.mathinfocus.com Conceptua Math www.conceptuamath.com 6