



Primary Mathematics U.S. & 3rd Ed Teacher's Guides provide, in both flexibility and detail, a clear framework for the Primary Mathematics textbooks. Each lesson is accompanied by numerous activities which expand and reinforce the concepts for that lesson and which are designed to fit both teachers who wish to adapt lessons to their own classroom situation, and teachers who desire easytofollow, effective teaching strategies. Through the notes to the teacher and the detailed objectives for each learning task in the text and activity in the guide, these Teacher Guides help teachers to fully understand the purpose and concept behind each set of problems, both within the context of the unit and the context of the overall curriculum. The teacher's guide contains answers for the textbooks and workbooks.
This version of Teacher's Guide can be used with Primary Mathematics U.S. Edition and 3rd Edition textbooks and workbooks. It cannot be used with Primary Mathematics Standards Edition books.
Teacher's Guide 1A (published by Rosenbaum Foundation)
Teaching Activity sequence:
1. Numbers 1 to 108 Sessions(page 1)
 Activity 11a: Mental image for digits 0 to 9.
 Activity 11b: Count within 10.
 Textbook: Page 10: Exercises 1, 2 and 3.
 Workbook I:Page 7: Exercise 2.
 Activity 11c: Match different representations of a number within 10.
 Workbook I:Page 5: Exercise 1.
 Activity 11 d: Compare two numbers within 10.
 Textbook: Page 13: Exercises 4 and 5.
 Workbook I: Page 9: Exercise 3.
 Activity 11e: Count from 0 to 10.
 Textbook: Page 14: Exercises 6 and 7.
 Workbook I: Page 11: Exercise 4.
 Activity 11f: Count backward from 10 to 0.
 Textbook: Page 14: Exercises 8 and 9.
 Activity 11g: Arrange numbers 0 to 10 in order.
 Textbook: Page 15: Exercise 10.
 Activity 11h: Application.
2. Numberbonds8 Sessions(page 14)
 Activity 21a: Numberstories.
 Activity 21b: Numberstories.
 Activity 21c: Numberbond diagrams.
 Textbook: Page 18: Exercises 1, 3 and 5.
 Activity 21d: Numbers that make a given number.
 Activity 21 e: Numberbonds of a given number.
 Textbook: Page 18: Exercises 2, 4, 6, 7 and 8.
 Workbook I: Page 13: Exercise 5, 6, 7, 8 and 9.
 Activity 21 f: Missing part of a numberbond.
 Textbook: Page 22: Exercises 9 and 10.
 Workbook I: Page 18: Exercise 10.
 Activity 21g: Number pairs that make 10.
 Workbook I: Page 21: Exercise 11.
 Activity 21h: Group activities.
3. Addition14 Sessions(page 24)
 Activity 31a: Adding.
 Activity 31b: Additionsentence.
 Activity 31c: Numberstories.
 Textbook: Page 27: Exercises 1, 2, and 3.
 Workbook I: Page 23: Exercises 12, 13 and 14.
 Activity 31d: Review.
 Activity 32a: Additionfacts.
 Textbook: Page 31: Exercises 1, 2 and 3.
 Workbook I: Page 29: Exercises 15 and 16.
 Activity 32b: Additionfacts.
 Activity 32c: Additionfacts.
 Activity 32d: Additionfacts.
 Activity 32e: Additionfacts.
 Workbook I: Page 34: Exercise 17.
 Activity 32f: Additionfacts.
 Activity 33a: “Count on” strategy.
 Textbook: Page 34: Exercises 1, 2, 3 and 4.
 Workbook I: Page 36: Exercise 18.
 Activity 33b: “Counton” game.
 Activity 33c: Make 10.
 Textbook: Page 36: Exercises 5, and 6.
 Workbook I: Page 38: Exercise 19.
 Activity 33d: Game: Additionfacts.
4. Subtraction15Sessions(page 41)
 Activity 41a: Takingaway and Minus.
 Activity 41b: Subtraction stories.
 Activity 41c: Comparison of subtraction and addition.
 Activity 41d: Comparison of subtraction and addition.
 Activity 41e: Review.
 Textbook: Page 41: Exercises 1 and 2.
 Workbook I: Page 39: Exercises 20 and 21.
 Activity 41f: Subtraction facts.
 Textbook: Page 43: Exercise 3.
 Workbook I: Page 43: Exercise 22.
 Activity 41g: Subtraction facts.
 Activity 42a: Takingaway and minus.
 Textbook: Pages 4446: Exercises 1, 2 and 3.
 Workbook I: Page 46: Exercises 23 and 24.
 Activity 42b: Addition and subtraction facts.
 Textbook: Page 47: Exercises 4.
 Workbook I: Page 50: Exercises 25 and 26.
 Activity 42c: Subtractionfacts.
 Activity 42d: Countback strategy.
 Textbook: Pages 4849: Exercises 58.
 Workbook I: Page 54: Exercise 27.
 Activity 42e: Countback game.
 Activity 42f: Adjacent numbers.
 Textbook: Page 50: Exercise 9.
 Activity 42g: Make 10.
 Textbook: Page 50: Exercises 10 and 11.
 Workbook I: Page 56: Exercise 28.
 Activity 42h: Review.
 Textbook: Page 51: Exercise 12.
PREFACE: Teacher’s Guide for Primary Mathematics (Singapore)
Why is a private, nongovernmental U.S. organization like the Rosenbaum Foundation creating American Teacher’s Guides for a foreign country’s proprietary mathematics books? Because the Foundation believes that Singapore’s Primary Mathematics books are the best elementary school math books available in English.
Once upon a time, acquisition of the beginning steps in arithmetic was taken for granted. These days, children’s school attendance no longer guarantees children’s learning. U.S. students’ failure to come in Number One In The World In Mathematics (TIMSS, the Third International Study of Science and Mathematics) became a national obsession. School math is now discussed daily in editorials, on radio and television, and even in the halls of Congress.
According to TIMSS, our 4^{th} graders rank only a bit above world average in math. That’s hard on our ambitions for our children. Even harder to take: the U.S. dropping further at 8^{th} grade, from above to below average.^{1} It seems that the longer our children are in school, the lower their math sinks in comparison to world level. Meantime, the coveted Number One position at both 4^{th} and 8^{th} grade is held instead by Singapore.
TIMSS data establishes more than countries’ ranking: it also pinpoints their math learning factors  both in success and in failure: teacher proficiency/lack in mathematics, coupled with quality of the school math curriculum^{2}. Accordingly, national concern brought a flurry of reform efforts: development of and experimentation with new math programs, textbooks and pedagogy. So far however the followup international study, TIMSSR, shows no improvement in U.S. students’ world standing.
Working with the professional mathematics community led the Rosenbaum Foundation to focus, not on reform experimentation, but on identifying those teaching materials and pedagogical practices that already have a solid, proven record of success. The mathematicians determined that the school math of Japan, China, Singapore, Korea, the former Soviet Union and a number of the small East European countries are all excellent. Further, Singapore’s existing English language school math materials were found as good as their students’ first place TIMSS standing would suggest. The central idea of all of mathematics is to discover how it is that knowing some few things will, via reasoning, permit us to know much else – without having to commit the new information to memory as separate facts. Mathematics is economy of information, not its unnecessary proliferation. Basic mathematics properly presented conveys this lesson. It is the connections, the reasoned, logical connections, that make mathematics manageable. Understanding the structure of mathematics is the key to success. Everyone can be “good at mathematics”, and this series, as has been proved in Singapore, shows how. These Singapore textbooks lead the student from the vocabulary of counting, shape and position, through the famous pitfalls of Word Problems (story problems), to the beginnings of algebra and geometry.
Singapore’s Primary Mathematics books are paperbound, small and light. They are clearly printed, and include enough exercises in the text to supply model explanations of new topics as they come up. Each new topic becomes enriched by new connections with other parts of mathematics and applications of greater difficulty. What is taught in the textbook, and as explained by the teacher or discussed with a class as a whole, is further reinforced with the Singapore workbook’s rich supply of exercises for students to do on their own. These deceptively thin texts were created with an impressive understanding of how children actually learn. For first grade, this involves subtleties like addition being made well understood before the word addition is introduced. Work with number bonds (combinations of numbers that can make up a given number) builds a lifelong familiarity and comfort with arithmetic processes.^{3}
The role of this Teacher’s Guide is to be the helpful interface between curriculum and classroom. How much can best be covered in one day’s math class? What variants work best when introducing a new topic? How to engage students individually and as a group? How to expand and reinforce the lesson, when and how to review? The operative word is “Guide”, since every teacher prepares his/her own daily lessons.
For our American Teachers’ Guide to be effective, it must convey the Singapore excellencies into the American teaching and learning environment. The Foundation was fortunate to engage the participation of Professor W. A. M. Alwis of The National University of Singapore as primary author. Dr. Alwis, partly on his University’s behalf and largely by his own preference, works closely with many of Singapore’s schools, teachers and students. Dr. Alwis has worked equally well with the Foundation’s own Mathematics Advisory Board, which includes members of the National Academy of Sciences as well as recipients of a Presidential Science Medal and a MacArthur “genius” Award.
Madge Goldman, President Gabriella and Paul Rosenbaum Foundation 1723 South Michigan Avenue Chicago, Illinois 60616 August 13, 2001
Information about Rosenbaum Foundation.








