A Guide to Effective Instruction in Mathematics - …

1 A Guide to EffectiveInstruction in MathematicsA Guide to EffectiveInstruction in MathematicsKindergarten to Grade 6A Resource in Five Volumes from the Ministry of EducationVVoolluummee FFiivvee TTeeaacchhiinngg BBaassiicc FFaaccttss aanndd MMuullttiiddiiggiitt CCoommppuuttaattiioonnssEvery effort has been made in this publication to identify Mathematics resources and tools( , manipulatives) in generic terms. In cases where a particular product is used by teachersin schools across Ontario, that product is identified by its trade name, in the interests of clarity.

2 Reference to particular products in no way implies an endorsement of those productsby the Ministry of publication quivalente est disponible en fran ais sous le titre suivant : Guide d enseignement efficace des math matiques, de la maternelle la 6eann ..v10. Approaches to Teaching Basic Facts and Multidigit Computations ..1 Introduction ..5 Using the Problem-Solving Approach to Teach Basic Facts and Multidigit Computations ..7 Basic Facts: Addition and Subtraction, and Multiplication and Division .. 12 Basic Addition and Subtraction Facts.

3 20 Basic Multiplication and Division Facts .. 27 Multidigit Whole Number Calculations .. 35 Appendices .. 57 References .. 113 ContentsvIntroductionThis is Volume Five of the five-volume reference Guide A Guide to Effective Instructionin Mathematics , Kindergarten to Grade 6. This volume contains Chapter 10. Chapter 10is devoted to the important subject of teaching basic facts and multidigit computa-tions the building blocks of students computational proficiency. Effective instruc-tion in this area is critical, as students ability to perform operations accurately andwith understanding will affect their achievement of expectations in all five strands ofthe curriculum.

4 The chapter lays out the approaches and strategies that have provedmost Effective in helping students understand, learn, and consolidate their learningof the basic facts. Games and activities, with accompanying blackline masters, arealso included here, to give teachers useful ideas for teaching the strategies to theirstudents.* (See the Introduction of Volume One for a summary of the organizationand contents of the complete five-volume Guide .)A list of suggested professional resources for teachers and administrators is includedin Volume One.

5 It is meant to provide useful suggestions, but should not be consid-ered comprehensive. A glossary of terms used throughout the Guide is also providedat the end of Volume One. References are listed at the end of each individual volume. This Guide contains a wide variety of forms and blackline masters, oftenprovided in appendices, that teachers can use in the classroom. Electronicversions of all of these materials can be found at electronic forms and blackline masters are in a Word format thatcan be modified by teachers to accommodate the needs of their students.

6 *Basic facts and multidigit computations are the focus of a group of expectations in the Number Senseand Numeration strand of the Ontario Mathematics curriculum. The companion documents to this guidethat focus on the Number Sense and Numeration strand also contain information and learning activitiesrelating to basic facts and multidigit to electronic versions of theforms and blackline mastersprovided throughout thisguide. They can be modifiedto meet classroom Guide to Effective Instruction in Mathematics , Kindergarten to Grade 6 Volume FiveLocating Information Specific to Kindergarten, Primary, and JuniorStudents in This GuideAn important feature of this Guide is the inclusion of grade-related information and examples that help clarify the principles articulated.

7 Such information is identified in the margins of this Guide by means oficons referring to the relevant grades K for Kindergarten, Grades 1 3 for primary, Grades 4 6 for junior. Examples and other materials that areappropriate for use at more than one level or are applicable to more thanone level are identified by the appropriate combination of Kindergarten1 3 Primary4 6 JuniorLook for the following icons inthe margins of this document: ..5 Using the Problem-Solving Approach to Teach Basic Facts and Multidigit Computations.

8 7 Problems for Basic Facts of Addition and Subtraction, and for Multidigit Computations Using Addition and Subtraction ..8 Types of Problems ..9 Problems for Basic Facts of Multiplication and Division, and for Multidigit Computations UsingMultiplication and Division .. 10 Types of Problems .. 11 Basic Facts: Addition and Subtraction, and Multiplication and Division .. 12 Principles for Teaching the Facts .. 13 Prior Learning Necessary for Developing Computational Sense .. 13 Developing Computational Sense.

9 14 Direct Modelling and Counting .. 15 Counting Strategies .. 15 Making Tens .. 15 Derived Facts .. 16 Using Worksheets With a Purpose .. 17 Strategy Flash Cards .. 18 Timed Tests .. 19 Approaches to Teaching Basic Facts and MultidigitComputations Chapter Contents2A Guide to Effective Instruction in Mathematics , Kindergarten to Grade 6 Volume FiveBasic Addition and Subtraction Facts .. 20 Using Models to Represent Facts of Addition and Subtraction .. 20 Strategies for Basic Facts of Addition and Subtraction.

10 21 One-More-Than and Two-More-Than Facts .. 23 Facts With Zero .. 23 Doubles .. 24 Near-Doubles or Doubles Plus One .. 24 Make-Ten Facts .. 25 Commutative Property .. 25 Subtraction as Think-Addition for Facts With Sums to 10 .. 25 Subtraction as Adding Up .. 25 One-Less-Than and Two-Less-Than Facts .. 26 Counting by Twos and Fives .. 26 Make Ten Extended .. 26 Back Down Through Ten .. 26 Practice and Consolidation of Facts for Additionand Subtraction .. 26 Basic Multiplication and Division Facts.