kindergarten to grade 8 mathematics curriculum framework 4 revisions to the kindergarten to grade 8

Kindergarten to Grade 8 Mathematics

Curriculum Framework

2013 Revisions

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2013 Manitoba Education

K i n d e r g a r t e n t o g r a d e 8 M a t h e M a t i c s c u r r i c u l u M F r a M e w o r K

2013 Revisions

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Manitoba Education Cataloguing in Publication Data

Kindergarten to Grade 8 mathematics curriculum framework [electronic resource] : 2013 revisions

Reflects revisions made to the Number strand of the 2008 ‘Kindergarten to Grade 8 mathematics : Manitoba curriculum framework of outcomes’.

Includes bibliographical references.

ISBN: 978-0-7711-5502-4

1. Mathematics—Study and teaching. 2. Mathematics—Study and teaching—Manitoba. 3. Mathematics—Manitoba—Curricula. I. Manitoba. Manitoba Education. II. Title: Kindergarten to Grade 8 mathematics : Manitoba curriculum framework of outcomes. 510.71

Manitoba Education School Programs Division Winnipeg, Manitoba, Canada

Every effort has been made to acknowledge original sources and to comply with copyright law. If cases are identified where this has not been done, please notify Manitoba Education. Errors or omissions will be corrected in a future edition. Sincere thanks to the authors and publishers who allowed their original material to be used.

Any websites referenced in this document are subject to change. Educators are advised to preview and evaluate websites and online resources before recommending them for student use.

This resource is available on the Manitoba Education website at .

Un document pour le programme d’immersion française et un document pour le programme français sont également disponibles.

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C o n t e n t s iii

c o n t e n t s

Acknowledgements v

Preface vii

Background 1

Introduction 3

Purpose of the Document 3

Beliefs about Students and Mathematics Learning 3

First Nations, Métis, and Inuit Perspectives 4

Affective Domain 4

Early Childhood 5

Goals for Students 5

Conceptual Framework for K–9 Mathematics 7

Nature of Mathematics 8

Change 8

Constancy 8

Number Sense 9

Patterns 9

Relationships 9

Spatial Sense 10

Uncertainty 10

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R e v i s i o n s t o t h e K i n d e r g a r t e n t o G r a d e 8 M a t h e m a t i c s C u r r i c u l u m F r a m e w o r kiv

Mathematical Processes 11 Communications [C] 11 Connections [CN] 11 Mental Mathematics and Estimation [ME] 12 Problem Solving [PS] 12 Reasoning [R] 13 Technology [T] 13 Visualization [V] 14

Strands 15 Number 15 Patterns and Relations 15 Shape and Space 15 Statistics and Probability 15

Learning Outcomes and Achievement 16 Summary 16 Instructional Focus 17

Addition and Subtraction Facts to 18 19

Multiplication and Division Facts to 81 22

Skip Counting 26

Adding, Subtracting, Multiplying, and Dividing Whole Numbers 27

Adding, Subtracting, Multiplying, and Dividing of Decimal Numbers 30

References 33

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A c k n o w l e d g e m e n t s v

a c K n o w l e d g e M e n t s

Manitoba Education would like to acknowledge the contributions of the following individuals in the development of Kindergarten to Grade 8 Mathematics Curriculum Framework: 2013 Revisions.

Manitoba Education School Programs Division

Staff

Nicole Allain Fox Project Leader

Curriculum, Development and Implementation Bureau de l’éducation française

Heather Anderson Consultant

Development Unit Instruction, Curriculum and Assessment Branch

Carole Bilyk Project Manager

Development Unit Instruction, Curriculum and Assessment Branch

Louise Boissonneault Coordinator

Document Production Services Unit Educational Resources Branch

Paule Buors Consultant

Curriculum, Development and Implementation Bureau de l’éducation française

Ian Donnelly Consultant

Development Unit Instruction, Curriculum and Assessment Branch

Linda Girling Project Leader

Development Unit Instruction, Curriculum and Assessment Branch

Philippe Leclercq Consultant

Curriculum, Development and Implementation Bureau de l’éducation française

Gilbert Le Néal Consultant

Curriculum, Development and Implementation Bureau de l’éducation française

Cyril Parent Desktop Publisher

Document Production Services Unit Educational Resources Branch

Sherry Perih Project Leader

Development Unit Instruction, Curriculum and Assessment Branch

Marjorie Poor Publications Editor

Document Production Services Unit Educational Resources Branch

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R e v i s i o n s t o t h e K i n d e r g a r t e n t o G r a d e 8 M a t h e m a t i c s C u r r i c u l u m F r a m e w o r kvi

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P r e f a c e vii

Kindergarten to Grade 8 Mathematics Curriculum Framework: 2013 Revisions is a document that reflects revisions that have been made to the Number strand of the 2008 Kindergarten to Grade 8 Mathematics: Manitoba Curriculum Framework of Outcomes. Manitoba Education has worked with provincial stakeholders to reinforce the importance of conceptual understanding, procedural thinking, and problem solving, and to clarify grade-level expectations. Revisions were made to the introduction and to some of the learning outcomes and achievement indicators in the Number strand.

P r e F a c e

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R e v i s i o n s t o t h e K i n d e r g a r t e n t o G r a d e 8 M a t h e m a t i c s C u r r i c u l u m F r a m e w o r kviii

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B a c k g r o u n d 1

The Western Canadian Protocol for Collaboration in Basic Education Kindergarten to Grade 12 was signed December 1993 by the Ministers of Education from Alberta, British Columbia, Manitoba, Northwest Territories, Saskatchewan,

and Yukon Territory. In February 2000, following the addition of Nunavut, the protocol was renamed the Western and Northern Canadian Protocol (WNCP) for Basic Education.

In 2005, the Ministers of Education from all the WNCP

jurisdictions unanimously concurred with the rationale of the original partnership because of the importance placed on

common educational goals the ability to collaborate to achieve common goals high standards in education planning an array of educational opportunities removing obstacles to accessibility for individual learners optimum use of limited educational resources

The Common Curriculum Framework for K–9 Mathematics was developed by the seven ministries of education in collaboration with teachers, administrators, parents, business representatives, post-secondary educators, and others.

The framework identifies beliefs about mathematics, general and specific student outcomes, and achievement indicators agreed upon by the seven jurisdictions. Each of the provinces and territories will determine when and how the framework will be implemented within its own jurisdiction.

Partner Jurisdictions: Alberta British Columbia Manitoba Northwest Territories

B a c K g r o u n d

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I n t r o d u c t i o n 3

Purpose of the Document

This document provides a common base for the curriculum expectations mandated by Manitoba

Education, Citizenship and Youth, which will result in consistent student outcomes in mathematics across Manitoba and enable easier transfer for students moving from one region to another. Its intent is to clearly communicate high expectations for students in

mathematics education to all education partners across Manitoba, and to facilitate the development of common learning resources.

Beliefs about Students and Mathematics Learning

Students are curious, active learners with individual interests, abilities, and needs. They come to classrooms with varying knowledge, life experiences, and backgrounds. A key component in successfully developing numeracy is making connections to these backgrounds and experiences.

Students learn by attaching meaning to what they do, and need to construct their own meaning of mathematics. This meaning is best developed when learners encounter mathematical experiences that proceed from the simple to the complex and from the concrete to the abstract. The use of manipulatives and a variety of pedagogical approaches can address the diversity of learning styles and developmental stages of students, and enhance the formation of sound, transferable mathematical concepts. At all levels, students benefit from working with a variety of materials, tools, and contexts when constructing meaning about new mathematical ideas. Meaningful student discussions can provide essential links among concrete, pictorial, and symbolic representations of mathematics.

Students need frequent opportunities to develop and reinforce their conceptual understanding, procedural thinking, and problem solving abilities. By addressing these three interrelated components, students will strengthen their ability to apply mathematical learning to their daily lives.

The learning environment should value and re