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Grade 8 Mathematics

Support Document for Teachers

2015

Manitoba Education and Advanced Learning

GR A D E 8 MA T H EMA T I C S

Support Document for Teachers

Manitoba Education and Advanced Learning Cataloguing in Publication Data Grade 8 mathematics [electronic resource] : support document for teachers

Includes bibliographical references.

ISBN: 978-0-7711-5905-3

1. Mathematics—Study and teaching (Secondary).

2. Mathematics—Study and teaching (Secondary)—Manitoba.

I. Manitoba. Manitoba Education and Advanced Learning.

372.7044

Copyright © 2015, the Government of Manitoba, represented by the Minister of

Education and Advanced Learning.

Manitoba Education and Advanced Learning

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 and Advanced Learning. Errors or omissions will be corrected in a future edition. Sincere thanks to the authors, artists, and publishers who allowed their original material to be used. All images found in this document are copyright protected and should not be extracted, accessed, or reproduced for any purpose other than for their intended educational use in this document. 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. Print copies of this resource can be purchased from the Manitoba Text

Book Bureau (stock number 80637). Order online at

. This resource is also available on the Manitoba Education and

Advanced

Learning website at

Available in alternate formats upon request.

Contentsiii

CO N T E N T S

Acknowledgements vii

Introduction 1

Overview 2

Conceptual Framework for Kindergarten to Grade 9 Mathematics 6

Assessment

10

Instructional Focus

12

Document Organization and Format

13

Number 1

Number and Shape and Space (Measurement)—8.N.1, 8.N.2, 8.SS.1 3

Number—8.N.3 25

Number—8.N.4, 8.N.5

41

Number—8.N.6, 8.N.8

57

Number—8.N.7

81

Patterns and Relations

1

Patterns and Relations (Patterns)—8.PR.1

3 Patterns and Relations (Variables and Equations)—8.PR.2 13

Shape and Space

1 Shape and Space (Measurement and 3-D Objects and 2-D Shapes)—

8.SS.2, 8.SS.3, 8.SS.4, 8.SS.5 3

Shape and Space (Transformations)—8.SS.6

31

Statistics and Probability

1 Statistics and Probability (Data Analysis)—8.SP.1 3 Statistics and Probability (Chance and Uncertainty)—8.SP.2 11

Bibliography 1

Grade 8 Mathematics: Support Document for Teachersiv

Grade 8 Mathematics Blackline Masters (BLMs)

BLM 8.N.1.1: Determining Squares

BLM 8.N.1.2: Determining Square Roots

BLM 8.N.1.3: I Have . . . , Who Has . . . ?

BLM 8.N.1.4: Pythagorean Theorem

BLM 8.N.3.1: Percent Pre-Assessment

BLM 8.N.3.2: Percent Self-Assessment

BLM 8.N.3.3: Percent Grids

BLM 8.N.3.4: Percent Scenarios

BLM 8.N.3.5: Percent Savings

BLM 8.N.3.6: Final Cost

BLM 8.N.3.7: Percent Increase and Decrease

BLM 8.N.4.1: Ratio Pre-Assessment

BLM 8.N.4.2: Meaning of

1 3

BLM 8.N.4.3: Problem Solving

BLM 8.N.6.1: Mixed Numbers and Improper Fractions

BLM 8.N.6.2: Mixed Number War

BLM 8.N.6.3: Decimal Addition Wild Card

BLM 8.N.6.4: Fraction Multiplication and Division

BLM 8.N.6.5: Multiplying and Dividing Proper Fractions, Improper Fractions, and Mixed

Numbers

BLM 8.N.6.6: Fraction Operations

BLM 8.N.7.1: Integer Pre-Assessment

BLM 8.N.7.2: Solving Problems with Integers (A)

BLM 8.N.7.3: Solving Problems with Integers (B)

BLM 8.N.7.4: Solving Problems with Integers (C)

BLM 8.N.7.5: Number Line Race

BLM 8.PR.1.1: Patterns Pre-Assessment

BLM 8.PR.1.2: Determine the Missing Values

BLM 8.PR.1.3: Break the Code

BLM 8.PR.1.4: Linear Relations

BLM 8.PR.1.5: Graphs

BLM 8.PR.2.1: Algebra Pre-Assessment

BLM 8.PR.2.2: Solving Equations Symbolically

BLM 8.PR.2.3: Algebra Match-up

BLM 8.PR.2.4: Analyzing Equations

BLM 8.PR.2.5: Analyzing Equations Assessment

BLM 8.PR.2.6: Solving Problems Using a Linear Equation

Contentsv

BLM 8.SS.2.1: Measurement Pre-Assessment

BLM 8.SS.2.2: Nets of 3-D Objects

BLM 8.SS.2.3: 3-D Objects

BLM 8.SS.2.4: Matching

BLM 8.SS.3.1: Nets

BLM 8.SS.3.2: Surface Area Problems

BLM 8.SS.4.1: Volume Problems

BLM 8.SS.6.1: Coordinate Image

BLM 8.SS.6.2: Tessellating the Plane

BLM 8.SS.6.3: Tessellation Slideshow

BLM 8.SS.6.4: Tessellation Recording Sheet

BLM 8.SS.6.5: Tessellation Transformation

BLM 8.SP.1.1: Data Analysis Pre-Assessment

BLM 8.SP.1.2: Data

BLM 8.SP.1.3: Graph Samples

BLM 8.SP.2.1: Probability Pre-Assessment

BLM 8.SP.2.2: Tree Diagram

BLM 8.SP.2.3: Table

BLM 8.SP.2.4: Probability Problems

BLM 8.SP.2.5: Probability Problem Practice

Grades 5 to 8 Mathematics Blackline Masters

BLM 5-8.1: Observation Form

BLM 5-8.2: Concept Description Sheet 1

BLM 5-8.3: Concept Description Sheet 2

BLM 5-8.4: How I Worked in My Group

BLM 5-8.5: Number Cards

BLM 5-8.6: Blank Hundred Squares

BLM 5-8.7: Place-Value Chart—Whole Numbers

BLM 5-8.8: Mental Math Strategies

BLM 5-8.9: Centimetre Grid Paper

BLM 5-8.10: Base-Ten Grid Paper

BLM 5-8.11: Multiplication Table

BLM 5-8.12: Fraction Bars

BLM 5-8.13: Clock Face

BLM 5-8.14: Spinner

BLM 5-8.15: Thousand Grid

Grade 8 Mathematics: Support Document for Teachersvi

BLM 5-8.16: Place-Value Mat—Decimal Numbers

BLM 5-8.17: Number Fan

BLM 5-8.18: KWL Chart

BLM 5-8.19: Double Number Line

BLM 5-8.20: Algebra Tiles

BLM 5-8.21: Isometric Dot Paper

BLM 5-8.22: Dot Paper

BLM 5-8.23: Understanding Words Chart

BLM 5-8.24: Number Line

BLM 5-8.25: My Success with Mathematical Processes

BLM 5-8.26: Percent Circle

Acknowledgementsvii

WriterAnita FedorukLouis Riel School Division

Grades 5 to 8

Mathematics

Support Document

Development Team

(2006-2008)

Holly ForsythFort La Bosse School Division

Linda GirlingLouis Riel School Division

Chris HarbeckWinnipeg School Division

Heidi HolstLord Selkirk School Division

Steven HuntIndependent School

Jan JebsenKelsey School Division

Betty JohnsUniversity of Manitoba

Dianna KicenkoEvergreen School Division

Kelly KuzykMountain View School Division

Judy MaryniukLord Selkirk School Division

Greg SawatzkyHanover School Division

Darlene WillettsEvergreen School Division

Manitoba Education

and Advanced Learning

School Programs

Division Staff

Heather Anderson

Consultant

(until June 2007)

Development Unit

Instruction, Curriculum and Assessment Branch

Carole Bilyk

Project Manager

Coordinator

Development Unit

Instruction, Curriculum and Assessment Branch

Louise Boissonneault

Coordinator

Document Production Services Unit

Educational Resources Branch

Kristin Grapentine

Desktop Publisher

Document Production Services Unit

Educational Resources Branch

Heather Knight Wells

Project Leader

Development Unit

Instruction, Curriculum and Assessment Branch

Susan Letkemann

Publications Editor

Document Production Services Unit

Educational Resources Branch

AC K N O W L E DGEME N T S

Manitoba Education and Advanced Learning wishes to acknowledge the contribution of and to thank the members of the Grades 5 to 8 Mathematics Support Document Development Team. Their dedication and hard work have made this document possible.

Introduction1

IN T R O D U C T I O N

Purpose of This Document

Grade 8 Mathematics: Support Document for Teachers provides various suggestions for instruction, assessment strategies, and learning resources that promote the meaningful engagement of mathematics learners in Grade 8. The document is intended to be used by teachers as they work with students in achieving the learning outcomes and achievement indicators identified in Kindergarten to Grade 8 Mathematics: Manitoba Curriculum Framework of Outcomes (2013) (Manitoba Education).

Background

Kindergarten to Grade 8 Mathematics: Manitoba Curriculum Framework of Outcomes is based on The Common Curriculum Framework for K-9 Mathematics, which resulted from ongoing collaboration with the Western and Northern Canadian Protocol (WNCP). In its work,

WNCP emphasized

common educational goals the ability to collaborate and achieve common goals high standards in education planning an array of educational activities removing obstacles to accessibility for individual learners optimum use of limited educational resources The growing effects of technology and the need for technology-related skills have become more apparent in the last half century. Mathematics and problem-solving skills are becoming more valued as we move from an industrial to an informational society. As a result of this trend, mathematics literacy has become increasingly important. Making connections between mathematical study and daily life, business, industry, government, and environmental thinking is imperative. The Kindergarten to Grade 12 mathematics curriculum is designed to support and promote the understanding that mathematics is a way of learning about our world part of our daily lives both quantitative and geometric in nature

2Grade 8 Mathematics: Support Document for Teachers

OVERVIEW

Beliefs about Students and Mathematics Learning

The Kindergarten to Grade 8 mathematics curriculum is designed with the understanding that students have unique interests, abilities, and needs. As a result, it is imperative to make connections to all students' prior knowledge, experiences, and backgrounds. Students are curious, active learners with individual interests, abilities, and needs. They come to classrooms with unique 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 they 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. 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 respect

all students' experiences and ways of thinking, so that learners are comfortable taking intellectual risks, asking questions, and posing conjectures. Students need to explore problem-solving situations in order to develop personal strategies and become mathematically literate. Learners must realize that it is acceptable to solve problems in different ways and that solutions may vary.

Conceptual understanding:

comprehending mathematical concepts, relations, and operations to build new knowledge. (Kilpatrick,

Swafford,

and Findell 5)

Procedural thinking: carrying out

procedures flexibly, accurately, efficiently, and appropriately.

Problem solving: engaging in

understanding and resolving problem situations where a method or solution is not immediately obvious. (OECD 12)

Introduction3

First Nations, Métis, and Inuit Perspectives

First Nations, Métis, and Inuit students in Manitoba come from diverse geographic areas with varied cultural and linguistic backgrounds. Students attend schools in a variety of settings, including urban, rural, and isolated communities. Teachers need to recognize and understand the diversity of cultures within schools and the diverse experiences of students. First Nations, Métis, and Inuit students often have a whole-world view of the environment; as a result, many of these students live and learn best in a holistic way. This means that students look for connections in learning, and learn mathematics best when it is contextualized and not taught as discrete content. Many First Nations, Métis, and Inuit students come from cultural environments where learning takes place through active participation. Traditionally, little emphasis was placed upon the written word. Oral communication along with practical applications and experiences are important to student learning and understanding. A variety of teaching and assessment strategies are required to build upon the diverse knowledge, cultures, communication styles, skills, attitudes, experiences, and learning styles of students. The strategies used must go beyond the incidental inclusion of topics and objects unique to a culture or region, and strive to achieve higher levels of multicultural education (Banks and Banks).

Affective Domain

A positive attitude is an important aspect of the affective domain that has a profound effect on learning. Environments that create a sense of belonging, encourage risk taking, and provide opportunities for success help students develop and maintain positive attitudes and self-confidence. Students with positive attitudes toward learning mathematics are likely to be motivated and prepared to learn, participate willingly in classroom learning activities, persist in challenging situations, and engage in reflective practices. Teachers, students, and parents* need to recognize the relationship between the affective and cognitive domains, and attempt to nurture those aspects of the affective domain that contribute to positive attitudes. To experience success, students must be taught to set achievable goals and assess themselves as they work toward reaching these goals. Striving toward success and becoming autonomous and responsible learners are ongoing, reflective processes that involve revisiting the setting and assessment of personal goals. ___________

In this document, the term parents refers to both parents and guardians and is used with the recognition that in

some cases only one parent may be involved in a child"s education. Grade 8 Mathematics: Support Document for Teachers4

Middle Years Education

Middle Years education is defined as the education provided for young adolescents in Grades 5, 6, 7, and 8. Middle Years learners are in a period of rapid physical, emotional, social, moral, and cognitive development. Socialization is very important to Middle Years students, and collaborative learning, positive role models, approval of significant adults in their lives, and a sense of community and belonging greatly enhance adolescents' engagement in learning and commitment to school. It is important to provide students with an engaging and social environment within which to explore mathematics and to construct meaning. Adolescence is a time of rapid brain development when concrete thinking progresses to abstract thinking. Although higher-order thinking and problem-solving abilities develop during the Middle Years, concrete, exploratory, and experiential learning is most engaging to adolescents. Middle Years students seek to establish their independence and are most engaged when their learning experiences provide them with a voice and choice. Personal goal setting, co-construction of assessment criteria, and participation in assessment, evaluation, and reporting help adolescents take ownership of their learning. Clear, descriptive, and timely feedback can provide important information to the mathematics student. Asking open-ended questions, accepting multiple solutions, and having students develop personal strategies will help students to develop their mathematical independence. Adolescents who see the connections between themselves and their learning, and between the learning inside the classroom and life outside the classroom, are more motivated and engaged in their learning than those who do not observe these connections. Adolescents thrive on challenges in their learning, but their sensitivity at this age makes them prone to discouragement if the challenges seem unattainable. Differentiated instruction allows teachers to tailor learning challenges to adolescents' individual needs, strengths, and interests. It is important to focus instruction on where students are and to see every contribution as valuable. The energy, enthusiasm, and unfolding potential of young adolescents provide both challenges and rewards to educators. Those educators who have a sense of humour and who see the wonderful potential and possibilities of each young adolescent will find teaching in the Middle Years exciting and fulfilling.

Introduction5

Mathematics Education Goals for Students

The main goals of mathematics education are to prepare students to communicate and reason mathematically use mathematics confidently, accurately, and efficiently to solve problems appreciate and value mathematics make connections between mathematical knowledge and skills and their applications commit themselves to lifelong learning become mathematically literate citizens, using mathematics to contribute to society and to think critically about the world

Students who have met these goals will

gain understanding and appreciation of the contributions of mathematics as a science, a philosophy, and an art exhibit a positive attitude toward mathematics engage and persevere in mathematical tasks and projects contribute to mathematical discussions take risks in performing mathematical tasks exhibit curiosity

Mathematics education

must prepare students to use mathematics to think critically aboutquotesdbs_dbs8.pdfusesText_14
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