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4.1 How does SEA-PLM Assess Mathematical Literacy? A vast majority of Filipino Grade 5 students had one textbook per student in English (73.8%) and ...
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Grade 8 Mathematics
Support Document for Teachers
2015Manitoba 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 teachersIncludes bibliographical references.
ISBN: 978-0-7711-5905-3
1. MathematicsStudy and teaching (Secondary).
2. MathematicsStudy and teaching (Secondary)Manitoba.
I. Manitoba. Manitoba Education and Advanced Learning.372.7044
Copyright © 2015, the Government of Manitoba, represented by the Minister ofEducation 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 TextBook Bureau (stock number 80637). Order online at
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 6Assessment
10Instructional Focus
12Document Organization and Format
13Number 1
Number and Shape and Space (Measurement)8.N.1, 8.N.2, 8.SS.1 3Number8.N.3 25
Number8.N.4, 8.N.5
41Number8.N.6, 8.N.8
57Number8.N.7
81Patterns and Relations
1Patterns and Relations (Patterns)8.PR.1
3 Patterns and Relations (Variables and Equations)8.PR.2 13Shape 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
31Statistics and Probability
1 Statistics and Probability (Data Analysis)8.SP.1 3 Statistics and Probability (Chance and Uncertainty)8.SP.2 11Bibliography 1
Grade 8 Mathematics: Support Document for TeachersivGrade 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 3BLM 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 MixedNumbers
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 EquationContentsv
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 ChartWhole 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 TeachersviBLM 5-8.16: Place-Value MatDecimal 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 ProcessesBLM 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 LearningSchool 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 nature2Grade 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 Teachers4Middle 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 worldStudents 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 curiosityMathematics education
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