Mathematics NB Curriculum Grade 8 2009 - STEM NORTH

Acknowledgements The Department of Education of New Brunswick gratefully acknowledges the
contributions of the following groups and individuals toward the
development of the New Brunswick Grade 8 Mathematics Curriculum Guide: . The Western and Northern Canadian Protocol (WNCP) for Collaboration in
Education: The Common Curriculum Framework for K-9 Mathematics, May 2006.
Reproduced (and/or adapted) by permission. All rights reserved. . Alberta Education (Department of Education) . Newfoundland and Labrador Department of Education . Prince Edward Island Department of Education . The Middle Level Mathematics Curriculum Development Advisory Committee . The Grade 8 Curriculum Development Team:
. Angela Buggie, School District 16
. Kim Clancy, School District 6
. Craig Crawford, School District 15
. Derrick Grant, School District 18
. Elizabeth Nowlan, School District 2
. Erin Schriver, School District 14
. Cathy Martin, Learning Specialist, K-8 Mathematics and Science, NB
Department of Education . The Mathematics Learning Specialists, Numeracy Leads, and Mathematics
teachers of New Brunswick who provided invaluable input and feedback
throughout the development and implementation of this document.
2009
Department of Education
Educational Programs and Services Additional copies of this document may be obtained using the Title Code:
844480
Table of Contents Curriculum Overview for K-9 Mathematics
Background and Rationale 2
Beliefs about Students and Mathematics Learning 2
Goals for Mathematically Literate Students 3
Opportunities for Success 3
Diverse Cultural Perspectives 4
Adapting to the Needs of All Learners 4
Connections Across the Curriculum 4
Assessment 5
Conceptual Framework for K - 9 Mathematics 6
Mathematical Processes 7
Communication 7
Connections 7
Reasoning 7
Mental Mathematics and Estimation 8
Problem Solving 8
Technology 9
Visualization 9
Nature of Mathematics 10
Change 10
Constancy 10
Number Sense 10
Relationships 10
Patterns 11
Spatial Sense 11
Uncertainty 11
Structure of the Mathematics Curriculum 12
Curriculum Document Format 13
Specific Curriculum Outcomes 14
Number 14
Patterns and Relations 42
Shape and Space 50
Statistics and Probability 74
Appendix A: Glossary of Models 82
Appendix B: List of Grade 8 Specific Curriculum Outcomes 89
Appendix C: References 90 BACKGROUND AND RATIONALE
Mathematics curriculum is shaped by a vision which fosters the development
of mathematically literate students who can extend and apply their learning
and who are effective participants in society. It is essential the mathematics curriculum reflects current research in
mathematics instruction. To achieve this goal, the Western and Northern
Canadian Protocol (WNCP) Common Curriculum Framework for K-9 Mathematics
(2006) has been adopted as the basis for a revised mathematics curriculum
in New Brunswick. The Common Curriculum Framework was developed by the
seven ministries of education (Alberta, British Columbia, Manitoba,
Northwest Territories, Nunavut, Saskatchewan and Yukon Territory) 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. This document is based on both national and international
research by the WNCP and the NCTM. There is an emphasis in the New Brunswick curriculum on particular key
concepts at each grade which will result in greater depth of understanding
and ultimately stronger student achievement. There is also a greater
emphasis on number sense and operations concepts in the early grades to
ensure students develop a solid foundation in numeracy. The intent of this document is to clearly communicate high expectations for
students in mathematics education to all education partners. Because of the
emphasis placed on key concepts at each grade level, time needs to be taken
to ensure mastery of these concepts.
Students must learn mathematics with understanding, actively building new
knowledge from experience and prior knowledge (NCTM Principles and
Standards, 2000). BELIEFS ABOUT STUDENTS AND MATHEMATICS LEARNING
The New Brunswick Mathematics Curriculum is based upon several key
assumptions or beliefs about mathematics learning which have grown out of
research and practice. These beliefs include:
. mathematics learning is an active and constructive process;
. learners are individuals who bring a wide range of prior knowledge and
experiences, and who learn via various styles and at different rates;
. learning is most likely to occur when placed in meaningful contexts and
in an environment that supports exploration, risk taking, and critical
thinking and that nurtures positive attitudes and sustained effort; and
. learning is most effective when standards of expectation are made clear
with on-going assessment and feedback.
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 develop a variety of mathematical ideas before they enter school.
Children make sense of their environment through observations and
interactions at home and in the community. Mathematics learning is embedded
in everyday activities, such as playing, reading, storytelling and helping
around the home. Such activities can contribute to the development of
number and spatial sense in children. Curiosity about mathematics is
fostered when children are engaged in activities such as comparing
quantities, searching for patterns, sorting objects, ordering objects,
creating designs, building with blocks and talking about these activities.
Positive early experiences in mathematics are as critical to child
development as are early literacy 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 models 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 and translating through a variety of materials, tools and
contexts when constructing meaning about new mathematical ideas. Meaningful
discussions can provide essential links among concrete, pictorial and
symbolic representations of mathematics. 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. GOALS FOR MATHEMATICALLY LITERATE STUDENTS
The main goals of mathematics education are to prepare students to:
. use mathematics confidently to solve problems
. communicate and reason mathematically
. appreciate and value mathematics
. make connections between mathematics and its applications
. commit themselves to lifelong learning
. become mathematically literate adults, using mathematics to contribute to
society. Students who have met these goals will:
. gain understanding and appreciation of the contributions of mathematics
as a science, philosophy and 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 OPPORTUNITIES FOR SUCCESS
A positive attitude has a profound effect on learning. Environments that
create a sense of belonging, encourage risk taking, and provide
opportunities for success help 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 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 these goals.
Striving toward success, and becoming autonomous and responsible learners
are ongoing, reflective processes that involve revisiting the setting and
assessing of personal goals.
DIVERSE CULTURAL PERSPECTIVES
Students attend schools in a variety of settings including urban, rural and
isolated communities. Teachers need to understand the diversity of cultures
and experiences of all students. Aboriginal students often have a whole-world view of the environment in
which they live and learn best in a holistic way. This means that students
look for connections in learning and learn best when mathematics is
contextualized and not taught as discrete components. Aboriginal student